Mathematical Collections and Translations, in Two Tomes/System of the World in Four Dialogues/Dialogue 2

by Galileo Galilei

GALILÆUS

Galilæus Lyncæus,

HIS

SYSTEME

OF THE

WORLD.

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The Second Dialogue.

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INTERLOCUTORS.

Salviatus, Sagredus, and Simplicius.

SALV.

THe yester-dayes diversions which led us out of the path of our principal discourse, were such and so many, that I know not how I can without your assistance recover the track in which I am to proceed.

Sagr.I wonder not, that you, who have your fancy charged and laden with both what hath been, and is to be spoken, do find your self in some confusion; but I, who as being onely an Auditor, have nothing to burthen my memory withal, but such things as I have heard, may haply by a succinct rehearsal of them, recover the first thred of our Discourse. As far therefore as my memory serves me, the sum of yester-dayes conferences were an examination of the Principles of Ptolomy and Copernicus, and which of their opinions is the more probable and rational; that, which affirmeth the substance of the Cœlestial bodies to be ingenerable, incorruptible, unalterable, impassible, and in a word, exempt from all kind of change, save that of local, and therefore to be a fifth essence, quite different from this of our Elementary bodies, which are generable, corruptible, alterable, &c. or else the other, which taking away such deformity from the parts of the World, holdeth the Earth to enjoy the same perfections as the other integral bodies of the universe; and esteemeth it a moveable and erratick Globe, no lesse than the Moon, Jupiter, Venus, or any other Planet: And lastly, maketh many particular parallels betwixt the Earth and Moon; and more with the Moon, than with any other Planet; haply by reason we have greater and more certain notice of it, as being lesse distant from us. And having, lastly, concluded this second opinion to have more of probability with it than the first, I should think it best in the subsequent discourses to begin to examine whether the Earth be esteemed immoveable, as it hath been till now believed by most men, or else moveable, as some ancient Philosophers held, and others of not very recesse times, were of opinion; and if it be moveable, to enquire of what kind its motion may be?

Salv.I see already what way I am to take; but before we offer to proceed any farther, I am to say something to you touching those last words which you spake, how that the opinion which holds the Earth to be endued with the same conditions that the Cœlestial bodies enjoy, seems to be more true than the contrary; for that I affirmed no such thing, nor would I have any of the Propositions in controversie, be made to speak to any definitive sense: but I onely intended to produce on either part, those reasons and answers, arguments and solutions, which have been hitherto thought upon by others, together with certain others, which I have stumbled upon in my long searching thereinto, alwayes remitting the decision thereof to the judgment of others.

Sagr.I was unawares transported by my own sense of the thing; and believing that others ought to judg as I did, I made that conclusion universal, which should have been particular; and therefore confesse I have erred, and the rather, in that I know not what Simplicius his judgment is in this particular.

Simpl.I must confesse, that I have been ruminating all this night of what past yesterday, and to say the truth, I meet therein with many acute, new, aud plausible notions; yet nevertheless, I find my self over-perswaded by the authority of so many great Writers, and in particular ——— &c. I see you shake your head Sagredus, and smile to your self, as if I had uttered some great absurdity.

Sagr.I not onely smile, but to tell you true, am ready to burst with holding in my self from laughing outright, for you have put me in mind of a very pretty passage, that I was a witnesse of, not many years since, together with some others of my worthy friends, which I could yet name unto you.

Salv.It would be well that you told us what it was, that so Simplicius may not still think that he gave you the occasion of laughter.

Sagr.I am content. I found one day, at home in his house, at Venice, a famous Phisician, to whom some flockt for their studies, and others out of curiosity, sometimes came thither to see certain Anatomies diffected by the hand of a no lesse learned, than careful and experienced Anatomist.The original of the Nerves, according to Aristotle, and according to Phisicians. It chanced upon that day, when I was there, that he was in search of the original and rise of the Nerves, about which there is a famous controversie between the Galenists and Peripateticks; and the Anatomist shewing, how that the great number of Nerves departing from the Brain, as their root, and passing by the nape of the Neck, distend themselves afterwards along by the Back-bone, and branch themselves thorow all the Body; and that a very small filament, as fine as a thred went to the Heart; he turned to a Gentleman whom he knew to be a Peripatetick Philosopher, and for whose sake he had with extraordinary exactnesse, discovered and proved every thing, and demanded of him, if he was at length satisfied and perswaded that the original of the Nerves proceeded from the Brain, and not from the Heart?The ridiculous answer of a Philosopher, determining the original of the Nerves. To which the Philosopher, after he had stood musing a while, answered; you have made me to see this businesse so plainly and sensibly, that did not the Text of Aristotle assert the contrary, which positively affirmeth the Nerves to proceed from the Heart, I should be constrained to confesse your opinion to be true.

Simpl.I would have you know my Masters, that this controversie about the original of the Nerves is not yet so proved and decided, as some may perhaps perswade themselves.

Sagr.Nor questionlesse ever shall it be, if it find such like contradictors; but that which you say, doth not at all lessen the extravagance of the answer of that Peripatetick, who against such sensible experience produced not other experiments, or reasons of Aristotle, but his bare authority and pure ipse dixit.

Simpl.Aristotle had not gained so great authority, but for the force of his Demonstrations, and the profoundnesse of his arguments; but it is requisite that we understand him, and not onely understand him, but have so great familiarity with his Books, that we form a perfect Idea thereof in our minds, so as that every saying of his may be alwayes as it were, present in our memory for he did not write to the vulgar, nor is he obliged to spin out his Sillogismes with the trivial method of disputes; nay rather, using a freedome, he hath sometimes placed the proof of one Proposition amongst Texts, which seem to treat of quite another point;Requisites to fit a man to philosophate well after the manner of Aristotle. and therefore it is requisite to be master of all that vast Idea, and to learn how to connect this passage with that, and to combine this Text with another far remote from it; for it is not to be questioned but that he who hath thus studied him, knows how to gather from his Books the demonstrations of every knowable deduction, for that they contein all things.

Sagr.But good Simplicius, like as the things scattered here and there in Aristotle, give you no trouble in collecting them, but that you perswade your self to be able by comparing and connecting several small sentences to extract thence the juice of some desired conclusion,A cunning way to gather Philosophy out of any book whatsoever. so this, which you and other egregious Philosophers do with the Text of Aristotle, I could do by the verses of Virgil, or of Ovid, composing thereof* A word signifying works composed of many fragments of verses collected out of the Poets. * Centones, and therewith explaining all the affairs of men, and secrets of Nature. But what talk I of Virgil, or any other Poet? I have a little Book much shorter than Aristotle and Ovid, in which are conteined all the Sciences, and with very little study, one may gather out of it a most perfect Idea, and this is the Alphabet; and there is no doubt but that he who knows how to couple and dispose aright this and that vowel, with those, or those other consonants, may gather thence the infallible answers to all doubts, and deduce from them the principles of all Sciences and Arts, just in the same manner as the Painter from divers simple colours, laid severally upon his Pallate, proceedeth by mixing a little of this and a little of that, with a little of a third, to represent to the life men, plants, buildings, birds, fishes, and in a word, counterfeiting what ever object is visible, though there be not on the Pallate all the while, either eyes, or feathers, or fins, or leaves, or stones. Nay, farther, it is necessary, that none of the things to be imitated, or any part of them, be actually among colours, if you would be able therewith to represent all things; for should there be amongst them v. gr. feathers, these would serve to represent nothing save birds, and plumed creatures.

Salv.And there are certain Gentlemen yet living, and in health, who were present, when a Doctor, that was Professor in a famous Academy,Invention of the Telescope taken from Aristotle. hearing the description of the Telescope, by him not seen as then, said, that the invention was taken from Aristotle, and causing his works to be fetch't, he turned to a place where the Philosopher gives the reason, whence it commeth, that from the bottom of a very deep Well, one may see the stars in Heaven, at noon day; and, addressing himself to the company, see here, saith he, the Well, which representeth the Tube, see here the gross vapours, from whence is taken the invention of the Crystals, and see here lastly the sight fortified by the passage of the rays through a diaphanous, but more dense and obscure medium.

Sagr.This is a way to comprehend all things knowable, much like to that wherewith a piece of marble conteineth in it one, yea, a thousand very beautiful Statua's, but the difficulty lieth in being able to discover them; or we may say, that it is like to the prophesies of Abbot Joachim, or the answers of the Heathen Oracles, which are not to be understood, till after the things fore-told are come to passe.

Salv.And why do you not adde the predictions of the Genethliacks, which are with like cleernesse seen after the event, in their Horoscopes, or, if you will, Configurations of the Heavens.

Sagr.In this manner the Chymists find,Chymists interpret the Fables of the Poets to be secrets for making of Gold. being led by their melancholly humour, that all the sublimest wits of the World have writ of nothing else in reality, than of the way to make Gold; but, that they might transmit the secret to posterity without discovering it to the vulgar, they contrived some one way, and some another how to conceal the same under several maskes; and it would make one merry to hear their comments upon the ancient Poets, finding out the important misteries, which lie hid under their Fables; and the signification of the Loves of the Moon, and her descending to the Earth for Endimion; her displeasure against Acteon, and what was meant by Jupiters turning himself into a showre of Gold; and into flames of fire; and what great secrets of Art are conteined in that Mercury the Interpreter; in those thefts of Pluto; and in those Branches of Gold.

Simpl.I believe, and in part know, that there want not in the World very extravagant heads, the vanities of whom ought not to redound to the prejudice of Aristotle, of whom my thinks you speak sometimes with too little respect, and the onely antiquity and bare name that he hath acquired in the opinions of so many famous men, should suffice to render him honourable with all that professe themselves learned.

Salv.You state not the matter rightly, Simplicius; There are some of his followers that fear before they are in danger, who give us occasion, or, to say better, would give us cause to esteem him lesse,Some of Aristotles Sectators impare the reputation of their Master, in going about to enhanse it. should we consent to applaud their Capricio's. And you, pray you tell me, are you for your part so simple, as not to know that had Aristotle been present, to have heard the Doctor that would have made him Author of the Telescope, he would have been much more displeased with him, than with those, who laught at the Doctor and his Comments? Do you question whether Aristotle, had he but seen the novelties discovered in Heaven, would not have changed his opinion, amended his Books, and embraced the more sensible Doctrine; rejecting those silly Gulls, which too scrupulously go about to defend what ever he hath said; not considering, that if Aristotle were such a one as they fancy him to themselves, he would be a man of an untractable wit, an obstinate mind, a barbarous soul, a stubborn will, that accounting all men else but as silly sheep, would have his Oracles preferred before the Senses, Experience, and Nature her self? They are the Sectators of Aristotle that have given him this Authority, and not he that hath usurped or taken it upon him; and because it is more easie for a man to sculk under anothers shield than to shew himself openly, they tremble, and are affraid to stir one step from him; and rather than they will admit some alterations in the Heaven of Aristotle, they will impertinently deny those they behold in the Heaven of Nature.

Sagr.These kind of Drolleries put me in mind of that Statuary which having reduced a great piece of Marble to the Image of an Hercules,A ridiculous passage of a certain Statuary. or a thundring Jupiter, I know not whether, and given it with admirable Art such a vivacity and threatning fury, that it moved terror in as many as beheld it; he himself began also to be affraid thereof, though all its sprightfulnesse, and life was his own workmanship; and his affrightment was such, that he had no longer the courage to affront it with his Chizzels and Mallet.

Salv.I have many times wondered how these nice maintainers of what ever fell from Aristotle, are not aware how great a prejudice they are to his reputation and credit; and how that the more they go about to encrease his Authority, the more they diminish it; for whilest I see them obstinate in their attempts to maintain those Propositions which I palpably discover to be manifestly false; and in their desires to perswade me that so to do, is the part of a Philosopher; and that Aristotle himself would do the same, it much abates in me of the opinion that he hath rightly philosophated about other conclusions, to me more abstruse: for if I could see them concede and change opinion in a manifest truth, I would believe, that in those in which they should persist, they may have some solid demonstrations to me unknown, and unheard of.

Sagr.Or when they should be made to see that they have hazarded too much of their own and Aristotle's repuatation in confessing, that they had not understood this or that conclusion found out by some other man; would it not be a less evil for them to seek for it amongst his Texts, by laying many of them together, according to the art intimated to us by Simplicius? for if his works contain all things knowable, it must follow also that they may be therein discovered.

Salv.Good Sagredus, make no jest of this advice, which me thinks you rehearse in too Ironical a way; for it is not long since that a very eminent Philosopher having composed a Book de animà, wherein, citing the opinion of Aristotle, about its being or not being immortal, he alledged many Texts, (not any of those heretofore quoted by Alexander ab Alexandro: for in those he said, that Aristotle had not so much as treated of that matter, much less determined any thing pertaining to the same, but others) by himself found out in other more abstruse places, which tended to an erroneous sense: and being advised, that he would find it an hard matter to get a Licence from the Inquisitors,A brave resolution of a certain Peripatetick Philosopher. he writ back unto his friend, that he would notwithstanding, with all expedition procure the same, for that if no other obstacle should interpose, he would not much scruple to change the Doctrine of Aristotle, and with other expositions, and other Texts to maintain the contrary opinion, which yet should be also agreeable to the sense of Aristotle.

Sagr.Oh most profound Doctor, this! that can command me that I stir not a step from Aristotle, but will himself lead him by the nose, and make him speak as he pleaseth. See how much it importeth to learn to take Time by the Fore-top. Nor is it seasonable to have to do with Hercules, whil'st he is enraged, and amongst the Furies, but when he is telling merry tales amongst the Meonion Damosels.The servile spirit of some of Aristotles followers. Ah, unheard of sordidnesse of servile souls! to make themselves willing slaves to other mens opinions; to receive them for inviolable Decrees, to engage themselves to seem satisfied and convinced by arguments, of such efficacy, and so manifestly concludent, that they themselves cannot certainly resolve whether they were really writ to that purpose, or serve to prove that assumption in hand, or the contrary. But, which is a greater madnesse, they are at variance amongst themselves, whether the Author himself hath held the affirmative part, or the negative. What is this, but to make an Oracle of a Log, and to run to that for answers, to fear that, to reverence and adore that?

Simpl.But in case we should recede from Aristotle, who have we to be our Guid in Philosophy? Name you some Author.

Salv.We need a Guid in unknown and uncouth wayes, but in champion places, and open plains, the blind only stand in need of a Leader; and for such, it is better that they stay at home. But he that hath eyes in his head, and in his mind, him should a man choose for his Guid.Too close adhering to Aristotle is blameable. Yet mistake me not, thinking that I speak this, for that I am against hearing of Aristotle; for on the contrary, I commend the reading, and diligently studying of him; and onely blame the servile giving ones self up a slave unto him, so, as blindly to subscribe to what ever he delivers, and without search of any farther reason thereof, to receive the same for an inviolable decree. Which is an abuse, that carrieth with it another great inconvenience, to wit, that others will no longer take pains to understand the validity of his Demonstrations. And what is more shameful, than in the middest of publique disputes, whilest one person is treating of demonstrable conclusions, to hear another interpose with a passage of Aristotle, and not seldome writ to quite another purpose, and with that to stop the mouth of his opponent? But if you will continue to study in this manner, I would have you lay aside the name of Philosophers; and call your selves either Historians or Doctors of Memory,It is not just, that those who never philosophate, should usurp the title of Philosophers. for it is not fit, that those who never philosophate, should usurp the honourable title of Philosophers. But it is best for us to return to shore, and not lanch farther into a boundlesse Gulph, out of which we shall not be able to get before night. Therefore Simplicius, come either with arguments and demonstrations of your own, or of Aristotle, and bring us no more Texts and naked authorities,The Sensible World. for our disputes are about the Sensible World, and not one of Paper. And forasmuch as in our discourses yesterday, we retriev'd the Earth from darknesse, and exposed it to the open skie, shewing, that the attempt to enumerate it amongst those which we call Cœlestial bodies, was not a position so foil'd, and vanquish't, as that it had no life left in it; it followeth next, that we proceed to examine what probability there is for holding of it fixt, and wholly immoveable, scilicet as to its entire Globe, what likelihood there is for making it moveable with some motion, and of what kind that may be. And forasmuch as in this same question I am ambiguous, and Simplicius is resolute, as likewise Aristotle for the opinion of its immobility, he shall one by one produce the arguments in favour of their opinion, and I will alledge the answers and reasons on the contrary part; and next Sagredus shall tell us his thoughts, and to which side he finds himself inclined.

Sagr.Content; provided alwayes that I may reserve the liberty to my self of alledging what pure natural reason shall sometimes dictate to me.

Salv.Nay more, it is that which I particularly beg of you; for, amongst the more easie, and, to so speak, material considerations, I believe there are but few of them that have been omitted by Writers, so that onely some of the more subtle, and remote can be desired, or wanting; and to investigate these, what other ingenuity can be more fit than that of the most acute and piercing wit of Sagredus? Sagr.I am what ever pleaseth Salviatus, but I pray you, let us not sally out into another kind of digression complemental; for at this time I am a Philosopher, and in the Schools, not in the Court.

Salv.Let our contemplation begin therefore with this consideration, that whatsoever motion may be ascribed to the Earth, it is necessary that it be to us, (as inhabitants upon it, and consequently partakers of the same) altogether imperceptible, and as if it were not at all, so long as we have regard onely to terrestrial things;The motions of the Earth are imperceptible to its inhabitants. but yet it is on the contrary, as necessary that the same motion do seem common to all other bodies, and visible objects, that being separated from the Earth, participate not of the same. So that the true method to find whether any kind of motion may be ascribed to the Earth, and that found, to know what it is, is to consider and observe if in bodies separated from the Earth,The Earth can have no other motions, than those which to us appear commune to all the rest of the Vniverse, the Earth excepted. one may discover any appearance of motion, which equally suiteth to all the rest; for a motion that is onely seen, v. gr. in the Moon, and that hath nothing to do with Venus or Jupiter, or any other Stars, cannot any way belong to the Earth, or to any other save the Moon alone. Now there is a most general and grand motion above all others, and it is that by which the Sun, the Moon,The Diurnal Motion, seemeth commune to all the Universe, save onely the Earth excepted. the other Planets, and the Fixed Stars, and in a word, the whole Universe, the Earth onely excepted, appeareth in our thinking to move from the East towards the West, in the space of twenty four hours; and this, as to this first appearance, hath no obstacle to hinder it, that it may not belong to the Earth alone, as well as to all the World besides, the Earth excepted; for the same aspects will appear in the one position, as in the other. Hence it is that Aristotle and Ptolomy,Aristotle and Ptolomy argue against the Diurnal Motion attributed to the Earth. as having hit upon this consideration, in going about to prove the Earth to be immoveable, argue not against any other than this Diurnal Motion; save onely that Aristotle hinteth something in obscure terms against another Motion ascribed to it by an Ancient, of which we shall speak in its place.

Sagr.I very well perceive the necessity of your illation: but I meet with a doubt which I know not how to free my self from, and this it is, That Copernicus assigning to the Earth another motion beside the Diurnal, which, according to the rule even now laid down, ought to be to us, as to appearance, imperceptible in the Earth, but visible in all the rest of the World; me thinks I may necessarily infer, either that he hath manifestly erred in assigning the Earth a motion, to which there appears not a general correspondence in Heaven; or else that if there be such a congruity therein, Ptolomy on the other hand hath been deficient in not confuting this, as he hath done the other.

Salv.You have good cause for your doubt: and when we come to treat of the other Motion, you shall see how far Copernicus excelled Ptolomey in clearness and sublimity of wit, in that he saw what the other did not, I mean the admirable harmony wherein that Motion agreed with all the other Cœlestial Bodies. But for the present we will suspend this particular, and return to our first consideration; touching which I will proceed to propose (begining with things more general) those reasons which seem to favour the mobility of the Earth,Why the diurnal motion more probably should belong to the Earth, than to the rest of the Universe. and then wait the answers which Simplicius shall make thereto. And first, if we consider onely the immense magnitude of the Starry Sphere, compared to the smalness of the Terrestrial Globe, contained therein so many millions of times; and moreover weigh the velocity of the motion which must in a day and night make an entire revolution thereof, I cannot perswade my self, that there is any man who believes it more reasonable and credible, that the Cœlestial Sphere turneth round, and the Terrestrial Globe stands still.

Sagr.If from the universality of effects, which may in nature have dependence upon such like motions, there should indifferently follow all the same consequences to an hair, aswell in one Hypothesis as in the other; yet I for my part, as to my first and general apprehension, would esteem, that he which should hold it more rational to make the whole Universe move, and thereby to salve the Earths mobility, is more unreasonable than he that being got to the top of your Turret, should desire, to the end onely that he might behold the City, and the Fields about it, that the whole Country might turn round, that so he might not be put to the trouble to stir his head. And yet doubtless the advantages would be many and great which the Copernican Hypothesis is attended with, above those of the Ptolomaique, which in my opinion resembleth, nay surpasseth that other folly; so that all this makes me think that far more probable than this. But haply Aristotle, Ptolomey, and Simplicius may find the advantages of their Systeme, which they would do well to communicate to us also, if any such there be; or else declare to me, that there neither are or can be any such things.

Salv.For my part, as I have not been able, as much as I have thought upon it, to find any diversity therein; so I think I have found, that no such diversity can be in them: in so much that I esteem it to no purpose to seek farther after it.Motion, as to the things that equally move thereby, is as if it never were, & so far operates as it hath relation to things deprived of motion. Therefore observe: Motion is so far Motion, and as Motion operateth, by how far it hath relation to things which want Motion: but in those things which all equally partake thereof it hath nothing to do, and is as if it never were. And thus the Merchandises with which a ship is laden, so far move, by how far leaving London, they pass by France, Spain, Italy, and sail to Aleppo, which London, France, Spain &c. stand still, not moving with the ship: but as to the Chests, Bales and other Parcels, wherewith the ship is stow'd and and laden, and in respect of the ship it self, the Motion from London to Syria is as much as nothing; and nothing-altereth the relation which is between them: and this, because it is common to all, and is participated by all alike: and of the Cargo which is in the ship, if a Bale were romag'd from a Chest but one inch onely, this alone would be in that Cargo, a greater Motion in respect of the Chest, than the whole Voyage of above three thousand miles, made by them as they were stived together.

Simpl.This Doctrine is good, sound, and altogether Peripatetick.

Salv.I hold it to be much more antient:A proposition taken by Aristotle from the Antients, but somewhat altered by him. and suspect that Aristotle in receiving it from some good School, did not fully understand it, and that therefore, having delivered it with some alteration, it hath been an occasion of confusion amongst those, who would defend whatever he saith. And when he writ, that whatsoever moveth, doth move upon something immoveable, I suppose that he equivocated, and meant, that whatever moveth, moveth in respect to something immoveable; which proposition admitteth no doubt, and the other many.

Sagr.Pray you make no digression, but proceed in the dissertation you began.

Salv.It being therefore manifest,The first discourse to prove that the diurnal motion belongs to the Earth. that the motion which is common to many moveables, is idle, and as it were, null as to the relation of those moveables between themselves, because that among themselves they have made no change: and that it is operative onely in the relation that those moveables have to other things, which want that motion, among which the habitude is changed: and we having divided the Universe into two parts, one of which is necessarily moveable, and the other immoveable; for the obtaining of whatsoever may depend upon, or be required from such a motion, it may as well be done by making the Earth alone, as by making all the rest of the World to move: for that the operation of such a motion consists in nothing else, save in the relation or habitude which is between the Cœlestial Bodies, and the Earth, the which relation is all that is changed. Now if for the obtaining of the same effect ad unguem, it be all one whether the Earth alone moveth, the rest of the Universe standing still;Nature never doth that by many things, which may be done by a few. or that, the Earth onely standing still, the whole Universe moveth with one and the same motion; who would believe, that Nature (which by common consent, doth not that by many things, which may be done by few) hath chosen to make an innumerable number of most vast bodies move, and that with an unconceivable velocity, to perform that, which might be done by the moderate motion of one alone about its own Centre?

Simpl.I do not well understand, how this grand motion signifieth nothing as to the Sun, as to the Moon, as to the other Planets, and as to the innumerable multitude of fixed stars: or why you should say that it is to no purpose for the Sun to pass from one Meridian to another; to rise above this Horizon, to set beneath that other; to make it one while day, another while night: the like variations are made by the Moon, the other Planets, and the fixed stars themselves.

Salv.All these alterations instanced by you, are nothing, save onely in relation to the Earth: and that this is true, do but imagine the Earth to move,The diurnal motion causeth no mutation amongst the Cœlestial Bodies, but all changes have relation to the Earth. and there will be no such thing in the World as the rising or setting of the Sun or Moon, nor Horizons, nor Meridians, nor days, nor nights; nor, in a word, will such a motion cause any mutation between the Moon and Sun, or any other star whatsoever, whether fixed or erratick; but all these changes have relation to the Earth: which all do yet in sum import no other than as if the Sun should shew it self now to China, anon to Persia, then to Egypt, Greece, France, Spain, America, &c. and the like holdeth in the Moon, and the rest of the Cœlestial Bodies: which self same effect falls out exactly in the same manner, if, without troubling so great a part of the Universe, the Terrestrial Globe be made to revolve in it self.A second confirmation that the diurnal motion belongs to the Earth. But we will augment the difficulty by the addition of this other, which is a very great one, namely, that if you will ascribe this Great Motion to Heaven, you must of necessity make it contrary to the particular motion of all the Orbs of the Planets, each of which without controversie hath its peculiar motion from the West towards the East, and this but very easie and moderate: and then you make them to be hurried to the contrary part, i. e. from East to West, by this most furious diurnal motion: whereas, on the contrary, making the Earth to move in it self, the contrariety of motions is taken away, and the onely motion from West to East is accommodated to all appearances, and exactly satisfieth every Phœnomenon.

Simpl.As to the contrariety of Motions it would import little,Circular motions are not contrary, according to Aristotle. for Aristotle demonstrateth, that circular motions, are not contrary to one another; and that theirs cannot be truly called contrariety.

Salv.Doth Aristotle demonstrate this, or doth he not rather barely affirm it, as serving to some certain design of his? If contraries be those things, that destroy one another, as he himself affirmeth, I do not see how two moveables that encounter each other in a circular line, should lesse prejudice one another, than if they interfered in a right line.

Sagr.Hold a little, I pray you. Tell me Simplicius, when two Knights encounter each other, tilting in open field, or when two whole Squadrons, or two Fleets at Sea, make up to grapple, and are broken and sunk, do you call these encounters contrary to one another?

Simpl.Yes, we say they are contrary.

Sagr.How then, is there no contrariety in circular motions. These motions, being made upon the superficies of the Earth or Water, which are, as you know, spherical, come to be circular. Can you tell, Simplicius, which those circular motions be, that are not contrary to each other? They are (if I mistake not) those of two circles, which touching one another without, one thereof being turn'd round, naturally maketh the other move the contrary ** As you see in a Mill, wherein the implicated cogs set the wheels on moving. way; but if one of them shall be within the other, it is impossible that their motion being made towards different points, they should not justle one another.

Salv.But be they contrary, or not contrary, these are but alterations of words; and I know, that upon the matter, it would be far more proper and agreeable with Nature, if we could salve all with one motion onely, than to introduce two that are (if you will not call them contrary) opposite; yet do I not censure this introduction (of contrary motions) as impossible; nor pretend I from the denial thereof, to inferre a necessary Demonstration, but onely a greater probability,A third confirmation of the same Doctrine. of the other. A third reason which maketh the Ptolomaique Hypothesis lesse probable is, that it most unreasonably confoundeth the order, which we assuredly see to be amongst those Cœlestial Bodies, the circumgyration of which is not questionable,The greater Orbs make their conversions in greater times. but most certain. And that Order is, that according as an Orb is greater, it finisheth its revolution in a longer time, and the lesser, in shorter. And thus Saturn describing a greater Circle than all the other Planets, compleateth the same in thirty yeares: Jupiter finisheth his; that is lesse, in twelve years: Mars in two: The Moon runneth thorow hers, so much lesse than the rest, in a Moneth onely. Nor do we lesse sensibly see that of the Medicean Stars,The times of the Medicean Planets conversions. which is nearest to Jupiter, to make its revolution in a very short time, that is, in four and forty hours, or thereabouts, the next to that in three dayes and an half, the third in seven dayes, and the most remote in sixteen. And this rate holdeth well enough, nor will it at all alter, whilest we assign the motion of 24 hours to the Terrestrial Globe, for it to move round its own center in that time; but if you would have the Earth immoveable, it is necessary, that when you have past from the short period of the Moon, to the others successively bigger, until you come to that of Mars in two years, and from thence to that of the bigger Sphere of Jupiter in twelve years, and from this to the other yet bigger of Saturn, whose period is of thirty years, it is necessary, I say, that you passe to another Sphere incomparably greater still than that, and make this to accomplish an entire revolution in twenty four hours.The motion of 24 hours ascribed to the highest Sphere disorders the period of the inferiour. And this yet is the least disorder that can follow. For if any one should passe from the Sphere of Saturn to the Starry Orb, and make it so much bigger than that of Saturn, as proportion would require, in respect of its very slow motion, of many thousands of years, then it must needs be a Salt much more absurd, to skip from this to another bigger, and to make it convertible in twenty four hours. But the motion of the Earth being granted, the order of the periods will be exactly observed, and from the very slow Sphere of Saturn, we come to the fixed Stars, which are wholly immoveable, The fourth Confirmation. and so avoid a fourth difficulty, which we must of necessity admit, if the Starry Sphere be supposed moveable, and that is the immense disparity between the motions of those stars themselves;Great disparity amongst the motions of the particular fixed stars, if their Sphere be moveable. of which some would come to move most swiftly in most vast circles, others most slowly in circles very small, according as those or these should be found nearer, or more remote from the Poles; which still is accompanied with an inconvenience, as well because we see those, of whose motion there is no question to be made, to move all in very immense circles; as also, because it seems to be an act done with no good consideration, to constitute bodies, that are designed to move circularly, at immense distances from the centre, and afterwards to make them move in very small circles. And not onely the magnitudes of the circles, and consequently the velocity of the motions of these Stars, shall be most different from the circles and motions of those others,The fifth Confirmation. but (which shall be the fifth inconvenience) the self-same Stars shall successively vary its circles and velocities:The motions of the fixed stars would accelerate and grow slow in divers times, if the starry Sphere were moveable. For that those, which two thousand years since were in the Equinoctial, and consequently did with their motion describe very vast circles, being in our dayes many degrees distant from thence, must of necessity become more slow of motion, and be reduced to move in lesser circles, and it is not altogether impossible but that a time may come, in which some of them which in aforetime had continually moved, shall be reduced by uniting with the Pole, to a state of rest, and then after some time of cessation, shall return to their motion again; whereas the other Stars, touching whose motion none stand in doubt, do all describe, as hath been said, the great circle of their Orb, and in that maintain themselves without any variation.The sixth Confirmation. The absurdity is farther enlarged (which let be the sixth inconvenience) to him that more seriously examineth the thing, in that no thought can comprehend what ought to be the solidity of that immense Sphere, whose depth so stedfastly holdeth fast such a multitude of Stars, which without ever changing site among themselves, are with so much concord carried about, with so great disparity of motions. Or else, supposing the Heavens to be fluid, as we are with more reason to believe, so as that every Star wandereth to and fro in it, by wayes of its own, what rules shall regulate their motions, and to what purpose, so, as that being beheld from the Earth, they appear as if they were made by one onely Sphere? It is my opinion, that they might so much more easily do that, and in a more commodious manner, by being constituted immoveable, than by being made errant, by how much more facile it is to number the quarries in the Pavement of a Piazza, than the rout of boyes which run up and down upon them.The Seventh Confirmation. And lastly, which is the seventh instance, if we attribute the Diurnal Motion to the highest Heaven, it must be constituted of such a force and efficacy, as to carry along with it the innumerable multitude of fixed Stars, Bodies all of vast magnitude, and far bigger than the Earth; and moreover all the Spheres of the Planets; notwithstanding that both these and those of their own nature move the contrary way. And besides all this, it must be granted, that also the Element of Fire, and the greater part of the Air, are likewise forcibly hurried along with the rest, and that the sole little Globe of the Earth pertinaciously stands still, and unmoved against such an impulse; a thing, which in my thinking, is very difficult; nor can I see how the Earth, a pendent body,The Earth a pendent Body, and equilibrated in a fluid Medium seems unable to resist the rapture of the Diurnal Motion. and equilibrated upon its centre, exposed indifferently to either motion or rest, and environed with a liquid ambient, should not yield also as the rest, and be carried about. But we find none of these obstacles in making the Earth to move; a small body, and insensible, compared to the Universe, and therefore unable to offer it any violence.

Sagr.I find my fancy disturbed with certain conjectures so confusedly sprung from your later discourses; that, if I would be enabled to apply my self with atention to what followeth, I must of necessity attempt whether I can better methodize them, and gather thence their true construction, if haply any can be made of them; and peradventure, the proceeding by interrogations may help me the more easily to expresse my self. Therefore I demand first of Simplicius, whether he believeth, that divers motions may naturally agree to one and the same moveable body, or else that it be requisite its natural and proper motion be onely one.

Simpl.To one single moveable,A single moveable hath but onely one natural motion, and all the rest are by participation. there can naturally agree but one sole motion, and no more; the rest all happen accidentally and by participation; like as to him that walketh upon the Deck of a Ship, his proper motion is that of his walk, his motion by participation that which carrieth him to his Port, whither he would never with his walking have arrived, if the Ship with its motion had not wafted him thither.

Sagr.Tell me secondly. That motion, which is communicated to any moveable by participation, whilest it moveth by it self, with another motion different from the participated, is it necessary, that it do reside in some certain subject by it self, or else can it subsist in nature alone, without other support.

Simpl.Aristotle giveth you an answer to all these questions,Motion cannot be made without its moveable subject. and tels you, that as of one sole moveable the motion is but one; so of one sole motion the moveable is but one; and consequently, that without the inherence in its subject, no motion can either subsist, or be imagined.

Sagr.I would have you tell me in the third place, whether you beblieve that the Moon and the other Planets and Cœlestial bodies, have their proper motions, and what they are.

Simpl.They have so, and they be those according to which they run through the Zodiack, the Moon in a Moneth, the Sun in a Year, Mars in two, the Starry Sphere in those so many thousand. And these are their proper, or natural motions.

Sagr.But that motion wherewith I see the fixed Stars, and with them all the Planets go unitedly from East to West, and return round to the East again in twenty four hours, how doth it agree with them?

Simpl.It suiteth with them by participation.

Sagr.This then resides not in them, and not residing in them, nor being able to subsist without some subject in which it is resident, it must of force be the proper and natural motion of some other Sphere.

Simpl.For this purpose Astronomers, and Philosophers have found another high Sphere, above all the rest, without Stars, to which Natural agreeth the Diurnal Motion; and this they call the Primum mobile; the which carrieth along with it all the inferiour Spheres, contributing and imparting its motion to them.

Sagr.But when, without introducing other Spheres unknown and hugely vast, without other motions or communicated raptures, with leaving to each Sphere its sole and simple motion, without intermixing contrary motions, but making all turn one way, as it is necessary that they do, depending all upon one sole principle, all things proceed orderly, and correspond with most perfect harmony, why do we reject this Phœnomenon, and give our assent to those prodigious and laborious conditions?

Simpl.The difficulty lyeth in finding out this so natural and expeditous way.

Sagr.In my judgment this is found. Make the Earth the Primum mobile, that is, make it turn round its own axis in twenty four hours, and towards the same point with all the other Spheres; and without participating this same motion to any other Planet or Star, all shall have their risings, settings, and in a word, all their other appearances.

Simpl.The business is, to be able to make the Earth move without a thousand inconveniences.

Salv.All the inconveniences shall be removed as fast as you propound them: and the things spoken hitherto are onely the primary and more general inducements which give us to believe that the diurnal conversion may not altogether without probability be applyed to the Earth, rather than to all the rest of the Universe: the which inducements I impose not upon you as inviolable Axioms, but as hints, which carry with them somewhat of likelihood.One single experiment, or sound demonstration battereth down all arguments meerly probable. And in regard I know very well, that one sole experiment, or concludent demonstration, produced on the contrary part, sufficeth to batter to the ground these and a thousand other probable Arguments; therefore it is not fit to stay here, but proceed forwards and hear what Simplicius answereth, and what greater probabilities, or stronger arguments he alledgeth on the contrary.

Simpl.I will first say something in general upon all these considerations together, and then I will descend to some particulars. It seems that you universally bottom all you say upon the greater simplicity and facility of producing the same effects, whilst you hold, that as to the causing of them, the motion of the Earth alone, serveth as well as that of all the rest of the World, the Earth deducted: but as to the operations, you esteem that much easier than this. To which I reply, that I am also of the same opinion, so long as I regard my own not onely finite, but feeble power; but having a respect to the strength of the Mover, which is infinite, its no lesse easie to move the Universe, than the Earth, yea than a straw. And if his power be infinite,Of an infinite power one would think a greater part should rather be imploy'd than a lesse. why should he not rather exercise a greater part thereof than a lesse? Therefore, I hold that your discourse in general is not convincing.

Salv.If I had at any time said, that the Universe moved not for want of power in the Mover, I should have erred, and your reproof would have been seasonable; and I grant you, that to an infinite power, it is as easie to move an hundred thousand, as one. But that which I did say, concerns not the Mover, but onely hath respect to the Moveables; and in them, not onely to their resistance, which doubtlesse is lesser in the Earth, than in the Universe; but to the many other particulars, but even now considered. As to what you say in the next place, that of an infinite power it is better to exercise a great part than a small: I answer, that of infinite one part is not greater than another, since both are infinite;Of infinity, one part is no bigger than another, although they are comparatively unequal. nor can it be said, that of the infinite number, an hundred thousand is a greater part than two, though that be fifty thousand times greater than this; and if to the moving of the Universe there be required a finite power, though very great in comparison of that which sufficeth to move the Earth onely; yet is there not implied therein a greater part of the infinite power, nor is that part lesse infinite which remaineth unimploy'd. So that to apply unto a particular effect, a little more, or a little lesse power, importeth nothing; besides that the operation of such vertue, hath not for its bound or end the Diurnal Motion onely; but there are several other motions in the World, which we know of, and many others there may be, that are to us unknown. Therefore if we respect the Moveables, and granting it as out of question, that it is a shorter and easier way to move the Earth, than the Universe; and moreover, having an eye to the so many other abreviations, and facilities that onely this way are to be obtained, an infallible Maxime of Aristotle, which he teacheth us, that, frustra fit per plura, quod potest fieri per pauciora, rendereth it more probable that the Diurnal Motion belongs to the Earth alone, than to the Universe, the Earth subducted.

Simpl.In reciting that Axiom, you have omitted a small clause, which importeth as much as all the rest, especially in our case, that is to say, the words æquè bene. It is requisite therefore to examine whether this Hypothesis doth equally well satisfie in all particulars, as the other.

Salv.The knowledg whether both these positions do æquè bene, satisfie, may be comprehended from the particular examination of the appearances which they are to satisfie; for hitherto we have discoursed, and will continue to argue ex hypothesi, namely, supposing, that as to the satisfaction of the appearances, both the assumptions are equally accomodated.In the Axiome Frustra fit per plura, &c. the addition of æque benè, is superfluous. As to the clause which you say was omitted by me, I have more reason to suspect that it was superfluously inserted by you. For the expression æquè bene, is a relative that necessarily requireth two terms at least, for a thing cannot have relation to its self, nor do we say, v. gr. rest to be equally good, as rest. And because, when we say, that is done in vain by many means, which may be done with fewer, we mean, that that which is to be done, ought to be the same thing, not two different ones; and because the same thing cannot be said to be done as well as its self; therefore, the addition of the Phrase æquè bene is superfluous, and a relation, that hath but one term onely.

Sagr.Unlesse you will have the same befal us, as did yesterday, let us return to our matter in hand; and let Simplicius begin to produce those difficulties that seem in his opinion, to thwart this new disposition of the World.

Simpl.That disposition is not new, but very old; and that you may see it is so, Aristotle confuteth it; and his confutations are these:Aristotles Arguments for the Earths quiessence. "First if the Earth moveth either in it self about its own Centre, or in an Excentrick Circle, it is necessary that that same motion be violent; for it is not its natural motion, for if it were, each of its parts would partake thereof; but each of them moveth in a right line towards its Centre. It being therefore violent and pteternatural, it could never be perpetual: But the order of the World is perpetual. Therefore, &c. Secondly, all the other moveables that move circularly, seem to* Restino indietzo, which is meant here of that motion which a bowl makes when its born by its byas to one side or other, and so hindered in its direct motion. * stay behind, and to move with more than one motion, the Primum Mobile excepted: Whence it would be necessary that the Earth also do move with two motions; and if that should be so, it would inevitably follow, that mutations should be made in the Fixed Stars, the which none do perceive; nay without any variation, the same Stars alwayes rise from towards the same places, and in the same places do set. Thirdly, the motion of the parts is the same with that of the whole, and naturally tendeth towards the Centre of the Universe; and for the same cause rest, being arrived thither. He thereupon moves the question whether the motion of the parts hath a tendency to centre of the Universe, or to the centre of the Earth; and concludeth that it goeth by proper instinct to the centre of the Universe, and per accidence to that of the Earth; of which point we largely discoursed yesterday. He lastly confirmeth the same with a fourth argument taken from the experiment of grave bodies, which faling from on high, descend perpendicularly unto the Earths surface; and in the same manner Projections shot perpendicularly upwards, do by the same lines return perpendicularly down again, though they were shot to a very great height. All which arguments necessarily prove their motion to be towards the Centre of the Earth, which without moving at all waits for, and receiveth them. He intimateth in the last place that the Astronomers alledg other reasons in confirmation of the same conclusions, I mean of the Earths being in the Centre of the Universe, and immoveable; and instanceth onely in one of them, to wit, that all the Phænomena or appearances that are seen in the motions of the Stars, perfectly agree with the position of the Earth in the Centre; which would not be so, were the Earth seated otherwise. The rest produced by Ptolomy and the other Astronomers, I can give you now if you please, or after you have spoken what you have to say in answer to these of Aristotle."

Salv.The arguments which are brought upon this occasion are of two kinds:Two kindes of Arguments touching the Earths motion or rest. some have respect to the accidents Terrestrial, without any relation to the Stars, and others are taken from the Phænomena and observations of things Cœlestial. The arguments of Aristotle are for the most part taken from things neer at hand, and he leaveth the others to Astronomers; and therefore it is the best way, if you like of it, to examine these taken from experiments touching the Earth, and then proceed to those of the other kind.Arguments of Ptolomy and Tycho, and other persons, over and above those of Aristotle. And because Ptolomy, Tycho, and the other Astronomers and Philosophers, besides the arguments of Aristotle by them assumed, confirmed, and made good, do produce certain others; we will put them all together, that so we may not answer twice to the same, or the like objections. Therefore Simplicius, choose whether you will recite them your self, or cause me to ease you of this task, for I am ready to serve you.

Simpl.It is better that you quote them, because, as having taken more pains in the study of them, you can produce them with more readinesse, and in greater number.

Salv.All,The first argument taken from grave bodies falling from on high to the ground. for the strongest reason, alledge that of grave bodies, which falling downwards from on high, move by a right line, that is perpendicular to the surface of the Earth, an argument which is held undeniably to prove that the Earth is immoveable: for in case it should have the diurnal motion, a Tower, from the top of which a stone is let fall, being carried along by the conversion of the Earth, in the time that the stone spends in falling, would be transported many hundred yards Eastward, and so far distant from the Towers foot would the stone come to ground. The which effect they back with another experiment;Which is confirmed by the experiment of a body let fall from the round top of a Ship. to wit, by letting a bullet of lead fall from the round top of a Ship, that lieth at anchor, and observing the mark it makes where it lights, which they find to be neer the ** That is, at the foot of the Mast, upon the upper deck. partners of the Mast; but if the same bullet be let fall from the same place when the ship is under sail, it shall light as far from the former place, as the ship hath run in the time of the leads descent; and this for no other reason, than because the natural motion of the ball being at liberty is by a right line towards the centre of the Earth.The second argument taken from a Projection shot very high. They fortifie this argument with the experiment of a projection shot on high at a very great distance; as for example, a ball sent out of a Cannon, erected perpendicular to the horizon, the which spendeth so much time in ascending and falling, that in our parallel the Cannon and we both should be carried by the Earth many miles towards the East, so that the ball in its return could never come neer the Peece, but would fall as far West,The third argument taken from the shots of a Cannon, towards the East, and towards the West. as the Earth had run East. They againe adde a third, and very evident experiment, scilicet, that shooting a bullet point blank (or as Gunners say, neither above nor under metal) out of a Culverin towards the East, and afterwards another, with the same charge, and at the same elevation or disport towards the West, the range towards the West should be very much greater then the other towards the East: for that whil'st the ball goeth Westward, and the Peece is carried along by the Earth Eastward, the ball will fall from the Peece as far distant as is the aggregate of the two motions, one made by it self towards the West, and the other by the Peece carried about by the Earth towards the East; and on the contrary, from the range of the ball shot Eastward you are to substract the space the Peece moved, being carried after it. Now suppose, for example, that the range of the ball shot West were five miles, and that the Earth in the same parallel and in the time of the Bals ranging should remove three miles, the Ball in this case would fall eight miles distant from the Culverin, namely, its own five Westward, and the Culverins three miles Eastward: but the range of the shot towards the East would be but two miles long, for so much is the remainder, after you have substracted from the five miles of the range, the three miles which the Peece had moved towards the same part. But experience sheweth the Ranges to be equal, therefore the Culverin, and consequently the Earth are immoveable.This argument is confirmed by two shots towards the South and towards the North. And the stability of the Earth is no lesse confirmed by two other shots made North and South; for they would never hit the mark, but the Ranges would be alwayes wide, or towards the West, by meanes of the remove the mark would make, being carried along with the Earth towards the East, whil'st the ball is flying.And it is likewise confirmed by two shots towards the East, and towards the West. And not onely shots made by the Meridians, but also those aimed East or West would prove uncertain; for those aim'd East would be too high, and those directed West too low, although they were shot point blank, as I said. For the Range of the Ball in both the shots being made by the Tangent, that is, by a line parallel to the Horizon, and being that in the diurnal motion, if it be of the Earth, the Horizon goeth continually descending towards the East, and rising from the West (therefore the Oriental Stars seem to rise, and the Occidental to decline) so that the Oriental mark would descend below the aime, and thereupon the shot would fly too high, and the ascending of the Western mark would make the shot aimed that way range too low; so that the Peece would never carry true towards any point; and for that experience telleth us the contrary, it is requisite to say, that the Earth is immoveable.

Simpl.These are solid reasons, and such as I believe no man can answer.

Salv.Perhaps they are new to you?

Simpl.Really they are; and now I see with how many admirable experiments Nature is pleased to favour us, wherewith to assist us in the knowledge of the Truth. Oh! how exactly one truth agreeth with another, and all conspire to render each other inexpugnable!

Sagr.What pity it is that Guns were not used in Aristotles age, he would with help of them have easily battered down ignorance, and spoke without hæsitation of these mundane points.

Salv.I am very glad that these reasons are new unto you, that so you may not rest in the opinion of the major part of Peripateticks, who believe, that if any one forsakes the Doctrine of Aristotle, it is because they did not understand or rightly apprehend his demonstrations.Copernicus his followers are not moved through ignorance of the arguments on the other part. But you may expect to hear of other Novelties, and you shall see the followers of this new Systeme produce against themselves observations, experiences, and reasons of farre greater force than those alledged by Aristotle, Ptolomy, and other opposers of the same conclusions, and by this means you shall come to ascertain your self that they were not induced through want of knowledge or experience to follow that opinion.

Sagr.It is requisite that upon this occasion I relate unto you some accidents that befell me, so soon as I first began to hear speak of this new doctrine. Being very young, and having scarcely finished my course of Philosophy, which I left off, as being set upon other employments, there chanced to come into these parts a certain Foreigner of Rostock, whose name, as I remember, was Christianus Vurstitius,Christianus Vurstitius read certain Lectures touching the opinion of Copernicus, & what ensued thereupon. a follower of Copernicus, who in an Academy made two or three Lectures upon this point, to whom many flock't as Auditors; but I thinking they went more for the novelty of the subject than otherwise, did not go to hear him: for I had concluded with my self that that opinion could be no other than a solemn madnesse. And questioning some of those who had been there, I perceived they all made a jest thereof, execpt one, who told me that the businesse was not altogether to be laugh't at, and because this man was reputed by me to be very intelligent and wary, I repented that I was not there, and began from that time forward as oft as I met with any one of the Copernican perswasion, to demand of them, if they had been alwayes of the same judgment; and of as many as I examined, I found not so much as one, who told me not that he had been a long time of the contrary opinion, but to have changed it for this, as convinced by the strength of the reasons proving the same: and afterwards questioning them, one by one, to see whether they were well possest of the reasons of the other side, I found them all to be very ready and perfect in them;The followers of Copernicus were all first against that opinion, but the Sectators of Aristotle & Ptolomy, were never of the other side. so that I could not truly say, that they had took up this opinion out of ignorance, vanity, or to shew the acutenesse of their wits. On the contrary, of as many of the Peripateticks and Ptolomeans as I have asked (and out of curiosity I have talked with many) what pains they had taken in the Book of Copernicus, I found very few that had so much as superficially perused it; but of those whom, I thought, had understood the same, not one; and moreover, I have enquired amongst the followers of the Peripatetick Doctrine, if ever any of them had held the contrary opinion, and likewise found none that had. Whereupon considering that there was no man who followed the opinion of Copernicus, that had not been first on the contrary side, and that was not very well acquainted with the reasons of Aristotle and Ptolomy; and, on the contrary, that there is not one of the followers of Ptolomy that had ever been of the judgment of Copernicus, and had left that, to imbrace this of Aristotle, considering, I say, these things, I began to think, that one, who leaveth an opinion imbued with his milk, and followed by very many, to take up another owned by very few, and denied by all the Schools, and that really seems a very great Paradox, must needs have been moved, not to say forced, by more powerful reasons. For this cause, I am become very curious to dive, as they say, into the bottom of this businesse, and account it my great good fortune that I have met you two, from whom I may without any trouble, hear all that hath been, and, haply, can be said on this argument, assuring my self that the strength of your reasons will resolve all scruples, and bring me to a certainty in this subject.

Simpl.But its possible your opinion and hopes may be disappointed, and that you may find your selves more at a losse in the end than you was at first.

Sagr.I am very confident that this can in no wise befal me.

Simpl.And why not? I have a manifest example in my self, that the farther I go, the more I am confounded.

Sagr.This is a sign that those reasons that hitherto seemed concluding unto you, and assured you in the truth of your opinion, begin to change countenance in your mind, and to let you by degrees, if not imbrace, at least look towards the contrary tenent; but I, that have been hitherto indifferent, do greatly hope to acquire rest and satisfaction by our future discourses, and you will not deny but I may, if you please but to hear what perswadeth me to this expectation.

Simpl.I will gladly hearken to the same, and should be no lesse glad that the like effect might be wrought in me.

Sagr.Favour me therefore with answering to what I shall ask you. And first, tell me, Simplicius, is not the conclusion, which we seek the truth of, Whether we ought to hold with Aristotle and Ptolomy, that the Earth onely abiding without motion in the Centre of the Universe, the Cœlestial bodies all move, or else, Whether the Starry Sphere and the Sun standing still in the Centre, the Earth is without the same, and owner of all those motions that in our seeming belong to the Sun and fixed Stars?

Simpl.These are the conclusions which are in dispute.

Sagr.And these two conclusions, are they not of such a nature, that one of them must necessarily be true, and the other false?

Simpl.They are so. We are in a Dilemma, one part of which must of necessity be true, and the other untrue; for between Motion and Rest, which are contradictories, there cannot be instanced a third, so as that one cannot say the Earth moves not, nor stands still; the Sun and Stars do not move, and yet stand not still.

Sagr.The Earth, the Sun, and Stars, what things are they in nature? are they petite things not worth our notice, or grand and worthy of consideration?

Simpl.They are principal, noble, integral bodies of the Universe, most vast and considerable.

Sagr.And Motion, and Rest, what accidents are they in Nature?

Simpl.So great and principal,Motion and rest principal accidents in nature. that Nature her self is defined by them.

Sagr.So that moving eternally, and the being wholly immoveable are two conditions very considerable in Nature, and indicate very great diversity; and especially when ascribed to the principal bodies of the Universe, from which can ensue none but very different events.

Simpl.Yea doubtlesse.

Sagr.Now answer me to another point. Do you believe that in Logick, Rhethorick, the Physicks, Metaphysicks, Mathematicks, and finally, in the universality of Disputations there are arguments sufficient to perswade and demonstrate to a person the fallacious, no lesse then the true conclusions?

Simpl.No Sir;Untruths cannot be demonstrated, as Truths are. rather I am very confident and certain, that for the proving of a true and necessary conclusion, there are in nature not onely one,For proof of true conclusions, many solid arguments may be produced, but to prove a falsity, none. but many very powerfull demonstrations: and that one may discusse and handle the same divers and sundry wayes, without ever falling into any absurdity; and that the more any Sophist would disturb and muddy it, the more clear would its certainty appear: And that on the contrary to make a false position passe for true, and to perswade the belief thereof, there cannot be any thing produced but fallacies, Sophisms, Paralogismes, Equivocations, and Discourses vain, inconsistant, and full of repugnances and contradictions.

Sagr.Now if eternal motion, and eternal rest be so principal accidents of Nature, and so different, that there can depend on them only most different consequences, and especially when applyed to the Sun, and to the Earth, so vast and famous bodies of the Universe; and it being, moreover, impossible, that one of two contradictory Propositions, should not be true, and the other false; and that for proof of the false one, any thing can be produced but fallacies; but the true one being perswadeable by all kind of concluding and demonstrative arguments, why should you think that he, of you two, who shall be so fortunate as to maintain the true Proposition ought not to perswade me? You must suppose me to be of a stupid wit, perverse judgment, dull mind and intellect, and of a blind reason, that I should not be able to distinguish light from darknesse, jewels from coals, or truth from falshood.

Simpl.I tell you now, and have told you upon other occasions, that the best Master to teach us how to discern Sophismes, Paralogismes, and other fallacies, was Aristotle, who in this particular can never be deceived.

Sagr.You insist upon Aristotle, who cannot speak. Yet I tell you,Aristotle would either refute his adversaries arguments, or would alter his opinion. that if Aristotle were here, he would either yield himself to be perswaded by us, or refuting our arguments, convince us by better of his own. And you your self, when you heard the experiments of the Suns related, did you not acknowledg and admire them, and confesse them more concludent than those of Aristotle? Yet neverthelesse I cannot perceive that Salviatus, who hath produced them, examined them, and with exquisite care scan'd them, doth confesse himself perswaded by them; no nor by others of greater force, which he intimated that he was about to give us an account of. And I know not on what grounds you should censure Nature, as one that for many Ages hath been lazie, and forgetful to produce speculative wits; and that knoweth not how to make more such, unlesse they be such kind of men as slavishly giving up their judgments to Aristotle, do understand with his brain, and resent with his senses. But let us hear the residue of those reasons which favour his opinion, that we may thereupon proceed to speak to them; comparing and weighing them in the ballance of impartiality.

Salv.Before I proceed any farther, I must tell Sagredus, that in these our Disputations, I personate the Copernican, and imitate him, as if I were his Zany; but what hath been effected in my private thoughts by these arguments which I seem to alledg in his favour, I would not have you to judg by what I say, whil'st I am in the heat of acting my part in the Fable; but after I have laid by my disguise, for you may chance to find me different from what you see me upon the Stage. Now let us go on.

Ptolomy and his followers produce another experiment like to that of the Projections,An argument taken from the Clouds, and from Birds. and it is of things that being separated from the Earth, continue a good space of time in the Air, such as are the Clouds, Birds of flight; and as of them it cannot be said that they are rapt or transparted by the Earth, having no adhesion thereto, it seems not possible, that they should be able to keep pace with the velocity thereof; nay it should rather seem to us, that they all swiftly move towards the West: And if being carried about by the Earth, passe our parallel in twenty four hours, which yet is at least sixteen thousand miles, how can Birds follow such a course or revolution? Whereas on the contrary, we see them fly as well towards the East, as towards the West,An argument taken from the air which we feel to beat upon us when we run a Horse at full speed. or any other part, without any sensible difference. Moreover, if when we run a Horse at his speed, we feel the air beat vehemently against our face, what an impetuous blast ought we perpetually to feel from the East, being carried with so rapid a course against the wind? and yet no such effect is perceived. Take another very ingenious argument inferred from the following experiment. An argument taken from the whirling of circular motion, which hath a faculty to extrude and dissipate. The circular motion hath a faculty to extrude and dissipate from its Centre the parts of the moving body, whensoever either the motion is not very slow, or those parts are not very well fastened together; and therefore, if v. g. we should turn one of those great wheels very fast about, wherein one or more men walking, crane up very great weights, as the huge massie stone, used by the Callander for pressing of Cloaths; or the fraighted Barks which being haled on shore, are hoisted out of one river into another; in case the parts of that same Wheel so swiftly turn'd round, be not very well joyn'd and pin'd together, they would all be shattered to pieces; and though many stones or other ponderous substances, should be very fast bound to its outward Rimme, yet could they not resist the impetuosity, which with great violence would hurl them every way far from the Wheel, and consequently from its Centre. So that if the Earth did move with such and so much greater velocity, what gravity, what tenacity of lime or plaister would keep together Stones, Buildings, and whole Cities, that they should not be tost into the Air by so precipitous a motion? And both men and beasts, which are not fastened to the Earth, how could they resist so great an impetus? Whereas, on the other side, we see both these, and far lesse resistances of pebles, sands, leaves rest quietly on the Earth, and to return to it in falling, though with a very slow motion. See here, Simplicius, the most potent arguments, taken, to so speak, from things Terrestrial; there remain those of the other kind, namely, such as have relation to the appearances of Heaven, which reasons, to confesse the truth, tend more to prove the Earth to be in the centre of the Universe, and consequently, to deprive it of the annual motion about the same, ascribed unto it by Copernicus. Which arguments, as being of somewhat a different nature, may be produced, after we have examined the strength of these already propounded.

Sagr.What say you Simplicius? do you think that Salviatus is Master of, and knoweth how to unfold the Ptolomean and Aristotelian arguments? Or do you think that any Peripatetick is equally verst in the Copernican demonstrations?

Simpl.Were it not for the high esteem, that the past discourses have begot in me of the learning of Salviatus, and of the acutenesse of Sagredus, I would by their good leave have gone my way without staying for their answers; it seeming to me a thing impossible, that so palpable experiments should be contradicted; and would, without hearing them farther, confirm my self in my old perswasion; for though I should be made to see that it was erroneous, its being upheld by so many probable reasons, would render it excuseable. And if these are fallacies, what true demonstrations were ever so fair?

Sagr.Yet its good that we hear the responsions of Salviatus; which if they be true, must of necessity be more fair, and that by infinite degrees; and those must be deformed, yea most deformed, if the Metaphysical Axiome hold,True and fair are one and the same, as also false and deformed. That true and fair are one and the same thing; as also false and deformed. Therefore Salviatus let's no longer lose time.

Salv.The first Argument alledged by Simplicius, if I well remember it, was this. The Earth cannot move circularly, because such motion would be violent to the same, and therefore not perpetual: that it is violent, the reason was: Because, that had it been natural, its parts would likewise naturally move round, which is impossible, for that it is natural for the parts thereof to move with a right motion downwards. To this my reply is, that I could gladly wish,The answer to Aristotles first argument. that Aristotle had more cleerly exprest himself, where he said; That its parts would likewise move circularly; for this moving circularly is to be understood two wayes, one is, that every particle or atome separated from its Whole would move circularly about its particular centre, describing its small Circulets; the other is, that the whole Globe moving about its centre in twenty four hours, the parts also would turn about the same centre in four and twenty hours. The first would be no lesse an impertinency, than if one should say, that every part of the circumference of a Circle ought to be a Circle; or because that the Earth is Spherical, that therefore every part thereof be a Globe, for so doth the Axiome require: Eadem est ratio totius, & partium. But if he took it in the other sense, to wit, that the parts in imitation of the Whole should move naturally round the Centre of the whole Globe in twenty four hours, I say, that they do so; and it concerns you, instead of Aristotle, to prove that they do not.

Simpl.This is proved by Aristotle in the same place, when he saith, that the natural motion of the parts is the right motion downwards to the centre of the Universe; so that the circular motion cannot naturally agree therewith.

Salv.But do not you see, that those very words carry in them a confutation of this solution?

Simpl.How? and where?

Salv.Doth not he say that the circular motion of the Earth would be violent? and therefore not eternal? and that this is absurd, for that the order of the World is eternal?

Simpl.He saith so.

Salv.But if that which is violent cannot be eternal,That which is violent, cannot be eternal, and that which cannot be eternal, cannot be natural. then by conversion, that which cannot be eternal, cannot be natural: but the motion of the Earth downwards cannot be otherwise eternal; therefore much lesse can it be natural: nor can any other motion be natural to it, save onely that which is eternal. But if we make the Earth move with a circular motion, this may be eternal to it, and to its parts, and therefore natural.

Simpl.The right motion is most natural to the parts of the Earth, and is to them eternal; nor shall it ever happen that they move not with a right motion; alwayes provided that the impediments be removed.

Salv.You equivocate Simplicius; and I will try to free you from the equivoke. Tell me, therefore, do you think that a Ship which should sail from the Strait of Gibralter towards Palestina can eternally move towards that Coast? keeping alwayes an equal course?

Simpl.No doubtlesse.

Salv.And why not?

Simpl.Because that Voyage is bounded and terminated between the Herculean Pillars, and the shore of the Holy-land; and the distance being limited, it is past in a finite time, unlesse one by returning back should with a contrary motion begin the same Voyage anew; but this would be an interrupted and no continued motion.

Salv.Very true. But the Navigation from the Strait of Magalanes by the Pacifick Ocean, the Moluccha's, the Cape di buona Speranza, and from thence by the same Strait, and then again by the Pacifick Ocean, &c. do you believe that it may be perpetuated?

Simpl.It may; for this being a circumgyration, which returneth about its self, with infinite replications, it may be perpetuated without any interruption.

Salv.A Ship then may in this Voyage continue sailing eternally.

Simpl.It may, in case the Ship were incorruptible, but the Ship decaying, the Navigation must of necessity come to an end.

Salv.But in the Mediterrane, though the Vessel were incorruptible, yet could she not sail perpetually towards Palestina, that Voyage being determined.Two things requisite to the end a motion may perpetuate it self; an unlimited space, and an incorruptible moveable. Two things then are required, to the end a moveable may without intermission move perpetually; the one is, that the motion may of its own nature be indeterminate and infinite; the other, that the moveable be likewise incorruptible and eternal.

Simpl.All this is necessary.

Salv.Therefore you may see how of your own accord you have confessed it impossible that any moveable should move eternally in a right line,Right motion cannot be eternal, and consequently cannot be natural to the Earth. in regard that right motion, whether it be upwards, or downwards, is by you your self bounded by the circumference and centre; so that if a Moveable, as suppose the Earth be eternal, yet forasmuch as the right motion is not of its own nature eternall, but most ** Terminatissimo terminate, it cannot naturally suit with the Earth. Nay, as was said ** By this expression he every where means the preceding Dialogue, or Giornata. yesterday, Aristotle himself is constrained to make the Terrestrial Globe eternally immoveable. When again you say, that the parts of the Earth evermore move downwards, all impediments being removed, you egregiously equivocate; for then, on the other side they must be impeded, contraried, and forced, if you would have them move; for, when they are once fallen to the ground, they must be violently thrown upwards, that they may a second time fall; and as to the impediments, these only hinder its arrival at the centre; but if there were a Well, that did passe thorow and beyond the centre, yet would not a cold of Earth passe beyond it, unlesse inasmuch as being transported by its impetus, it should passe the same to return thither again, and in the end there to rest. As therefore to the defending, that the motion by a right line doth or can agree naturally neither to the Earth, nor to any other moveable, whil'st the Universe retaineth its perfect order, I would have you take no further paines about it, but (unlesse you will grant them the circular motion) your best way will be to defend and maintain their immobility.

Simpl.As to their immoveablenesse, the arguments of Aristotle, and moreover those alledged by your self seem in my opinion necessarily to conclude the same, as yet; and I conceive it will be a hard matter to refute them.

Salv.Come we therefore to the second Argument, which was, That those bodies,The answer to the second argument. which we are assured do move circularly, have more than one motion, unlesse it be the Primum Mobile; and therefore, if the Earth did move circularly, it ought to have two motions; from which alterations would follow in the rising and setting of the Fixed Stars: Which effect is not perceived to ensue. Therefore, &c. The most proper and genuine answer to this Allegation is contained in the Argument it self; and even Aristotle puts it in our mouths, which it is impossible, Simplicius, that you should not have seen.

Simpl.I neither have seen it, nor do I yet apprehend it.

Salv.This cannot be, sure, the thing is so very plain.

Simpl.I will with your leave, cast an eye upon the Text.

Sagr.We will command the Text to be brought forthwith.

Simpl.I alwayes carry it about with me: See here it is, and I know the place perfectly well, which is in lib. 2. De Cœlo, cap. 16. Here it is, Text 97. Preterea omnia, quæ feruntur latione circulari subdeficere videntur, ac moveri pluribus una latione, præter primam Sphæram; quare & Terram necessariam est, sive circa medium, sive in medio posita feratur, duabus moveri lationibus. Si autem hoc acciderit, necessariam est fieri mutationes, ac conversiones fixorum astrorum. Hoc autem non videtur fieri, sed semper eadem, apud eadem loca ipsius, & oriuntur, & occidunt. [In English thus:] Furthermore all that are carried with circular motion, seem to ** Subdesicere. foreslow, and to move with more than one motion, except the first Sphere; wherefore it is necessary that the Earth move with two motions, whether it be carried about the ** Or Centre. middle, or placed in the middle. But if it be so, there would of necessity be alterations and conversions made amongst the fixed Stars. But no such thing is seen to be done, but the same Star doth alwayes rise and set in the same place. In all this I find not any falacy, and my thinks the argument is very forcible.

Salv.And this new reading of the place hath confirmed me in the fallacy of the Sillogisme, and moreover, discovered another falsity. Therefore observe. The Positions, or if you will, Conclusions, which Aristotle endeavours to oppose, are two; one is that of those, who placing the Earth in the midst of the World, do make it move in it self about its own centre. The other is of those, who constituting it far from the middle, do make it revolve with a circular motion about the middle of the Universe. And both these Positions he conjointly impugneth with one and the same argument. Now I affirm that he is out in both the one and the other impugnation; and that his error against the first Position is an Equivoke or Paralogisme;Aristotles argument against the Earths motion, is defective in two things and his mistake touching the second is a false consequence. Let us begin with the first Assertion, which constituteth the Earth in the midst of the World, and maketh it move in it self about its own centre; and let us confront it with the objection of Aristotle; saying, All moveables, that move circularly, seem to ** The same word which a little above I tendred stay behind, as a bowle when it meets with rubs. foreslow, and move with more than one Byas, except the first Sphere (that is the primum mobile) therefore the Earth moving about its own centre, being placed in the middle, must of necessity have two byasses, and foreslow. But if this were so, it would follow, that there should be a variation in the rising and setting of the fixed Stars, which we do not perceive to be done: Therefore the Earth doth not move, &c. Here is the Paralogisme, and to discover it, I will argue with Aristotle in this manner. Thou saist, oh Aristotle, that the Earth placed in the middle of the World, cannot move in it self (i. e. upon its own axis) for then it would be requisite to allow it two byasses; so that, if it should not be necessary to allow it more than one Byas onely, thou wouldest not then hold it impossible for it to move onely with that one; for thou would'st unnecessarily have confined the impossibility to the plurality of byasses, if in case it had no more but one, yet it could not move with that. And because that of all the moveables in the World, thou makest but one alone to move with one sole byas; and all the rest with more than one; and this same moveable thou affirmest to be the first Sphere, namely, that by which all the fixed and erratick Stars seem harmoniously to move from East to West, if in case the Earth may be that first Sphere, that by moving with one byas onely, may make the Stars appear to move from East to West, thou wilt not deny them it: But he that affirmeth, that the Earth being placed in the midst of the World, moveth about its own Axis, ascribes unto it no other motion, save that by which all the Stars appear to move from East to West; and so it cometh to be that first Sphere, which thou thy self acknowledgest to move with but one byas onely. It is therefore necessary, oh Aristotle, if thou wilt conclude any thing, that thou demonstrate, that the Earth being placed in the midst of the World, cannot move with so much as one byas onely; or else, that much lesse can the first Sphere have one sole motion; for otherwise thou doest in thy very Sillogisme both commit the falacy, and detect it, denying, and at that very time proving the same thing. I come now to the second Position, namely, of those who placing the Earth far from the midst of the Universe, make it moveable about the same; that is, make it a Planet and erratick Star; against which the argument is directed, and as to form is concludent, but faileth in matter. For it being granted, that the Earth doth in that manner move, and that with two byasses, yet doth it not necessarily follow that though it were so, it should make alterations in the risings and settings of the fixed Stars, as I shall in its proper place declare. And here I could gladly excuse Aristotle; rather I could highly applaud him for having light upon the most subtil argument that could be produced against the Copernican Hypothesis; and if the objection be ingenious, and to outward appearance most powerful, you may see how much more acute and ingenious the solution must be, and not to be found by a wit lesse piercing than that of Copernicus; and again from the difficulty in understanding it, you may argue the so much greater difficulty in finding it. But let us for the present suspend our answer, which you shall understand in due time and place, after we have repeated the objection of Aristotle, and that in his favour, much strengthened. Now passe we to Aristotles third Argument,The answer to the third argument. touching which we need give no farther reply, it having been sufficiently answered betwixt the discourses of yesterday and to day: In as much as he urgeth, that the motion of grave bodies is naturally by a right line to the centre; and then enquireth, whether to the centre of the Earth, or to that of the Universe, and concludeth that they tend naturally to the centre of the Universe, but accidentally to that of the Earth. Therefore we may proceed to the fourth,The answer to the fourth argument. upon which its requisite that we stay some time, by reason it is founded upon that experiment, from whence the greater part of the remaining arguments derive all their strength. Aristotle saith therefore, that it is a most convincing argument of the Earths immobility, to see that projections thrown or shot upright, return perpendicularly by the same line unto the same place from whence they were shot or thrown. And this holdeth true, although the motion be of a very great height; which could never come to passe, did the Earth move: for in the time that the projected body is moving upwards and downwards in a state of separation from the Earth, the place from whence the motion of the projection began, would be past, by means of the Earths revolution, a great way towards the East, and look how great that space was, so far from that place would the projected body in its descent come to the ground. So that hither may be referred the argument taken from a bullet shot from a Canon directly upwards; as also that other used by Aristotle and Ptolomy, of the grave bodies that falling from on high, are observed to descend by a direct and perpendicular line to the surface of the Earth. Now that I may begin to unite these knots, I demand of Simplicius that in case one should deny to Ptolomy and Aristotle that weights in falling freely from on high, descend by a right and perpendicular line, that is, directly to the centre, what means he would use to prove it?

Simpl.The means of the senses; the which assureth us, that that Tower or other altitude, is upright and perpendicular, and sheweth us that that stone, or other grave body, doth slide along the Wall, without inclining a hairs breadth to one side or another, and light at the foot thereof just under the place from whence it was let fall.

Salv.But if it should happen that the Terrestrial Globe did move round, and consequently carry the Tower also along with it, and that the stone did then also grate and slide along the side of the Tower, what must its motion be then?

Simpl.In this case we may rather say its motions: for it would have one wherewith to descend from the top of the Tower to the bottom, and should necessarily have another to follow the course of the said Tower.

Salv.So that its motion should be compounded of two, to wit, of that wherewith it measureth the Tower, and of that other wherewith it followeth the same: From which composition would follow, that the stone would no longer describe that simple right and perpendicular line, but one transverse, and perhaps not streight.

Simpl.I can say nothing of its non-rectitude, but this I know very well, that it would of necessity be transverse, and different from the other directly perpendicular, which it doth describe, the Earth standing still.

Salv.You see then, that upon the meer observing the falling stone to glide along the Tower, you cannot certainly affirm that it describeth a line which is streight and perpendicular, unless you first suppose that the Earth standeth still.

Simpl.True; for if the Earth should move, the stones motion would be transverse, and not perpendicular.

Salv.Behold then the Paralogism of Aristotle and Ptolomey to be evident and manifest,The Paralogism of Aristotle and Ptolomey in supposing that for known, which is in question. and discovered by you your self, wherein that is supposed for known, which is intended to be demonstrated.

Simpl.How can that be? To me it appeareth that the Syllogism is rightly demonstrated without petitionem principii.

Salv.You shall see how it is; answer me a little. Doth he not lay down the conclusion as unknown?

Simpl.Unknown; why otherwise the demonstrating it would be superfluous.

Salv.But the middle term, ought not that to be known?

Simpl.Its necessary that it should; for otherwise it would be a proving ignotum per æquè ignotum.

Salv.Our conclusion which is to be proved, and which is unknown, is it not the stability of the Earth?

Simpl.It is the same.

Salv.The middle term, which ought to be known, is it not the streight and perpendicular descent of the stone?

Simpl.It is so.

Salv.But was it not just now concluded, that we can have no certain knowledg whether that same shall be direct and perpendicular, unless we first know that the Earth stands still? Therefore in your Syllogism the certainty of the middle term is assumed from the uncertainty of the conclusion. You may see then, what and how great the Paralogism is.

Sagr.I would, in favour of Simplicius, defend Aristotle if it were possible, or at least better satisfie my self concerning the strength of your illation. You say, that the seeing the stone rake along the Tower, is not sufficient to assure us, that its motion is perpendicular (which is the middle term of the Syllogism) unless it be presupposed, that the Earth standeth still, which is the conclusion to be proved: For that if the Tower did move together with the Earth, and the stone did slide along the same, the motion of the stone would be transverse, and not perpendicular. But I shall answer, that should the Tower move, it would be impossible that the stone should fail gliding along the side of it; and therefore from its falling in that manner the stability of the Earth is inferred.

Simpl.It is so; for if you would have the stone in descending to grate upon the Tower, though it were carried round by the Earth, you must allow the stone two natural motions, to wit, the straight motion towards the Centre, and the circular about the Centre, the which is impossible.

Salv.Aristotles defense then consisteth in the impossibilitie, or at least in his esteeming it an impossibility, that the stone should move with a motion mixt of right and circular: for if he did not hold it impossible that the stone could move to the Centre, and about the Centre at once, he must have understood, that it might come to pass that the cadent stone might in its descent, race the Tower as well when it moved as when it stood still; and consequently he must have perceived, that from this grating nothing could be inferred touching the mobility or immobility of the Earth. But this doth not any way excuse Aristotle; aswell because he ought to have exprest it, if he had had such a conceit, it being so material a part of his Argument; as also because it can neither be said that such an effect is impossible, nor that Aristotle did esteem it so. The first cannot be affirmed, for that by and by I shall shew that it is not onely possible, but necessary: nor much less can the second be averred,Aristotle admitteth that the Fire moveth directly upwards by nature, and round about by participation. for that Aristotle himself granteth fire to move naturally upwards in a right line, and to move about with the diurnal motion, imparted by Heaven to the whole Element of Fire, and the greater part of the Air: If therefore he held it not impossible to mix the right motion upwards, with the circular communicated to the Fire and Air from the concave of the Moon, much less ought he to account impossible the mixture of the right motion downwards of the stone, with the circular which we presuppose natural to the whole Terrestrial Globe, of which the stone is a part.

Simpl.I see no such thing: for if the element of Fire revolve round together with the Air, it is a very easie, yea a necessary thing, that a spark of fire which from the Earth mounts upwards, in passing thorow the moving air, should receive the same motion, being a body so thin, light, and easie to be moved: but that a very heavy stone, or a Canon bullet, that descendeth from on high, and that is at liberty to move whither it will, should suffer it self to be transported either by the air or any other thing, is altogether incredible. Besides that, we have the Experiment, which is so proper to our purpose, of the stone let fall from the round top of the Mast of a ship, which when the ship lyeth still, falleth at the Partners of the Mast; but when the ship saileth, falls so far distant from that place, by how far the ship in the time of the stones falling had run forward; which will not be a few fathoms, when the ships course is swift.

Salv.There is a great disparity between the case of the Ship and that of the Earth,The disparity between the fall of a stone from the round top of a ship, and from the top of a tower. if the Terrestrial Globe be supposed to have a diurnal motion. For it is a thing very manifest, that the motion of the Ship, as it is not natural to it, so the motion of all those things that are in it is accidental, whence it is no wonder that the stone which was retained in the round top, being left at liberty, descendeth downwards without any obligation to follow the motion of the Ship. But the diurnal conversion is ascribed to the Terrestrial Globe for its proper and natural motion, and consequently, it is so to all the parts of the said Globe; and, as being impress'd by nature, is indelible in them; and therefore that stone that is on the top of the Tower hath an intrinsick inclination of revolving about the Centre of its Whole in twenty four hours, and this same natural instinct it exerciseth eternally, be it placed in any state whatsoever. And to be assured of the truth of this, you have no more to do but to alter an antiquated impression made in your mind; and to say, Like as in that I hitherto holding it to be the property of the Terrestrial Globe to rest immoveable about its Centre, did never doubt or question but that all whatsoever particles thereof do also naturally remain in the same state of rest: So it is reason, in case the Terrestrial Globe did move round by natural instinct in twenty four hours, that the intrinsick and natural inclination of all its parts should also be, not to stand still, but to follow the same revolution. And thus without running into any inconvenience, one may conclude, that in regard the motion conferred by the force of **That you may not suspect my translation, or wonder what Oars have to do with a ship, you are to know that the Author intends the Gallies used in the Mediterrane. Oars on the Ship, and by it on all the things that are contained within her, is not natural but forreign, it is very reasonable that that stone, it being separated from the ship, do reduce its self to its natural disposure, and return to exercise its pure simple instinct given it by nature.The part of the Air inferiour to the higher mountains doth follow the motion of the Earth. To this I add, that it's necessary, that at least that part of the Air which is beneath the greater heights of mountains, should be transported and carried round by the roughness of the Earths surface; or that, as being mixt with many Vapours, and terrene Exhalations, it do naturally follow the diurnal motion, which occurreth not in the Air about the ship rowed by Oars: So that your arguing from the ship to the Tower hath not the force of an illation; because that stone which falls from the round top of the Mast, entereth into a medium, which is unconcern'd in the motion of the ship: but that which departeth from the top of the Tower, finds a medium that hath a motion in common with the whole Terrestrial Globe; so that without being hindred, rather being assisted by the motion of the air, it may follow the universal course of the Earth.

Simpl.I cannot conceive that the air can imprint in a very great stone,The motion of the Air apt to carry with it light things but not heavy. or in a gross Globe of Wood or Ball of Lead, as suppose of two hundred weight, the motion wherewith its self is moved, and which it doth perhaps communicate to feathers, snow, and other very light things: nay, I see that a weight of that nature, being exposed to any the most impetuous wind, is not thereby removed an inch from its place; now consider with your self whether the air will carry it along therewith.

Salv.There is great difference between your experiment and our case. You introduce the wind blowing against that stone, supposed in a state of rest, and we expose to the air, which already moveth, the stone which doth also move with the same velocity; so that the air is not to conferr a new motion upon it, but onely to maintain, or to speak better, not to hinder the motion already acquired: you would drive the stone with a strange and preternatural motion, and we desire to conserve it in its natural. If you would produce a more pertinent experiment, you should say, that it is observed, if not with the eye of the forehead, yet with that of the mind, what would evene, if an eagle that is carried by the course of the wind, should let a stone fall from its talons; which, in regard that at its being let go, it went along with the wind, and after it was let fall it entered into a medium that moved with equal velocity, I am very confident that it would not be seen to descend in its fall perpendicularly, but that following the course of the wind, and adding thereto that of its particular gravity, it would move with a transverse motion.

Simpl.But it would first be known how such an experiment may be made; and then one might judg according to the event. In the mean time the effect of the ship doth hitherto incline to favour our opinion.

Salv.Well said you hitherto, for perhaps it may anon change countenance. And that I may no longer hold you in suspense, tell me, Simplicius, do you really believe, that the Experiment of the ship squares so very well with our purpose, as that it ought to be believed, that that which we see happen in it, ought also to evene in the Terrestrial Globe?

Simpl.As yet I am of that opinion; and though you have alledged some small disparities, I do not think them of so great moment, as that they should make me change my judgment.

Salv.I rather desire that you would continue therein, and hold for certain, that the effect of the Earth would exactly answer that of the ship: provided, that when it shall appear prejudicial to your cause, you would not be humorous and alter your thoughts. You may haply say, Forasmuch as when the ship stands still, the stone falls at the foot of the Mast, and when she is under sail, it lights far from thence, that therefore by conversion, from the stones falling at the foot is argued the ships standing still, and from its falling far from thence is argued her moving; and because that which occurreth to the ship, ought likewise to befall the Earth: that therefore from the falling of the stone at the foot of the Tower is necessarily inferred the immobility of the Terrestrial Globe. Is not this your argumentation?

Simpl.It is, and reduced into that conciseness, as that it is become most easie to be apprehended.

Salv.Now tell me; if the stone let fall from the Round-top, when the ship is in a swift course, should fall exactly in the same place of the ship, in which it falleth when the ship is at anchor, what service would these experiments do you, in order to the ascertaining whether the vessel doth stand still or move?

Simpl.Just none: Like as, for exemple, from the beating of the pulse one cannot know whether a person be asleep or awake, seeing that the pulse beateth after the same manner in sleeping as in waking.

Salv.Very well. Have you ever tryed the experiment of the Ship?

Simpl.I have not; but yet I believe that those Authors which alledg the same, have accurately observed it; besides that the cause of the disparity is so manifestly known, that it admits of no question.

Salv.That it is possible that those Authors instance in it, without having made tryal of it, you your self are a good testimony, that without having examined it, alledg it as certain, and in a credulous way remit it to their authority; as it is now not onely possible, but very probable that they likewise did; I mean, did remit the same to their Predecessors, without ever arriving at one that had made the experiment: for whoever shall examine the same, shall find the event succeed quite contrary to what hath been written of it: that is, he shall see the stone fall at all times in the same place of the Ship, whether it stand still, or move with any whatsoever velocity.The stone falling from the Mast of a ship lights in the same place, whether the ship doth move or ly still. So that the same holding true in the Earth, as in the Ship, one cannot from the stones falling perpendicularly at the foot of the Tower, conclude any thing touching the motion or rest of the Earth.

Simpl.If you should refer me to any other means than to experience, I verily believe our Disputations would not come to an end in haste; for this seemeth to me a thing so remote from all humane reason, as that it leaveth not the least place for credulity or probability.

Salv.And yet it hath left place in me for both.

Simpl.How is this? You have not made an hundred, no nor one proof thereof, and do you so confidently affirm it for true? I for my part will return to my incredulity, and to the confidence I had that the Experiment hath been tried by the principal Authors who made use thereof, and that the event succeeded as they affirm.

Salv.I am assured that the effect will ensue as I tell you; for so it is necessary that it should: and I farther add, that you know your self that it cannot fall out otherwise, however you feign or seem to feign that you know it not. Yet I am so good at taming of wits, that I will make you confess the same whether you will or no. But Sagredus stands very mute, and yet, if I mistake not, I saw him make an offer to speak somewhat.

Sagr.I had an intent to say something, but to tell you true, I know not what it was; for the curiosity that you have moved in me, by promising that you would force Simplicius to discover the knowledg which he would conceal from us, hath made me to depose all other thoughts: therefore I pray you to make good your vaunt.

Salv.Provided that Simplicius do consent to reply to what I shall ask him, I will not fail to do it.

Simpl.I will answer what I know, assured that I shall not be much put to it, for that of those things which I hold to be false, I think nothing can be known, in regard that Science respecteth truths and not falshoods.

Salv.I desire not that you should say or reply, that you know any thing, save that which you most assuredly know. Therefore tell me; If you had here a flat superficies as polite as a Looking-glass, and of a substance as hard as steel, and that it were not paralel to the Horizon, but somewhat inclining, and that upon it you did put a Ball perfectly spherical, and of a substance grave and hard, as suppose of brass; what think you it would do being let go? do not you believe (as for my part I do) that it would lie still?

Simpl.If that superficies were inclining?

Salv.Yes; for so I have already supposed.

Simpl.I cannot conceive how it should lie still: nay, I am confident that it would move towards the declivity with much propensness.

Salv.Take good heed what you say, Simplicius, for I am confident that it would lie still in what ever place you should lay it.

Simpl.So long as you make use of such suppositions, Salvictus, I shall cease to wonder if you inferr most absurd conclusions.

Salv.Are you assured, then, that it would freely move towards the declivity?

Simpl.Who doubts it?

Salv.And this you verily believe, not because I told you so, (for I endeavoured to perswade you to think the contrary) but of your self, and upon your natural judgment.

Simpl.Now I see what you would be at; you spoke not this as really believing the same; but to try me, and to wrest matter out of my own mouth wherewith to condemn me.

Salv.You are in the right. And how long would that Ball move, and with what velocity? But take notice that I instanced in a Ball exactly round, and a plain exquisitely polished, that all external and accidental impediments might be taken away. And so would I have you remove all obstructions caused by the Airs resistance to division, and all other casual obstacles, if any other there can be.

Simpl.I very well understand your meaning, and as to your demand, I answer, that the Ball would continue to move in infinitum, if the inclination of the plain should so long last, and continually with an accelerating motion; for such is the nature of ponderous moveables, that vires acquirant eundo: and the greater the declivity was, the greater the velocity would be.

Salv.But if one should require that that Ball should move upwards on that same superficies, do you believe that it would so do?

Simpl.Not spontaneously; but being drawn, or violently thrown, it may.

Salv.And in case it were thrust forward by the impression of some violent impetus from without, what and how great would its motion be?

Simpl.The motion would go continually decreasing and retarding, as being contrary to nature; and would be longer or shorter, according to the greater or less impulse, and according to the greater or less acclivity.

Salv.It seems, then, that hitherto you have explained to me the accidents of a moveable upon two different Planes; and that in the inclining plane, the grave moveable doth spontaneously descend, and goeth continually accelerating, and that to retain it in rest, force must be used therein: but that on the ascending plane, there is required a force to thrust it forward, and also to stay it in rest, and that the motion impressed goeth continually diminishing, till that in the end it cometh to nothing. You say yet farther, that in both the one and the other case, there do arise differences from the planes having a greater or less declivity or acclivity; so that the greater inclination is attended with the greater velocity; and contrariwise, upon the ascending plane, the same moveable thrown with the same force, moveth a greater distance, by how much the elevation is less. Now tell me, what would befall the same moveable upon a superficies that had neither acclivity nor declivity?

Simpl.Here you must give me a little time to consider of an answer. There being no declivity, there can be no natural inclination to motion: and there being no acclivity, there can be no resistance to being moved; so that there would arise an indifference between propension and resistance of motion; therefore, methinks it ought naturally to stand still. But I had forgot my self: it was but even now that Sagredus gave me to understand that it would so do.

Salv.So I think, provided one did lay it down gently: but if it had an impetus given it towards any part, what would follow?

Simpl.There would follow, that it should move towards that part.

Salv.But with what kind of motion? with the continually accelerated, as in declining planes; or with the successively retarded, as in those ascending.

Simpl.I cannot tell how to discover any cause of acceleration, or retardation, there being no declivity or acclivity.

Salv.Well: but if there be no cause of retardation, much less ought there to be any cause of rest. How long therefore would you have the moveable to move?

Simpl.As long as that superficies, neither inclined nor declined shall last.

Salv.Therefore if such a space were interminate, the motion upon the same would likewise have no termination, that is, would be perpetual.

Simpl.I think so, if so be the moveable be of a matter durable.

Salv.That hath been already supposed, when it was said, that all external and accidental impediments were removed, and the brittlenesse of the moveable in this our case, is one of those impediments accidental. Tell me now, what do you think is the cause that that same Ball moveth spontaneously upon the inclining plane, and not without violence upon the erected?

Simpl.Because the inclination of grave bodies is to move towards the centre of the Earth, and onely by violence upwards towards the circumference; and the inclining superficies is that which acquireth vicinity to the centre, and the ascending one, remotenesse.

Salv.Therefore a superficies, which should be neither declining nor ascending, ought in all its parts to be equally distant from the centre. But is there any such superficies in the World?

Simpl.There is no want thereof: Such is our Terrestrial Globe, if it were more even, and not as it is rough and montainous; but you have that of the Water, at such time as it is calm and still.

Salv.Then a ship which moveth in a calm at Sea, is one of those moveables, which run along one of those superficies that are neither declining nor ascending, and therefore disposed, in case all obstacles external and accidental were removed, to move with the impulse once imparted incessantly and uniformly.

Simpl.It should seem to be so.

Salv.And that stone which is on the round top, doth not it move, as being together with the ship carried about by the circumference of a Circle about the Centre; and therefore consequently by a motion in it indelible, if all extern obstacles be removed? And is not this motion as swift as that of the ship.

Simpl.Hitherto all is well. But what followeth?

Salv.Then in good time recant, I pray you, that your last conclusion, if you are satisfied with the truth of all the premises.

Simpl.By my last conclusion, you mean, That that same stone moving with a motion indelibly impressed upon it, is not to leave, nay rather is to follow the ship, and in the end to light in the self same place, where it falleth when the ship lyeth still; and so I also grant it would do, in case there were no outward impediments that might disturb the stones motion, after its being let go, the which impediments are two, the one is the moveables inability to break through the air with its meer impetus onely, it being deprived of that of the strength of Oars, of which it had been partaker, as part of the ship, at the time that it was upon the Mast; the other is the new motion of descent, which also must needs be an hinderance of that other progressive motion.

Salv.As to the impediment of the Air, I do not deny it you; and if the thing falling were a light matter, as a feather, or a lock of wool, the retardation would be very great, but in an heavy stone is very exceeding small. And you your self but even now did say, that the force of the most impetuous wind sufficeth not to stir a great stone from its place; now do but consider what the calmer air is able to do, being encountred by a stone no more swift than the whole ship. Neverthelesse, as I said before, I do allow you this small effect, that may depend upon such an impediment; like as I know, that you will grant to me, that if the air should move with the same velocity that the ship and stone hath, then the impediment would be nothing at all. As to the other of the additional motion downwards; in the first place it is manifest, that these two, I mean the circular, about the centre, and the streight, towards the centre, are not contraries, or destructive to one another, or incompatible. Because that as to the moveable, it hath no repugnance at all to such motions, for you your self have already confest the repugnance to be against the motion which removeth from the centre, and the inclination to be towards the motion which approacheth to the centre. Whence it doth of necessity follow, that the moveable hath neither repugnance, nor propension to the motion which neither approacheth, nor goeth from the centre, nor consequently is there any cause for the diminishing in it the faculty impressed. And forasmuch as the moving cause is not one alone, which it hath attained by the new operation of retardation; but that they are two, distinct from each other, of which, the gravity attends only to the drawing of the moveable towards the centre, and the vertue impress't to the conducting it about the centre, there remaineth no occasion of impediment.

Simpl.Your argumentation, to give you your due, is very probable; but in reality it is invelloped with certain intricacies, that are not easie to be extricated. You have all along built upon a supposition,The project according to Aristotle, is not moved by vertue impressed, but by the medium. which the Peripatetick Schools will not easily grant you, as being directly contrary to Aristotle, and it is to take for known and manifest, That the project separated from the projicient, continueth the motion by vertue impressed on it by the said projicient, which vertue impressed is a thing as much detested in Peripatetick Philosophy, as the passage of any accident from one subject into another. Which doctrine doth hold, as I believe it is well known unto you, that the project is carried by the medium, which in our case happeneth to be the Air. And therefore if that stone let fall from the round top, ought to follow the motion of the ship, that effect should be ascribed to the Air, and not to the vertue impressed. But you presuppose that the Air doth not follow the motion of the ship, but is tranquil. Moreover, he that letteth it fall, is not to throw it, or to give it impetus with his arm, but ought barely to open his hand and let it go; and by this means, the stone, neither through the vertue impressed by the projicient, nor through the help of the Air, shall be able to follow the ships motion, and therefore shall be left behind.

Salv.I think then that you would say, that if the stone be not thrown by the arm of that person, it is no longer a projection.

Simpl.It cannot be properly called a motion of projection.

Salv.So then that which Aristotle speaks of the motion, the moveable, and the mover of the projects, hath nothing to do with the businesse in hand; and if it concern not our purpose, why do you alledg the same?

Simpl.I produce it on the oceasion of that impressed vertue, named and introduced by you, which having no being in the World, can be of no force; for non-entium nullae sunt operationes; and therefore not onely of projected, but of all other preternatural motions, the moving cause ought to be ascribed to the medium, of which there hath been no due consideration had; and therefore all that hath been said hitherto is to no purpose.

Salv.Go to now, in good time. But tell me, seeing that your instance is wholly grounded upon the nullity of the vertue impressed, if I shall demonstrate to you, that the medium hath nothing to do in the continuation of projects, after they are separated from the projicient, will you admit of the impressed vertue, or will you make another attempt to overthrow it?

Simpl.The operation of the medium being removed, I see not how one can have recourse to any thing else save the faculty impressed by the mover.

Salv.It would be well, for the removing, as much as is possible, the occasions of multiplying contentions, that you would explain with as much distinctnesse as may be, what is that operation of the medium in continuing the motion of the project.Operation of the medium in continuing the motion of the project.

Simpl.The projicient hath the stone in his hand, and with force and violence throws his arm, with which jactation the stone doth not move so much as the circumambient Air; so that when the stone at its being forsaken by the hand, findeth it self in the Air, which at the same time moveth with impetousity, it is thereby born away; for, if the air did not operate, the stone would fall at the foot of the projicient or thrower.

Salv.And was you so credulous,Many experiments, and reasons against the cause of the motion of projects, assigned by Aristotle. as to suffer your self to be perswaded to believe these fopperies, so long as you had your senses about you to confute them, and to understand the truth thereof? Therefore tell me, that great stone, and that Canon bullet, which but onely laid upon a table, did continue immoveable against the most impetuous winds, according as you a little before did affirm, if it had been a ball of cork or other light stuffe, think you that the wind would have removed it from its place?

Simpl.Yes, and I am assured that it would have blown it quite away, and with so much more velocity, by how much the matter was lighter, for upon this reason we see the clouds to be transported with a velocity equal to that of the wind that drives them.

Salv.And what is the Wind?

Simpl.The Wind is defined to be nothing else but air moved.

Salv.Then the moved air doth carry light things more swiftly, and to a greater distance, then it doth heavy.

Simpl.Yes certainly.

Salv.But if you were to throw with your arm a stone, and a lock of cotton wool, which would move swiftest and farthest?

Simpl.The stone by much; nay the wool would fall at my feet.

Salv.But, if that which moveth the projected substance, after it is delivered from the hand, be no other than the air moved by the arm, and the moved air do more easily bear away light than grave matters, how cometh it that the project of wool flieth not farther, and swifter than that of stone? Certainly it argueth that the stone hath some other impulse besides the motion of the air. Furthermore, if two strings of equal length did hang at yonder beam, and at the end of one there was fastened a bullet of lead, and a ball of cotton wool at the other, and both were carried to an equal distance from the perpendicular, and then let go; it is not to be doubted, but that both the one and the other would move towards the perpendicular, and that being carried by their own impetus, they would go a certain space beyond it, and afterwards return thither again. But which of these two pendent Globes do you think, would continue longest in motion, before that it would come to rest in its perpendicularity?

Simpl.The ball of lead would swing to and again many times, and that of wool but two or three at the most.

Salv.So that the impetus and that mobility whatsoever is the cause thereof, would conserve its self longer in grave substances, than light; I proceed now to another particular, and demand of you, why the air doth not carry away that Lemon which is upon that same Table?

Simpl.Because that the air it self is not moved

Salv.It is requisite then, that the projicient do confer motion on the Air, with which it afterward moveth the project. But if such a motion cannot be impressed [i. e. imparted] it being impossible to make an accident passe out of one subject into another, how can it passe from the arm into the Air? Will you say that the Air is not a subject different from the arm?

Simpl.To this it is answered that the Air, in regard it is neither heavy nor light in its own Region, is disposed with facility to receive every impulse, and also to retain the same.

Salv.But if those penduli even now named, did prove unto us, that the moveable, the lesse it had of gravity, the lesse apt it was to conserve its motion, how can it be that the Air which in the Air hath no gravity at all, doth of it self alone retain the motion acquired? I believe, and know that you by this time are of the same opinion, that the arm doth not sooner return to rest, than doth the circumambient Air. Let's go into the Chamber, and with a towel let us agitate the Air as much as we can, and then holding the cloth still, let a little candle be brought, that was lighted in the next room, or in the same place let a leaf of beaten Gold be left at liberty to flie any way, and you shall by the calm vagation of them be assured that the Air is immediately reduced to tranquilty. I could alledg many other experiments to the same purpose, but if one of these should not suffice, I should think your folly altogether incurable.

Sagr.When an arrow is shot against the Wind, how incredible a thing is it, that that same small filament of air, impelled by the bow-string, should in despite of fate go along with the arrow? But I would willingly know another particular of Aristotle, to which I intreat Simplicius would vouchsafe me an answer. Supposing that with the same Bow there were shot two arrows, one just after the usual manner, and the other side-wayes, placing it long-wayes upon the Bow-string, and then letting it flie, I would know which of them would go farthest. Favour me, I pray you with an answer, though the question may seem to you rather ridiculous than otherwise; and excuse me, for that I, who am, as you see, rather blockish, than not, can reach no higher with my speculative faculty.

Simpl.I have never seen an arrow shot in that manner, yet neverthelesse I believe, that it would not flie side-long, the twentieth part of the space that it goeth end-wayes.

Sagr.And for that I am of the same opinion, hence it is, that I have a doubt risen in me, whether Aristotle doth not contradict experience. For as to experience, if I lay two arrows upon this Table, in a time when a strong Wind bloweth, one towards the course of the wind, and the other sidelong, the wind will quickly carry away this later, and leave the other where it was; and the same to my seeming, ought to happen, if the Doctrine of Aristotle were true, of those two shot out of a Bow: forasmuch as the arrow shot sideways is driven by a great quantity of Air, moved by the bowstring, to wit by as much as the said string is long, whereas the other arrow receiveth no greater a quantity of air, than the small circle of the strings thickness. And I cannot imagine what may be the reason of such a difference, but would fain know the same.

Simpl.The cause seemeth to me sufficiently manifest; and it is, because the arrow shot endways, hath but a little quantity of air to penetrate, and the other is to make its way through a quantity as great as its whole length.

Salv.Then it seems the arrows shot, are to penetrate the air? but if the air goeth along with them, yea, is that which carrieth them, what penetration can they make therein? Do you not see that, in this case, the arrow would of necessity move with greater velocity than the air? and this greater velocity, what doth confer it on the arrow? Will you say the air giveth them a velocity greater than its own? Know then, Simplicius, that the business proceeds quite contrary to that which Aristotle saith,The medium doth impede and not confer the motion of projects. and that the medium conferreth the motion on the project, is as false, as it is true, that it is the onely thing which procureth its obstruction; and having known this, you shall understand without finding any thing whereof to make question, that if the air be really moved, it doth much better carry the dart along with it longways, than endways, for that the air which impelleth it in that posture, is much, and in this very little. But shooting with the Bow, forasmuch as the air stands still, the transverse arrow, being to force its passage through much air, comes to be much impeded, and the other that was nock't easily overcometh the obstruction of the small quantity of air, which opposeth it self thereto.

Salv.How many Propositions have I observed in Aristotle, (meaning still in Natural Philosophy) that are not onely false, but false in such sort, that its diametrical contrary is true, as it happens in this case. But pursuing the point in hand, I think that Simplicius is perswaded, that, from seeing the stone always to fall in the same place, he cannot conjecture either the motion or stability of the Ship: and if what hath been hitherto spoken, should not suffice, there is the Experiment of the medium which may thorowly assure us thereof; in which experiment, the most that could be seen would be, that the cadent moveable might be left behind, if it were light, and that the air did not follow the motion of the ship: but in case the air should move with equal velocity, no imaginable diversity could be found either in this, or any other experiment whatsoever, as I am anon to tell you. Now if in this case there appeareth no difference at all, what can be pretended to be seen in the stone falling from the top of the Tower, where the motion in gyration is not adventitious, and accidental, but natural and eternal; and where the air exactly followeth the motion of the Tower, and the Tower that of the Terrestrial Globe? have you any thing else to say, Simplicius, upon this particular?

Simpl.No more but this, that I see not the mobility of the Earth as yet proved.

Salv.Nor have I any intention at this time, but onely to shew, that nothing can be concluded from the experiments alledged by our adversaries for convincing Arguments: as I think I shall prove the others to be.

Sagr.I beseech you, Salviatus, before you proceed any farther, to permit me to start certain questions, which have been rouling in my fancy all the while that you with so much patience and equanimity, was minutely explaining to Simplicius the experiment of the Ship.

Salv.We are here met with a purpose to dispute, and it's fit that every one should move the difficulties that he mets withall; for this is the way to come to the knowledg of the truth. Therefore speak freely.

Sagr.If it be true, that the impetus wherewith the ship moves, doth remain indelibly impress'd in the stone, after it is let fall from the Mast; and if it be farther true, that this motion brings no impediment or retardment to the motion directly downwards, natural to the stone:An admirable accident in the motion of projects. it's necessary, that there do an effect ensue of a very wonderful nature. Let a Ship be supposed to stand still, and let the time of the falling of a stone from the Masts Round-top to the ground, be two beats of the pulse; let the Ship afterwards be under sail, and let the same stone depart from the same place, and it, according to what hath been premised, shall still take up the time of two pulses in its fall, in which time the ship will have run, suppose, twenty yards; so that the true motion of the stone will be a transverse line, considerably longer than the first straight and perpendicular line, which is the length of the ** By the length of the mast he means the distance between the upper-deck and Round-top. Mast, and yet nevertheless the ** La palla. stone will have past it in the same time. Let it be farther supposed, that the Ships motion is much more accelerated, so that the stone in falling shall be to pass a transverse line much longer than the other; and in sum, increasing the Ships velocity as much as you will, the falling stone shall describe its transverse lines still longer and longer, and yet shall pass them all in those self same two pulses. And in this fashion, if a Canon were level'd on the top of a Tower, and shots were made therewith point blank, that is, paralel to the Horizon, let the Piece have a greater or less charge, so as that the ball may fall sometimes a thousand yards distant, sometimes four thousand, sometimes six, sometimes ten, &c. and all these shots shall curry or finish their ranges in times equal to each other, and every one equal to the time which the ball would take to pass from the mouth of the Piece to the ground, being left, without other impulse, to fall simply downwards in a perpendicular line. Now it seems a very admirable thing, that in the same short time of its falling perpendicularly down to the ground, from the height of, suppose, an hundred yards, the same ball, being thrust violently out of the Piece by the Fire, should be able to pass one while four hundred, another while a thousand, another while four, another while ten thousand yards, so as that the said ball in all shots made point blank, always continueth an equal time in the air.

Salv.The consideration for its novelty is very pretty, and if the effect be true, very admirable: and of the truth thereof, I make no question: and were it not for the accidental impediment of the air, I verily believe, that, if at the time of the balls going out of the Piece, another were let fall from the same height directly downwards, they would both come to the ground at the same instant, though that should have curried ten thousand miles in its range, and this but an hundred onely: presupposing the surface of the Earth to be equal, which to be assured of, the experiment may be made upon some lake. As for the impediment which might come from the air, it would consist in retarding the extreme swift motion of the shot. Now, if you think fit, we will proceed to the solution of the other Objections, seeing that Simplicius (as far as I can see) is convinc'd of the nullity of this first, taken from things falling from on high downwards.

Simpl.I find not all my scruples removed, but it may be the fault is my own, as not being of so easie and quick an apprehension as Sagredus. And it seems to me, that if this motion, of which the stone did partake whilst it was on the Round-top of the Ships Mast, be, as you say, to conserve it self indelibly in the said stone, even after it is separated from the Ship, it would follow, that likewise in case any one, riding a horse that was upon his speed, should let a bowl drop out of his hand, that bowl being fallen to the ground would continue its motion and follow the horses steps, without tarrying behind him: the which effect, I believe, is not to be seen, unless when he that is upon the horse should throw it with violence that way towards which he runneth; but otherwise, I believe it will stay on the ground in the same place where it fell.

Salv.I believe that you very much deceive your self, and am certain, that experience will shew you the contrary, and that the ball being once arrived at the ground, will run together with the horse, not staying behind him, unless so far as the asperity and unevenness of the Earth shall hinder it. And the reason seems to me very manifest: for if you, standing still, throw the said ball along the ground, do you think it would not continue its motion even after you had delivered it out of your hand? and that for so much a greater space, by how much the superficies were more smooth, so that v. g. upon ice it would run a great way?

Simpl.There is no doubt of it, if I give it impetus with my arm; but in the other case it is supposed, that he who is upon the horse, onely drops it out of his hand.

Salv.So I desire that it should be: but when you throw it with your arm, what other remaineth to the ball being once gone out of your hand, than the motion received from your arm, which motion being conserved in the boul, it doth continue to carry it forward? Now, what doth it import, that that impetus be conferred on the ball rather from the arm than from the horse? Whilst you were on horseback, did not your hand, and consequently the ball run as fast as the horse it self? Doubtless it did: therefore in onely opening of the hand, the ball departs with the motion already coceived, not from your arm, by your particular motion, but from the motion dependant on the said horse, which cometh to be communicated to you, to your arm, to your hand, and lastly to the ball. Nay, I will tell you farther, that if the rider upon his speed fling the ball with his arm to the part contrary to the course, it shall, after it is fallen to the ground, sometimes (albeit thrown to the contrary part) follow the course of the horse, and sometimes lie still on the ground; and shall onely move contrary to the said course, when the motion received from the arm, shall exceed that of the carrier in velocity. And it is a vanity, that of some, who say that a horseman is able to cast a javelin thorow the air, that way which the horse runs, and with the horse to follow and overtake the same; and lastly, to catch it again. It is, I say, a vanity, for that to make the project return into the hand, it is requisite to cast it upwards, in the same manner as if you stood still. For, let the carrier be never so swift, provided it be uniform, and the project not over-light, it shall always fall back again into the hand of the projicient, though never so high thrown.

Sagr.By this Doctrine I come to know some Problems very curious upon this subject of projections;Sundry curious Problems, touching the motions of projects. the first of which must seem very strange to Simplicius. And the Problem is this; I affirm it to be possible, that the ball being barely dropt or let fall, by one that any way runneth very swiftly, being arrived at the Earth, doth not onely follow the course of that person, but doth much out go him. Which Problem is connexed with this, that the moveable being thrown by the projicient above the plane of the Horizon, may acquire new velocity, greater by far than that confer'd upon it by the projicient. The which effect I have with admiration observed, in looking upon those who use the sport of tops, which, so soon as they are set out of the hand, are seen to move in the air with a certain velocity, the which they afterwards much encrease at their coming to the ground; and if whipping them, they rub at any uneven place that makes them skip on high, they are seen to move very slowly through the air, and falling again to the Earth, they still come to move with a greater velocity: But that which is yet more strange, I have farther observed, that they not onely turn always more swiftly on the ground, than in the air, but of two spaces both upon the Earth, sometimes a motion in the second space is more swift than in the first. Now what would Simplicius say to this?

Simpl.He would say in the first place, that he had never made such an observation. Secondly, he would say, that he did not believe the same. He would say again, in the third place, that if you could assure him thereof, and demonstratively convince him of the same, he would account you a great Dæmon.

Sagr.I hope then that it is one of the Socratick, not infernal ones. But that I may make you understand this particular, you must know, that if a person apprehend not a truth of himself, it is impossible that others should make him understand it: I may indeed instruct you in those things which are neither true nor false; but the true, that is, the necessary, namely, such as it is impossible should be otherwise, every common capacity either comprehendeth them of himself, or else it is impossible he should ever know them. And of this opinion I am confident is Salviatus also: and therefore I tell you, that the reasons of the present Problems are known by you, but it may be, not apprehended.

Simpl.Let us, for the present, pass by that controversie, and permit me to plead ignorance of these things you speak of, and try whether you can make me capable of understanding these Problems.

Sagr.This first dependeth upon another, which is, Whence cometh it, that setting a top with the lash, it runneth farther, and consequently with greater force, than when its set with the fingers?

Simpl.Aristotle also makes certain Problems about these kinds of projects.

Salv.He doth so; and very ingenious they are: particularly, That, Whence it cometh to pass that round tops run better than the square?

Sagr.And cannot you, Simplicius, give a reason for this, without others prompting you?

Simpl.Very good, I can so; but leave your jeering.

Sagr.In like manner you do know the reason of this other also. Tell me therefore; know you that a thing which moveth, being impeded stands still?

Simpl.I know it doth, if the impediment be so great as to suffice.

Sagr.Do you know, that moving upon the Earth is a greater impediment to the moveable, than moving in the air, the Earth being rough and hard, and the air soft and yielding?

Simpl.And knowing this, I know that the top will turn faster in the air, than on the ground, so that my knowledg is quite contrary to what you think it.

Sagr.Fair and softly, Simplicius. You know that in the parts of a moveable, that turneth about its centre, there are found motions towards all sides; so that some ascend, others descend; some go forwards, others backwards?

Simpl.I know it, and Aristotle taught me the same.

Sagr.And with what demonstration, I pray you?

Simpl.With that of sense.

Sagr.Aristotle, then, hath made you see that which without him you would not have seen? Did he ever lend you his eyes? You would say, that Aristotle hath told, advertised, remembered you of the same; and not taught you it. When then a top, without changing place, turns round, (or in the childrens phrase, sleepeth) not paralel, but erect to the Horizon, some of its parts ascend, and the opposite descend; the superiour go one way, the inferiour another. Fancie now to your self, a top, that without changing place, swiftly turns round in that manner, and stands suspended in the air, and that in that manner turning, it be let fall to the Earth perpendicularly, do you believe, that when it is arrived at the ground, it will continue to turn round in the same manner, without changing place, as before?

Simpl.No, Sir.

Sagr.What will it do then?

Simpl.It will run along the ground very fast.

Sagr.And towards what part?

Simpl.Towards that, whither its ** Vertigine. reeling carrieth it.

Sagr.In its reeling there are parts, that is the uppermost, which do move contrary to the inferiour; therefore you must instance which it shall obey: for as to the parts ascending and descending, the one kind will not yield to the other; nor will they all go downwards, being hindered by the Earth, nor upwards as being heavy.

Simpl.The top will run reeling along the floor towards that part whither its upper parts encline it.

Sagr.And why not whither the contrary parts tend, namely, those which touch the ground?

Simpl.Because those upon the ground happen to be impeded by the roughness of the touch, that is, by the floors unevenness; but the superiour, which are in the tenuous and flexible air, are hindred very little, if at all; and therefore the top will obey their inclination.

Sagr.So that that taction, if I may so say, of the neither parts on the floor, is the cause that they stay, and onely the upper parts spring the top forward.

Salv.And therefore, if the top should fall upon the ice, or other very smooth superficies, it would not so well run forward, but might peradventure continue to revolve in it self, (or sleep) without acquiring any progressive motion.

Sagr.It is an easie thing for it so to do; but yet nevertheless, it would not so speedily come to sleep, as when it falleth on a superficies somewhat rugged. But tell me, Simplicius, when the top-turning round about it self, in that manner, is let fall, why doth it not move forwards in the air, as it doth afterwards when it is upon the ground?

Simpl.Because having air above it, and beneath, neither those parts, nor these have any where to touch, and not having more occasion to go forward than backward, it falls perpendicularly.

Sagr.So then the onely reeling about its self, without other impetus, can drive the top forward, being arrived at the ground, very nimbly. Now proceed we to what remains. That lash, which the driver tyeth to his Top-stick, and with which, winding it about the top, he sets it (i. e. makes it go) what effect hath it on the said top?

Simpl.It constrains it to turn round upon its toe, that so it may free it self from the Top-lash.

Sagr.So then, when the top arriveth at the ground, it cometh all the way turning about its self, by means of the lash. Hath it not reason then to move in it self more swiftly upon the ground, than it did whilst it was in the air?

Simpl.Yes doubtless; for in the air it had no other impulse than that of the arm of the projicient; and if it had also the reeling, this (as hath been said) in the air drives it not forward at all▪ but arriving at the floor, to the motion of the arm is added the progression of the reeling, whereby the velocity is redoubled. And I know already very well, that the top skipping from the ground, its velocity will deminish, because the help of its circulation is wanting; and returning to the Earth will get it again, and by that means move again faster, than in the air. It onely rests for me to understand, whether in this second motion on the Earth it move more swiftly, than in the first; for then it would move in infinitum, alwayes accelerating.

Sagr.I did not absolutely affirm, that this second motion is more swift than the first; but that it may happen so to be sometimes.

Simpl.This is that, which I apprehend not, and which I desire to know.

Sagr.And this also you know of your self. Therefore tell me: When you let the top fall out of your hand, without making it turn round (i. e. setting it) what will it do at its coming to the ground?

Simpl.Nothing, but there lie still.

Sagr.May it not chance, that in its fall to the ground it may acquire a motion? Think better on it.

Simpl.Unlesse we let it fall upon some inclining stone, as children do playing at ** A Game in Italy, which is, to glide bullets down an inclining stone, &c. Chiosa, and that falling side-wayes upon the same, it do acquire the motion of turning round upon its toe, wherewith it afterwards continueth to move progressively on the floor, I know not in what other manner it can do any thing but lie still where it falleth.

Sagr.You see then that in some case it may acquire a new revolution. When then the top jerked up from the ground, falleth down again, why may it not casually hit upon the declivity of some stone fixed in the floor, and that hath an inclination that way towards which it moveth, and acquiring by that slip a new whirle over and above that conferred by the lash, why may it not redouble its motion, and make it swifter than it was at its first lighting upon the ground?

Simpl.Now I see that the same may easily happen. And I am thinking that if the top should turn the contrary way, in arriving at the ground, it would work a contrary effect, that is, the motion of the accidental whirl would retard that of the projicient.

Sagr.And it would sometimes wholly retard and stop it, in case the revolution of the top were very swift. And from hence ariseth the resolution of that slight, which the more skilful Tennis Players use to their advantage; that is, to gull their adversary by cutting (for so is their Phrase) the Ball; which is, to return it with a side Rachet, in such a manner, that it doth thereby acquire a motion by it self contrary to the projected motion, and so by that means, at its coming to the ground, the rebound, which if the ball did not turn in that manner, would be towards the adversary, giving him the usual time to tosse it back again, doth fail, and the ball runs tripping along the ground, or rebounds lesse than usual, and breaketh the time of the return. Hence it is that you see, those who play at **A Game in Italy, wherein they strive who shall trundle or throw a wooden bowle neerest to an assigned mark. Stool-ball, when they play in a stony way, or a place full of holes and rubs that make the ball trip an hundred several wayes, never suffering it to come neer the mark, to avoid them all, they do not trundle the ball upon the ground, but throw it, as if they were to pitch a quait. But because in throwing the ball, it issueth out of the hand with some roling conferred by the fingers, when ever the hand is under the ball, as it is most commonly held; whereupon the ball in its lighting on the ground neer to the mark, between the motion of the projicient and that of the roling, would run a great way from the same: To make the ball stay, they hold it artificially, with their hand uppermost, and it undermost, which in its delivery hath a contrary twirl or roling conferred upon it by the fingers, by means whereof in its coming to the ground neer the mark it stays there, or runs very very little forwards. But to return to our principal problem which gave occasion for starting these others; I say it is possible that a person carried very swiftly, may let a ball drop out of his hand, that being come to the Earth, shall not onely follow his motion, but also out-go it, moving with a greater velocity. And to see such an effect, I desire that the course may be that of a Chariot, to which on the out-side let a declining board be fastened; so as that the neither part may be towards the horses, and the upper towards the hind Wheel. Now, if in the Chariots full career, a man within it, let a ball fall gliding along the declivity of that board, it shall in roling downward acquire a particular vertigo or turning, the which added to the motion impressed by the Chariot, will carrie the ball along the ground much faster than the Chariot. And if one accommodate another declining board over against it, the motion of the Chariot may be qualified so, that the ball, gliding downwards along the board, in its coming to the ground shall rest immoveable, and also shall sometimes run the contrary way to the Chariot. But we are strayed too far from the purpose, therefore if Simplicius be satisfied with the resolution of the first argnment against the Earths mobility, taken from things falling perpendicularly, we may passe to the rest.

Salv.The digressions made hitherto, are not so alienated from the matter in hand, as that one can say they are wholly strangers to it. Besides these argumentations depend on those things that start up in the fancy not of one person, but of three, that we are: And moreover we discourse for our pleasure, nor are we obliged to that strictnesse of one who ex professo treateth methodically of an argument, with an intent to publish the same. I will not consent that our Poem should be so confined to that unity, as not to leave us fields open for Epsody's, which every smalll connection should suffice to introduce; but with almost as much liberry as if we were met to tell stories, it shall be lawful for me to speak, what ever your discourse brings into my mind.

Sagr.I like this motion very well; and since we are at this liberty, let me take leave, before we passe any farther to ask of you Salviatus, whether you did ever consider what that line may be that is described by the grave moveable naturally falling down from the top of a Tower; and if you have reflected on it, be pleased to tell me what you think thereof.

Salv.I have sometimes considered of it, and make no question, that if one could be certain of the nature of that motion wherewith the grave body descendeth to approach the centre of the Terrestrial Globe, mixing it self afterwards with the common circular motion of the diurnal conversion; it might be exactly found what kind of line that is, that the centre of gravity of the moveable describeth in those two motions.

Sagr.Touching the simple motion towards the centre dependent on the gravity, I think that one may confidently, without error, believe that it is by a right line, as it would be, were the Earth immoveable.

Salv.As to this particular, we may not onely believe it, but experience rendereth us certain of the same.

Sagr.But how doth experience assure us thereof, if we never see any motions but such as are composed of the two, circular and descending.

Salv.Nay rather Sagredus we onely see the simple motion of descent; since that other circular one common to the Earth, the Tower and our selves remains imperceptible, and as if it never were, and there remaineth perceptible to us that of the stone, onely not participated by us, and for this, sense demonstrateth that it is by a right line, ever parallel to the said Tower, which is built upright and perpendicular upon the Terrestrial surface.

Sagr.You are in the right; and this was but too plainly demonstrated to me even now, seeing that I could not remember so easie a thing; but this being so manifest, what more is it that you say you desire, for understanding the nature of this motion downwards?

Salv.It sufficeth not to know that it is streight, but its requisite to know whether it be uniform, or irregular; that is, whether it maintain alwayes one and the same velocity, or else goeth retarding or accelerating.

Sagr.It is already clear, that it goeth continually accellerating.

Salv.Neither doth this suffice, but its requisite to know according to what proportion such accelleration is made; a Problem, that I believe was never hitherto understood by any Philosopher or Mathematician; although Philosophers, and particularly the Peripateticks, have writ great and entire Volumes, touching motion.

Simpl.Philosophers principally busie themselves about universals; they find the definitions and more common symptomes, omitting certain subtilties and niceties, which are rather curiosities to the Mathematicians. And Aristotle did content himself to define excellently what motion was in general; and of the local, to shew the principal qualities, to wit, that one is natural, another violent; one is simple, another compound; one is equal, another accellerate; and concerning the accelerate, contents himself to give the reason of acceleration, remitting the finding out of the proportion of such acceleration, and other particular accidents to the Mechanitian, or other inferiour Artist.

Sagr.Very well Simplicius. But you Salviatus, when you descend sometimes from the Throne of Peripatetick Majesty, have you ever thrown away any of your hours in studying to find this proportion of the acceleration of the motion of descending grave bodies?

Salv.There was no need that I should study for it, in regard that the Academick our common friend, heretofore shewed me a Treatise of hisThis is that excellent tract which we give the first place in our second Volume.De Motu, where this, and many other accidents were demonstrated. But it would be too great a digression, if for this particular, we should interrupt our present discourse, (which yet it self is also no better than a digression) and make as the Saying is, a Comedy within a Comedy.

Sagr.I am content to excuse you from this narration for the present, provided that this may be one of the Propositions reserved to be examined amongst the rest in another particular meeting, for that the knowledg thereof is by me very much desired; and in the mean time let us return to the line described by the grave body in its fall from the top of the Tower to its base.

Salv.If the right motion towards the centre of the Earth was uniforme, the circular towards the East being also uniforme, you would see composed of them both a motion by a spiral line, of that kind with those defined by Archimedes in his Book De Spiralibus; which are, when a point moveth uniformly upon a right line, whilest that line in the mean time turneth uniformly about one of its extreme points fixed, as the centre of his gyration. But because the right motion of grave bodies falling, is continually accelerated, it is necessary, that the line resulting of the composition of the two motions do go alwayes receding with greater and greater proportion from the circumference of that circle, which the centre of the stones gravity would have designed, if it had alwayes staid upon the Tower; it followeth of necessity that this recession at the first be but little, yea very small, yea, more, as small as can be imagined, seeing that the descending grave body departing from rest, that is, from the privation of motion, towards the bottom and entring into the right motion downwards, it must needs passe through all the degrees of tardity, that are betwixt rest, and any assigned velocity; the which degrees are infinite; as already hath been at large discoursed and proved.

It being supposed therefore, that the progresse of the acceleration being after this manner, and it being moreover true, that the descending grave body goeth to terminate in the centre of the Earth,The line described by a moveable in its natural descent, the motion of the Earth about its own centre being presupposed, would probably be the circumference of a circle. it is necessary that the line of its mixt motion be such, that it go continually receding with greater and greater proportion from the top of the Tower, or to speak more properly, from the circumference of the circle described by the top of the Tower, by means of the Earths conversion; but that such recessions be lesser and lesser in infinitum; by how much the moveable finds it self to be lesse and lesse removed from the first term where it rested. Moreover it is necessary, that this line of the compounded motion do go to terminate in the centre of the Earth. Now having presupposed these two things, I come to describe about the centre A [in Fig. 1. of this second Dialogue;] with the semidiameter A B, the circle B I, representing to me the Terrestrial Globe, and prolonging the semidiameter A B to C, I have described the height of the Tower B C; the which being carried about by the Earth along the circumference B I, describeth with its top the arch C D: Dividing, in the next place, the line C A in the middle at E; upon the centre E, at the distance E C, I describe the semicircle C I A: In which, I now affirm, that it is very probable that a stone falling from the top of the Tower C, doth move, with a motion mixt of the circular, which is in common, and of its peculiar right motion. If therefore in the circumference C D, certain equal parts C F, F G, G H, H L, be marked, and from the points F, G, H, L, right lines be drawn towards the centre A, the parts of them intercepted between the two circumferences C D and B I, shall represent unto us the same Tower C B, transported by the Terrestrial Globe towards D I; in which lines the points where they come to be intersected by the arch of the semicircle C I, are the places by which from time to time the falling stone doth passe; which points go continually with greater and greater proportion receding from the top of the Tower. And this is the cause why the right motion made along the side of the Tower apeareth to us more and more accelerate. It appeareth also, how by reason of the infinite acutenesse of the contact of those two circles D C, C I, the recession of the cadent moveable from the circumference C F D; namely, from the top of the Tower, is towards the beginning extream small, which is as much as if one said its motion downwards is very slow, and more and more slow in infinitum, according to its vicinity to the term C, that is to the state of rest. And lastly it is seen how in the end this same motion goeth to terminate in the centre of the Earth A.

Sagr.I understand all this very well, nor can I perswade my self that the falling moveable doth describe with the centre of its gravity any other line, but such an one as this.

Salv.But stay a little Sagredus, for I am to acquaint you also with three Observations of mine, that its possible will not displease you.A moveable falling from the top of the Tower, moveth in the circumference of a circle. The first of which is, that if we do well consider, the moveable moveth not really with any more than onely one motion simply circular, as when being placed upon the Tower, it moved with one single and circular motion. The second is yet more pleasant; for,It moveth neither more nor lesse, than if it had staid alwayes there. it moveth neither more nor lesse then if it had staid continually upon the Tower, being that to the arches C F, F G, G H, &c. that it would have passed continuing alwayes upon the Tower, the arches of the circumference C I are exactly equal, answering under the same C F, F G, G H, &c. Whence followeth the third wonder,It moveth with an uniform, not an accelerate motion. That the true and real motion of the stone is never accelerated, but alwayes even and uniforme, since that all the equal arches noted in the circumference C D, and their respondent ones marked in the circumference C I, are past in equal times; so that we are left at liberty to seek new causes of acceleration, or of other motions, seeing that the moveable, as well standing upon the Tower, as descending thence, alwayes moveth in the same fashion, that is, circularly, with the same velocity, and with the same uniformity. Now tell me what you think of this my fantastical conjecture.

Sagr.I must tell you, that I cannot with words sufficiently expresse how admirable it seemeth to me; and for what at present offereth it self to my understanding, I cannot think that the business happeneth otherwise; and would to God that all the demonstrations of Philosophers were but half so probable as this. However for my perfect satisfaction I would gladly hear how you prove those arches to be equal.

Salv.The demonstration is most easie. Suppose to your self a line drawn from I to E. And the Semidiameter of the circle C D, that is, the line C A, being double the Semidiameter C E of the circle C I, the circumference shall be double to the circumference, and every arch of the greater circle double to every like arch of the lesser; and consequently, the half of the arch of the greater circle, equal to the whole arch of the lesse. And because the angle C E I made in the centre E of the lesser circle, and which insisteth upon the arch CI, is double the angle C A D, made in the centre A of the greater circle, to which the arch C D subtendeth; therefore the arch C D is half of the arch of the greater circle like to the arch C I, and therefore the two arches C D and C I are equal; and in the same manner we may demonstrate of all their parts. But that the business, as to the motion of descending grave bodies, proceedeth exactly thus, I will not at this time affirm; but this I will say, that if the line described by the cadent moveable be not exactly the same with this, it doth extream neerly resemble the same.

Sagr.But I,Right motion seemeth wholly excluded in nature.Salviatus, am just now considering another particular very admirable; and this it is; That admitting these considerations, the right motion doth go wholly ** Vadia del tutto a monte, rendered in the Latine omnino pessum eat. mounting, and that Nature never makes use thereof, since that, even that that use, which was from the beginning granted to it, which was of reducing the parts of integral bodies to their place, when they were separated from their whole, and therefore constituted in a depraved disposition, is taken from it, and assigned to the circular motion.

Salv.This would necessarily follow, if it were concluded that the Terrestrial Globe moveth circularly; a thing, which I pretend not to be done, but have onely hitherto attempted, as I shall still, to examine the strength of those reasons, which have been alledged by Philosophers to prove the immobility of the Earth, of which this first taken from things falling perpendicularly, hath begat the doubts, that have been mentioned; which I know not of what force they may have seemed to Simplicius; and therefore before I passe to the examination of the remaining arguments, it would be convenient that he produce what he hath to reply to the contrary.

Simpl.As to this first, I confesse indeed that I have heard sundry pretty notions, which I never thought upon before, and in regard they are new unto me, I cannot have answers so ready for them, but this argument taken from things falling perpendicularly, I esteem it not one of the strongest proofs of the mobility of the Earth; and I know not what may happen touching the shots of great Guns, especially those aimed contrary to the diurnal motion.

Sagr.The flying of the birds as much puzzleth me as the objection of the Gun-shot, and all the other experiments above alledged. For these birds which at their pleasure flie forwards and backwards, and wind to and again in a thousand fashions, and, which more importeth, lie whole hours upon the wing, these I say do not a little pose me, nor do I see, how amongst so many circumgyrations, they should not lose the motion of the Earth, and how they should be able to keep pace with so great a velocity as that which they so far exceed with their flight.

Salv.To speak the truth, your scruple is not without reason, and its possible Copernicus himself could not find an answer for it, that was to himself entirely satisfactory; and therefore haply past it over in silence; albeit he was, indeed, very brief in examining the other allegations of his adversaries, I believe through his height of wit, placed on greater aud sublimer contemplations, like as Lions are not much moved at the barking of little Dogs. We will therefore reserve the instance of birds to the last place, and for the present, see if we can give Simplicius satisfaction in the others, by shewing him in our wonted manner, that he himself hath their answers at hand, though upon first thoughts he doth not discover them. And to begin with the shots made at randome, with the self same piece, powder, and ball, the one towards the East, the other towards the West (if the diurnal conversion belonged to the Earth) ought to be much longer than that towards the East.

Simpl.I am moved so to think; because in the shot made towards the East,The reason why a Gun should seem to carry farther towards the West than towards the East. the ball whil'st it is out of the piece, is followed by the said piece, the which being carried round by the Earth, runneth also with much velocity towards the same part, whereupon the fall of the ball to the ground, cometh to be but little distant from the piece. On the contrary in the shot towards the West, before that the ball falleth to the ground, the piece is retired very far towards the East, by which means the space between the ball and the piece, that is Range, will appear longer than the other, by how much the piece, that is the Earth, had run in the time that both the bals were in the air.

Salv.I could wish, that we did know some way to make an experiment corresponding to the motion of these projects, as that of the ship doth to the motion of things perpendicularly falling from on high; and I am thinking how it may be done.

Sagr.I believe, that it would be a very opposite proof, to take an open Chariot,The experiment of a running chariot to find out the difference of Ranges. and to accomodate therein a ** Balestrone da bolzoni. Stock-bow at half elevation, to the end the flight may prove the greatest that my be, and whil'st the horses shall run, to shoot first towards the part whither you drive, and then another backwards towards the contrary part, causing some one to mark diligently where the Chariot was in that moment f time when the shaft came to the ground, as well in the one shot as in the other: for thus you may see exactly how much one shaft flew farther than the other.

Simpl.In my thoughts this experiment is very proper: and I do not doubt but that the flight, that is, the space between the shaft and the place where the chariot was at the shafts fall, will be less by much when one shooteth towards the chariots course, than when one shooteth the contrary way. For an example, let the flight of it self be three hundred yards, and the course of the chariot in the time whilst the shaft stayeth in the air, an hundred yards, therefore shooting towards the course, of the three hundred yards of the flight, the chariot will have gone one hundred; so then at the shafts coming to the ground, the space between it and the chariot, shall be but two hundred yards onely; but on the contrary, in the other shoot, the chariot running contrary to the shaft, when the shaft shall have passed its three hundred yards, and the chariot its other hundred the contrary way, the distance interposing shall be found to be four hundred yards.

Salv.Is there any way to shoot so that these flights may be equal?

Simpl.I know no other way, unless by making the chariot to stand still.

Salv.This we know; but I mean when the chariot runneth in full carreer.

Simpl.In that case you are to draw the Bow higher in shooting forwards, and to slack it in shooting the contrary way.

Salv.Then you see that there is one way more. But how much is the bow to be drawn, and how much slackened?

Simpl.In our case, where we have supposed that the bow carried three hundred yards, it would be requisite to draw it so, as that it might carry four hundred, and in the other to slacken it so, as that it might carry no more than two hundred. For so each of the flights would be but three hundred in relation to the chariot, the which, with its course of an hundred yards which it substracts from the shoot of four hundred, and addeth to that of two hundred, would reduce them both to three hundred.

Salv.But what effect hath the greater or less intensness of the bow upon the shaft?

Simpl.The stiffer bow carrieth it with greater velocity, and the weaker with less; and the same shaft flieth so much farther at one time than another, with how much greater velocity it goeth out of the tiller at one time, than another.

Salv.So that to make the shaft shot either way, to flie at equal distance from the running chariot, it is requisite, that if in the first shoot of the precedent example, it goeth out of the tiller with v. g. four degrees of velocity, that then in the other shoot it depart but with two onely: but if the same bow be used, it always receiveth thence three degrees.

Simpl.It doth so; and for this reason, shooting with the same bow in the chariots course, the shoots cannot be equal.

Salv.I had forgot to ask, with what velocity it is supposed in this particular experiment, that the chariot runneth.

Simpl.The velocity of the chariot must be supposed to be one degree in comparison to that of the bow, which is three,

Salv.Very right, for so computation gives it. But tell me, when the chariot moveth, doth not all things in the same move with the same velocity?

Simpl.Yes doubtless.

Salv.Then so doth the shaft also, and the bow, and the string, upon which the shaft is nock't.

Simpl.They do so.

Salv.Why then, in discharging the shaft towards the course of the chariot, the bow impresseth its three degrees of velocity on a shaft that had one degree of velocity before, by means of the chariot which transported it so fast towards that part; so that in its going off it hath four degrees of velocity. On the contrary, in the other shoot, the same bow conferreth its same three degrees of velocity on a shaft that moveth the contrary way, with one degree; so that in its departing from the bow-string, it hath no more left but onely two degrees of velocity. But you your self have already said, that the way to make the shoots equal, is to cause that the shaft be let flie the first time with four degrees of velocity, and the second time with two. Therefore without changing the bow, the very course of the chariot is that which adjusteth the flights,The solution of the argument taken from great Guns shot towards the East & West. and the experiment doth so represent them to any one who is not either wilfully or naturally incapable of reason. Now apply this discourse to Gunnery, and you shall find, that whether the Earth move or stand still, the shots made with the same force, will always curry equal ranges, to what part soever aimed. The error of Aristotle, Ptolomey, Tycho, your self, and all the rest, is grounded upon that fixed and strong persuasion, that the Earth standeth still, which you have not judgment nor power to depose, no not when you have a desire to argue of that which would ensue, presupposing the Earth to move. And thus, in the other argument, not considering that whil'st the stone is upon the Tower, it doth, as to moving or not moving, the same that the Terrestrial Globe doth, because you have concluded with your self, that the Earth stands still, you always discourse touching the fall of the stone, as if it were to depart from rest: whereas it behooveth to say, that if the Earth standeth still, the stone departeth from rest, and descendeth perpendicularly; but if the Earth do move, the stone likewise moveth with like velocity, nor doth it depart from rest, but from a motion equal to that of the Earth, wherewith it intermixeth the supervenient motion of descent, and of those two composeth a third which is transversal or side-ways.

Simpl.But for Gods sake, if it move transversly, how is it that I behold it to move directly and perpendicularly? This is no better than the denial of manifest sense; and if we may not believe sense, at what other door shall we enter into disquisitions of Philosophy?

Salv.In respect to the Earth, to the Tower, and to our selves, which all as one piece move with the diurnal motion together with the stone, the diurnal motion is as if it never had been, and becometh insensible, imperceptible, and without any action at all; and the onely motion which we can perceive, is that of which we partake not, that is the descent gliding along the side of the Tower: You are not the first that hath felt great repugnance in apprehending this non-operating of motion upon things to which it is common.

Sagr.Now I do remember a certain conceipt,A notable case of Sagredus, to shew the non-operating of common motion. that came one day into my fancy, whilst I sailed in my voyage to Aleppo, whither I went Consul for our Countrey, and possibly it may be of some use, for explaining this nullity of operation of common motion, and being as if it never were to all the partakers thereof. And if it stand with the good liking of Simplicius, I will reason with him upon that which then I thought of by my self alone.

Simpl.The novelty of the things which I hear, makes me not so much a patient, as a greedy and curious auditor: therefore go on.

Sagr.If the neb of a writing pen, that I carried along with me in the ship, through all my navigation from Venice to ** Alessandretta Scanderon, had had a facultie of leaving visible marks of its whole voyage, what signs, what marks, what lines would it have left?

Simpl.It would have left a line distended from Venice thither, not perfectly streight, or to say better, distended in a perfect arch of a circle, but in some places more, in some less curved, according as the vessel had gone more or less fluctuating; but this its inflecting in some places a fathom or two to the right hand or to the left, upwards or downwards, in a length of many hundred miles, would have brought but little alteration to the intire tract of the line, so that it would have been hardly sensible; and without any considerable error, might have been called the part of a perfect arch.

Sagr.So that the true and most exact motion of the neb of my pen would have also been an arch of a perfect circle, if the vessels motion, the fluctuation of the billows ceasing, had been calm and tranquill. And if I had continually held that per in my hand, and had onely moved it sometimes an inch or two this way or that way, what alteration should I have made in that its principal, and very long tract or stroke?

Simpl.Less than that which the declining in several places from absolute rectitude, but the quantity of a flea's eye makes in a right line of a thousand yards long.

Sagr.If a Painter, then, at our launching from the Port, had began to design upon a paper with that pen, and continued his work till he came to Scanderon, he would have been able to have taken by its motion a perfect draught of all those figures perfectly interwoven and shadowed on several sides with countreys, buildings, living creatures, and other things; albeit all the true, real, and essential motion traced out by the neb of that pen, would have been no other than a very long, but simple line: and as to the proper operation of the Painter, he would have delineated the same to an hair, if the ship had stood still. That therefore of the huge long motion of the pen there doth remain no other marks, than those tracks drawn upon the paper, the reason thereof is because the grand motion from Venice to Scanderon, was common to the paper, the pen, and all that which was in the ship: but the petty motions forwards and backwards, to the right, to the left, communicated by the fingers of the Painter unto the pen, and not to the paper, as being peculiar thereunto, might leave marks of it self upon the paper, which did not move with that motion. Thus it is likewise true, that the Earth moving, the motion of the stone in descending downwards, was really a long tract of many hundreds and thousands of yards, and if it could have been able to have delineated in a calm air, or other superficies, the track of its course, it would have left behind an huge long transverse line. But that part of all this motion which is common to the stone, the Tower, and our selves, is imperceptible to us, and as if it had never been, and that part onely remaineth observable, of which neither the Tower nor we are partakers, which is in fine, that wherewith the stone falling measureth the Tower.

Salv.A most witty conceipt to clear up this point, which was not a little difficult to many capacities. Now if Simplicius will make no farther reply, we may pass to the other experiments, the unfolding of which will receive no small facility from the things already declared.

Simpl.I have nothing more to say: and I was well-nigh transported with that delineation, and with thinking how those strokes drawn so many ways, hither, thither, upwards, downwards, forwards, backwards, and interwoven with thousands of turnings, are not essentially or really other, than small pieces of one sole line drawn all one way, and the same without any other alteration save the declining the direct rectitude, sometimes a very insensible matter towards one side or another, and the pens moving its neb one while softer, another while slower, but with very small inequality. And I think that it would in the same manner write a letter, and that those frollike penmen, who to shew their command of hand, without taking their pen from the paper in one sole stroke, with infinite turnings draw a pleasant knot, if they were in a boat that did tide it along swiftly they would convert the whole motion of the pen, which in reality is but one sole line, drawn all towards one and the same part, and very little curved, or declining from perfect rectitude, into a knot or flourish. And I am much pleased that Sagredus hath helped me to this conceit: therefore let us go on, for the hope of meeting with more of them, will make me the stricter in my attention.

Sagr.If you have a curiosity to hear such like subtilties,Subtilties sufficiently insipid, ironically, spoken and taken from a certain Encyclopædia. which occurr not thus to every one, you will find no want of them, especially in this particular of Navigation; and do you not think that a witty conceit which I met with likewise in the same voyage, when I observed that the mast of the ship, without either breaking or bending, had made a greater voyage with its round-top, that is with its top-gallant, than with its foot; for the round top being more distant from the centre of the Earth than the foot is, it had described the arch of a circle bigger than the circle by which the foot had passed.

Simpl.And thus when a man walketh he goeth farther with his head than with his feet.

Sagr.You have found out the matter your self by help of your own mother-wit: But let us not interrupt Salviatus.

Salv.It pleaseth me to see Simplicius how he sootheth up himself in this conceit, if happly it be his own, and that he hath not borrowed it from a certain little pamphlet of conclusions, where there are a great many more such fancies no less pleasant & witty. It followeth that vve speak of the peice of Ordinance mounted perpendicular to the Horizon,An instance against the diurnal motion of the earth, taken from the shot of a Peece of Ordinance perpendicularly. that is, of a shot towards our vertical point, and to conclude, of the return of the ball by the same line unto the same peice, though that in the long time which it is separated from the peice, the earth hath transported it many miles towards the East; now it seemeth, that the ball ought to fall a like distance from the peice towards the West; the which doth not happen: therefore the peice without having been moved did stay expecting the same. The answer is the same with that of the stone falling from the Tower;The answer to the objection, shewing the equivoke. and all the fallacy, and equivocation consisteth in supposing still for true, that which is in question; for the Opponent hath it still fixed in his conceit that the ball departs from its rest, being discharged by the fire from the piece; and the departing from the state of rest, cannot be, unlesse the immobility of the Terrestrial Globe be presupposed, which is the conclusion of that was in dispute; Therefore, I reply, that those who make the Earth moveable, answer, that the piece, and the ball that is in it, partake of the same motion with the Earth; nay that they have this together with her from nature; and that therefore the ball departs in no other manner from its quiescence, but conjoyned with its motion about the centre, the which by its projection upwards, is neither taken away, nor hindered; and in this manner following, the universal motion of the Earth towards the East, it alwayes keepeth perpendicular over the said piece, as well in its rise as in its return. And the same you see to ensue, in making the experiment in a ship with a bullet shot upwards perpendicularly with a Crosse-bow, which returneth to the same place whether the ship doth move, or stand still.

Sagr.This satisfieth very well to all;Another answer to the same objection. but because that I have seen that Simplicius taketh pleasure with certain subtilties to puzzle his companions, I will demand of him whether, supposing for this time that the Earth standeth still, and the piece erected upon it perpendicularly, directed to our Zenith, he do at all question that to be the true perpendicular shot, and that the ball in departing, and in its return is to go by the same right line, still supposing all external and accidental impediments to be removed?

Simpl.I understand that the matter ought to succeed exactly in that manner.

Sagr.But if the piece were placed, not perpendicularly, but inclining towards some place, what would the motion of the ball be? Would it go haply, as in the other shot, by the perpendicular line, and return again by the same?

Simpl.It would not so do; but issuing out of the piece, it would pursue its motion by a right line which prolongeth the erect perpendicularity of the concave cylinder of the piece, unlesse so far as its own weight would make it decline from that erection towards the Earth.

Sagr.So that the mounture of the cylinder is the regulator of the motion of the ball, nor doth it, or would it move out of that line, if its own gravity did not make it decline downwards. And therefore placing the cylinder perpendicularly,Projects continue their motion by the right line that followeth the direction of the motion, made together with the projicient, whil'st they were conjoin'd therewith. and shooting the ball upwards, it returneth by the same right line downwards; because the motion of the ball dependent on its gravity is downward, by the same perpendicular. The journey therefore of the ball out of the piece, continueth or prolongeth the rectitude or perpendicularity of that small part of the said journey, which it made within the said piece; is it not so?

Simpl.So it is, in my opinion.

Sagr.Now imagine the cylinder to be erected, and that the Earth doth revolve about with a diurnal motion, carrying the piece along with it, tell me what shall be the motion of the ball within the cylinder, having given fire?

Simpl.It shall be a streight and perpendicular motion, the cylinder being erected perpendicularly.

Sagr.Consider well what you say: for I believe that it will not be perpendicular. It would indeed be perpendicular, if the Earth stood still, for so the ball would have no other motion but that proceeding from the fire.The revolution of the Earth supposed, the ball in the piece erected perpendicularly, doth not move by a perpendicular, but an inclined line. But in case the Earth turns round, the ball that is in the piece, hath likewise a diurnal motion, so that there being added to the same the impulse of the fire, it moveth from the breech of the piece to the muzzle with two motions, from the composition whereof it cometh to passe that the motion made by the centre of the balls gravity is an inclining line. And for your clearer understanding the same, let the piece AC [in Fig. 2.] be erected, and in it the ball B; it is manifest, that the piece standing immoveable, and fire being given to it, the ball will make its way out by the mouth A, and with its centre, passing thorow the the piece, shall have described the perpendicular line BA, and it shall pursue that rectitude when it is out of the piece, moving toward the Zenith. But in case the Earth should move round, and consequently carry the piece along with it, in the time that the ball driven out of the piece shall move along the cylinder, the piece being carried by the Earth, shall passe into the situation DE, and the ball B, in going off, would be at the cornish D, and the motion of the bals centre, would have been according to the line BD, no longer perpendicular, but inclining towards the East; and the ball (as hath been concluded) being to continue its motion through the air, according to the direction of the motion made in the piece, the said motion shall continue on according to the inclination of the line BD, and so shall no longer be perpendicular, but inclined towards the East, to which part the piece doth also move; whereupon the ball may follow the motion of the Earth, and of the piece. Now Simplicius, you see it demonstrated, that the Range which you took to be perpendicular, is not so.

Simpl.I do not very well understand this business; do you, Salviatus?

Salv.I apprehend it in part; but I have a certain kind of scruple, which I wish I knew how to express. It seems to me, that according to what hath been said, if the Piece be erected perpendicular, and the Earth do move, the ball would not be to fall, as Aristotle and Tycho will have it, far from the Piece towards the West, nor as you would have it, upon the Piece, but rather far distant towards the East. For according to your explanation, it would have two motions, the which would with one consent carry it thitherward, to wit, the common motion of the Earth, which carrieth the Piece and the ball from CA towards ED; and the fire which carrieth it by the inclined line BD, both motions towards the East, and therefore they are superiour to the motion of the Earth.

Sagr.Not so, Sir. The motion which carrieth the ball towards the East, cometh all from the Earth, and the fire hath no part at all therein: the motion which mounteth the ball upwards, is wholly of fire, wherewith the Earth hath nothing to do. And that it is so, if you give not fire, the ball will never go out of the Piece, nor yet rise upwards a hairs breadth; as also if you make the Earth immoveable, and give fire, the ball without any inclination shall go perpendicularly upwards. The ball therefore having two motions, one upwards, and the other in gyration, of both which the transverse line BD is compounded, the impulse upward is wholly of fire, the circular cometh wholly from the Earth, and is equal to the Earths motion: and being equal to it, the ball maintaineth it self all the way directly over the mouth of the Piece, and at last falleth back into the same: and because it always observeth the erection of the Piece, it appeareth also continually over the head of him that is near the Piece, and therefore it appeareth to mount exactly perpendicular towards our Zenith, or vertical point.

Simpl.I have yet one doubt more remaining, and it is, that in regard the motion of the ball is very swift in the Piece, it seems not possible, that in that moment of time the transposition of the Piece from CA to AD should confer such an inclination upon the transverse line CD, that by means thereof, the ball when it cometh afterwards into the air should be able to follow the course of the Earth.

Sagr.You err upon many accounts; and first, the inclination of the transverse line CD, I believe it is much greater than you take it to be, for I verily think that the velocity of the Earths motion, not onely under the Equinoctial, but in our paralel also, is greater than that of the ball whilst it moveth in the Piece; so that the interval CE would be absolutely much bigger than the whole length of the Piece, and the inclination of the transverse line consequently bigger than half a right angle: but be the velocity of the Earth more, or be it less, in comparison of the velocity of the fire, this imports nothing; for if the velocity of the Earth be small, and consequently the inclination of the transverse line be little also; there is then also need but of little inclination to make the ball suspend it self in its range directly over the Piece. And in a word, if you do but attentively consider, you will comprehend, that the motion of the Earth in transferring the Piece along with it from CA to ED, conferreth upon the transverse line CD, so much of little or great inclination, as is required to adjust the range to its perpendicularity. But you err, secondly, in that you referr the faculty of carrying the ball along with the Earth to the impulse of the fire, and you run into the same error, into which Salviatus, but even now seemed to have fallen; for the faculty of following the motion of the Earth, is the primary and perpetual motion, indelibly and inseparably imparted to the said ball, as to a thing terrestrial, and that of its own nature doth and ever shall possess the same.

Salv.Let us yield,The manner how Fowlers shoot birds flying. Simplicius, for the business is just as he saith. And now from this discourse let us come to understand the reason of a Venatorian Problem, of those Fowlers who with their guns shoot a bird flying; and because I did imagine, that in regard the bird flieth a great pace, therefore they should aim their shot far from the bird, anticipating its flight for a certain space, and more or less according to its velocity and the distance of the bird, that so the bullet hasting directly to the mark aimed at, it might come to arrive at the self same time in the same point with its motion, and the bird with its flight, and by that means one to encounter the other: and asking one of them, if their practise was not so to do; He told me, no; but that the slight was very easie and certain, and that they took aim just in the same manner as if they had shot at a bird that did sit still; that is, they made the flying bird their mark, and by moving their fowling-piece they followed her, keeping their aim still full upon her, till such time as they let fly, and in this manner shot her as they did others sitting still. It is necessary therefore that that motion, though slow, which the fowling-piece maketh in turning and following after the flight of the bird do communicate it self to the bullet also, and that it be joyned with that of the fire; so that the ball hath from the fire the motion directly upwards, and from the concave Cylinder of the barrel the declination according to the flight of the Bird, just as was said before of the shot of a Canon; where the ball receiveth from the fire a virtue of mounting upwards towards the Zenith, and from the motion of the Earth its winding towards the East, and of both maketh a compound motion that followeth the course of the Earth, and that to the beholder seemeth onely to go directly upwards, and return again downwards by the same line. The holding therefore of the gun continually directed towards the mark, maketh the shoot hit right, and that you may keep your gun directed to the mark, in case the mark stands still, you must also hold your gun still; and if the mark shall move, the gun must be kept upon the mark by moving.The answer to the objection taken from the shots of great Guns made towards the North and South. And upon this dependeth the proper answer to the other argument taken from the shot of a Canon, at the mark placed towards the South or North: wherein is alledged, that if the Earth should move, the shots would all range Westward of the mark, because that in the time whilst the ball, being forc'd out of the Piece, goeth through the air to the mark, the said mark being carried toward the East, would leave the ball to the Westward. I answer therefore, demanding whether if the Canon be aimed true at the mark, and permitted so to continue, it will constantly hit the said mark, whether the Earth move or stand still? It must be replied, that the aim altereth not at all, for if the mark doth stand still, the Piece also doth stand still, and if it, being transported by the Earths motion, doth move, the Piece doth also move at the same rate, and, the aim maintained, the shot proveth always true, as by what hath been said above, is manifest.

Sagr.Stay a little, I entreat you, Salviatus, till I have propounded a certain conceit touching these shooters of birds flying, whose proceeding I believe to be the same which you relate, and believe the effect of hitting the bird doth likewise follow: but yet I cannot think that act altogether conformable to this of shooting in great Guns, which ought to hit as well when the piece and mark moveth, as when they both stand still; and these, in my opinion, are the particulars in which they disagree. In shooting with a great Gun both it and the mark move with equal velocity, being both transported by the motion of the Terrestrial Globe: and albeit sometimes the piece being planted more towards the Pole, than the mark, and consequently its motion being somewhat flower than the motion of the mark, as being made in a lesser circle, such a difference is insensible, at that little distance of the piece from the mark: but in the shot of the Fowler the motion of the Fowling-piece wherewith it goeth following the bird, is very slow in comparison of the flight of the said bird; whence me thinks it should follow, that that small motion which the turning of the Birding-piece conferreth on the bullet that is within it, cannot, when it is once gone forth of it, multiply it self in the air, untill it come to equal the velocity of the birds flight, so as that the said bullet should always keep direct upon it: nay, me thinketh the bird would anticipate it and leave it behind. Let me add, that in this act, the air through which the bullet is to pass, partaketh not of the motion of the bird: whereas in the case of the Canon, both it, the mark, and the intermediate air, do equally partake of the common diurnal motion. So that the true cause of the Marks-man his hitting the mark, as it should seem, moreover and besides the following the birds flight with the piece, is his somewhat anticipating it, taking his aim before it; as also his shooting (as I believe) not with one bullet, but with many small balls (called shot) the which scattering in the air possess a great space; and also the extreme velocity wherewith these shot, being discharged from the Gun, go towards the bird.

Salv.See how far the winged wit of Sagredus anticipateth, and out-goeth the dulness of mine; which perhaps would have light upon these disparities,The answer to the Argument taken from the shots at point blanck towards the East & West. but not without long studie. Now turning to the matter in hand, there do remain to be considered by us the shots at point blank, towards the East and towards the West; the first of which, if the Earth did move, would always happen to be too high above the mark, and the second too low; forasmuch as the parts of the Earth Eastward, by reason of the diurnal motion, do continually descend beneath the tangent paralel to the Horizon, whereupon the Eastern stars to us appear to ascend; and on the contrary, the parts Westward do more and more ascend, whereupon the Western stars do in our seeming descend: and therefore the ranges which are leveled according to the said tangent at the Oriental mark, (which whilst the ball passeth along by the tangent descendeth) should prove too high, and the Occidental too low by means of the elevation of the mark, whilst the ball passeth along the tangent. The answer is like to the rest: for as the Eastern mark goeth continually descending, by reason of the Earths motion, under a tangent that continueth immoveable; so likewise the piece for the same reason goeth continually inclining, and with its mounture pursuing the said mark: by which means the shot proveth true.

But here I think it a convenient opportunity to give notice of certain concessions,The followers of Copernicus too freely admit certain propositions for true, which are very doubtfull. which are granted perhaps over liberally by the followers of Copernicus unto their Adversaries: I mean of yielding to them certain experiments for sure and certain, which yet the Adversaries themselves had never made tryal of: as for example, that of things falling from the round-top of a ship whilst it is in motion, and many others; amongst which I verily believe, that this of experimenting whether the shot made by a Canon towards the East proveth too high, and the Western shot too low, is one: and because I believe that they have never made tryal thereof, I desire that they would tell me what difference they think ought to happen between the said shots, supposing the Earth moveable, or supposing it moveable; and let Simplicius for this time answer for them.

Simpl.I will not undertake to answer so confidently as another more intelligent perhaps might do; but shall speak what thus upon the sudden I think they would reply; which is in effect the same with that which hath been said already, namely, that in case the Earth should move, the shots made Eastward would prove too high, &c. the ball, as it is probable, being to move along the tangent.

Salv.But if I should say, that so it falleth out upon triall, how would you censure me?

Simpl.It is necessary to proceed to experiments for the proving of it.

Salv.But do you think, that there is to be found a Gunner so skilful, as to hit the mark at every shoot, in a distance of v.g. five hundred paces?

Simpl.No Sir; nay I believe that there is no one, how good a marks-man soever that would promise to come within a pace of the mark,

Salv.How can we then, with shots so uncertain, assure our selves of that which is in dispute?

Simpl.We may be assured thereof two wayes; one, by making many shots; the other, because in respect of the great velocity of the Earths motion, the deviation from the mark would in my opinion be very great.

Salv.Very great, that is more than one pace; in regard that the varying so much, yea and more, is granted to happen ordinarily even in the Earths mobility.

Simpl.I verily believe the variation from the mark would be more than so.

Salv.Now I desire that for our satisfaction we do make thus in grosse a slight calculation,A Computation how much the ranges of great shot ought to vary from the marke, the Earths motion being granted. if you consent thereto, which will stand us in stead likewise (if the computation succeed as I expect) for a warning how we do in other occurrences suffer our selves, as the saying is, to be taken with the enemies shouts, and surrender up our belief to what ever first presents it self to our fancy. And now to give all advantages to the Peripateticks and Tychonicks, let us suppose our selves to be under the Equinoctial, there to shoot a piece of Ordinance point blank Eastwards at a mark five hundred paces off. First, let us see thus (as I said) in a level, what time the shot after it is gone out of the Piece taketh to arrive at the mark; which we know to be very little, and is certainly no more than that wherein a travailer walketh two steps, which also is less than the second of a minute of an hour; for supposing that the travailer walketh three miles in an hour, which are nine thousand paces, being that an hour containes three thousand, six hundred second minutes, the travailer walketh two steps and an half in a second, a second therefore is more than the time of the balls motion. And for that the diurnal revolution is twenty four hours, the Western horizon riseth fifteen degrees in an hour, that is, fifteen first minutes of a degree, in one first minute of an hour; that is, fifteen seconds of a degree, in one second of an hour; and because one second is the time of the shot, therefore in this time the Western horizon riseth fifteen seconds of a degree, and so much likewise the mark; and therefore fifteen seconds of that circle, whose semidiameter is five hundred paces (for so much the distance of the mark from the Piece was supposed.) Now let us look in the table of Arches and Chords (see here is Copernicus his book) what part is the chord of fifteen seconds of the semidiameter, that is, five hundred paces. Here you see the chord (or subtense) of a first minute to be less than thirty of those parts, of which the semidiameter is an hundred thousand. Therefore the chord of a second minute shall be less then half of one of those parts, that is less than one of those parts, of which the semidiameter is two hundred thousand; and therefore the chord of fifteen conds shall be less than fifteen of those same two hundred thousand parts; but that which is less than (a)(a) That is, in plainer termes the fraction 15/200000, is more than the fraction 4/50000, for dividing the denominators by their nominators, and the first produceth 133331/3, the other but 12500. fifteen parts of two hundred thousand, is also more than that which is four centesmes of five hundred; therefore the ascent of the mark in the time of the balls motion is lesse than four centesmes, that is, than one twenty fifth part of a pace; it shall be therefore (b)(b) It shall be neer 22/5 inches, accounting the pace to be Geometrical, containing 5 foot. about two inches: And so much consequently shall be the variation of each Western shot, the Earth being supposed to have a diurnal motion. Now if I shall tell you, that this variation (I mean of falling two inches short of what they would do in case the Earth did not move) upon triall doth happen in all shots, how will you convince me Simplicius, shewing me by an experiment that it is not so? Do you not see that it is impossible to confute me, unless you first find out a way to shoot at a mark with so much exactnesse, as never to misse an hairs bredth? For whilst the ranges of great shot consist of different numbers of paces, as de facto they do, I will affirm that in each of those variations there is contained that of two inches caused by the motion of the Earth.

Sagr.Pardon me,It is demonstrated with great subtilty, that the Earths motion supposed, Canon shot ought not to vary more than in rest. Salviatus, you are too liberal. For I would tell the Peripateticks, that though every shot should hit the very centre of the mark, that should not in the least disprove the motion of the Earth. For the Gunners are so constantly imployed in levelling the sight and gun to the mark, as that they can hit the same, notwithstanding the motion of the Earth. And I say, that if the Earth should stand still, the shots would not prove true; but the Occidental would be too low, and the Oriental too high: now let Simplicius disprove me if he can.

Salv.This is a subtilty worthy of Sagredus: But whether this variation be to be observed in the motion, or in the rest of the Earth, it must needs be very small, it must needs be swallowed up in those very great ones which sundry accidents continually produce. It is requisite to be very cautious in admitting experiments for true, to those who never tried them. And all this hath been spoken and granted on good grounds to Simplicius, and only with an intent to advertise him how much it importeth to be cautious in granting many experiments for true to those who never had tried them, but only eagerly alledged them just as they ought to be for the serving their purpose: This is spoken, I say, by way of surplussage and Corollary to Simplicius, for the real truth is,Experiments and arguments against the Earths motion seem so far concluding, as they lie hid under equivokes. that as concerning these shots, the same ought exactly to befall aswell in the motion as in the rest of the Terrestrial Globe; as likewise it will happen in all the other experiments that either have been or can be produced, which have at first blush so much semblance of truth, as the antiquated opinion of the Earths motion hath of equivocation.

Sagr.As for my part I am fully satisfied, and very well understand that who so shall imprint in his fancy this general community of the diurnal conversion amongst all things Terrestrial, to all which it naturally agreeth, aswell as in the old conceit of its rest about the centre, shall doubtlesse discern the fallacy and equivoke which made the arguments produced seem eoncluding. There yet remains in me some hæsitancy (as I have hinted before) touching the flight of birds; the which having as it were an animate faculty of moving at their pleasure with a thousand motions, and to stay long in the Air separated from the Earth, and therein with most irregular windings to go fluttering to and again, I cannot conceive how amongst so great a confusion of motions, they should be able to retain the first commune motion; and in what manner, having once made any stay behind, they can get it up again, and overtake the same with flying, and keep pace with the Towers and trees which hurry with so precipitant a course towards the East; I say so precipitant, for in the great circle of the Globe it is little lesse than a thousand miles an hour, whereof the flight of the swallow I believe makes not fifty.

Salv.If the birds were to keep pace with the course of the trees by help of their wings, they would of necessity flie very fast; and if they were deprived of the universal conversion, they would lag as far behind; and their flight would seem as furious towards the West, and to him that could discern the same, it would much exceed the flight of an arrow; but I think we could not be able to perceive it, no more than we see a Canon bullet, whil'st driven by the fury of the fire, it flieth through the Air: But the truth is that the proper motion of birds, I mean of their flight, hath nothing to do with the universal motion, to which it is neither an help, nor an hinderance; and that which maintaineth the said motion unaltered in the birds, is the Air it self, thorough which they flie, which naturally following the Vertigo of the Earth, like as it carrieth the clouds along with it, so it transporteth birds and every thing else which is pendent in the same; in so much that as to the businesse of keeping pace with the Earth, the birds need take no care thereof, but for that work might sleep perpetually.

Sagr.That the Air can carry the clouds along with it, as being matters easie for their lightnesse to be moved and deprived of all other contrary inclination, yea more, as being matters that partake also of the conditions and properties of the Earth; I comprehend without any difficulty; but that birds, which as having life, may move with a motion quite contrary to the diurnal, once having surceased the said motion, the Air should restore them to it, seems to me a little strange, and the rather for that they are solid and weighty bodies; and withal, we see; as hath been said, stones and other grave bodies to lie unmoved against the impetus of the air; and when they suffer themselves to be overcome thereby, they never acquire so much velocity as the wind which carrieth them.

Salv.We ascribe not so little force, Sagredus, to the moved Air, which is able to move and bear before it ships full fraught, to tear up trees by the roots, and overthrow Towers when it moveth swiftly; and yet we cannot say that the motion of the Air in these violent operations is neer so violent, as that of the diurnal revolution.

Simpl.You see then that the moved Air may also cotinue the motion of projects, according to the Doctrine of Aristotle; and it seemed to me very strange that he should have erred in this particular.

Salv.It may without doubt, in case it could continue it self, but lik as when the wind ceasing neither ships go on, nor trees are blown down, so the motion in the Air not continuing after the stone is gone out of the hand, and the Air ceasing to move, it followeth that it must be something else besides the Air that maketh the projects to move.

Simpl.But how upon the winds being laid, doth the ship cease to move? Nay you may see that when the wind is down, and the sails furl'd, the vessel continueth to run whole miles.

Salv.But this maketh against your self Simplicius, for that the wind being laid that filling the sails drove on the ship, yet neverthelesse doth it without help of the medium continue its course.

Simpl.It might be said that the water was the medium which carried forward the ship, and maintain'd it in motion.

Salv.It might indeed be so affirmed, if you would speak quite contrary to truth; for the truth is, that the water, by reason of its great resistance to the division made by the hull of the ship, doth with great noise resist the same; nor doth it permit it of a great while to acquire that velocity which the wind would confer upon it, were the obstacle of the water removed. Perhaps Simplicius you have never considered with what fury the water besets a bark, whil'st it forceth its way through a standing water by help of Oars or Sails: for if you had ever minded that effect, you would not now have produced such an absurdity. And I am thinking that you have hitherto been one of those who to find out how such things succeed, and to come to the knowledg of natural effects, do not betake themselves to a Ship, a Crosse-bow, or a piece of Ordinance, but retire into their studies, and turn over Indexes and Tables to see whether Aristotle hath spoken any thing thereof, and being assured of the true sense of the Text, neither desire nor care for knowing any more.

Sagr.This is a great felicity,The great felicity for which they are much to be envied who perswade themselves that they know every thing. and they are to be much envied for it. For if knowledg be desired by all, and if to be wise, be to think ones self so, they enjoy a very great happinesse, for that they may perswade themselves that they know and understand all things, in scorn of those who knowing, that they understand not what these think they understand, and consequently seeking that they know not the very least particle of what is knowable, kill themselves with waking and studying, and consume their days in experiments and observations. But pray you let us return to our birds; touching which you have said, that the Air being moved with great velocity, might restore unto them that part of the diurnal motion which amongst the windings of their flight they might have lost; to which I reply, that the agitated Air seemeth unable to confer on a solid and grave body, so great a velocity as its own: And because that of the Air is as great as that of the Earth, I cannot think that the Air is able to make good the losse of the birds retardation in flight.

Salv.Your discourse hath in it much of probability, and to stick at trivial doubts is not for an acute wit; yet neverthelesse the probability being removed, I believed that it hath not a jot more force than the others already considered and resolved.

Sagr.It is most certain that if it be not necessarily concludent, its efficacy must needs be just nothing at all, for it is onely when the conclusion is necessary that the opponent hath nothing to alledg on the contrary.

Salv.Your making a greater scruple of this than of the other instances dependeth, if I mistake not, upon the birds being animated, and thereby enabled to use their strength at pleasure against the primary motion in-bred in terrene bodies: like as for example, we see them whil'st they are alive to fly upwards, a thing altogether impossible for them to do as they are grave bodies; whereas being dead they can onely fall downwards; and therefore you hold that the reasons that are of force in all the kinds of projects above named, cannot take place in birds: Now this is very true; and because it is so, Sagredus, that doth not appear to be done in those projects,The answer to the argument taken from the flight of birds contrary to the motion of the Earth. which we see the birds to do. For if from the top of a Tower you let fall a dead bird and a live one, the dead bird shall do the same that a stone doth, that is, it shall first follow the general motion diurnal, and then the motion of descent, as grave; but if the bird let fall, be a live, what shall hinder it, (there ever remaining in it the diurnal motion) from soaring by help of its wings to what place of the Horizon it shall please? and this new motion, as being peculiar to the bird, and not participated by us, must of necessity be visible to us; and if it be moved by help of its wings towards the West, what shall hinder it from returning with a like help of its wings unto the Tower. And, because, in the last place, the bird swending its flight towards the West was no other than a withdrawing from the diurnal motion, (which hath, suppose ten degrees of velocity) one degree onely, there did thereupon remain to the bird whil'st it was in its flight nine degrees of velocity, and so soon as it did alight upon the the Earth, the ten common degrees returned to it, to which, by flying towards the East it might adde one, and with those eleven overtake the Tower. And in short, if we well consider, and more narrowly examine the effects of the flight of birds, they differ from the projects shot or thrown to any part of the World in nothing, save onely that the projects are moved by an external projicient,An experiment with which alone is shewn the nullity of all the objections produced against the motion of the Earth. and the birds by an internal principle. And here for a final proof of the nullity of all the experiments before illedged, I conceive it now a time and place convenient to demonstrate a way how to make an exact trial of them all. Shut your self up with some friend in the grand Cabbin between the decks of some large Ship, and there procure gnats, flies, and such other small winged creatures: get also a great tub (or other vessel) full of water, and within it put certain fishes; let also a certain bottle be hung up, which drop by drop letteth forth its water into another bottle placed underneath, having a narrow neck: and, the Ship lying still, observe diligently how those small winged animals fly with like velocity towards all parts of the Cabin; how the fishes swim indifferently towards all sides; and how the distilling drops all fall into the bottle placed underneath. And casting any thing towards your friend, you need not throw it with more force one way then another, provided the distances be equal: and leaping, as the saying is, with your feet closed, you will reach as far one way as another. Having observed all these particulars, though no man doubteth that so long as the vessel stands still, they ought to succeed in this manner; make the Ship to move with what velocity you please; for (so long as the motion is uniforme, and not fluctuating this way and that way) you shall not discern any the least alteration in all the forenamed effects; nor can you gather by any of them whether the Ship doth move or stand still. In leaping you shall reach as far upon the floor, as before; nor for that the Ship moveth shall you make a greater leap towards the poop than towards the prow; howbeit in the time that you staid in the Air, the floor under your feet shall have run the contrary way to that of your jump; and throwing any thing to your companion you shall not need to cast it with more strength that it may reach him, if he shall be towards the prow, and you towards the poop, then if you stood in a contrary situation; the drops shall all distill as before into the inferiour bottle, and not so much as one shall fall towards the poop, albeit whil'st the drop is in the Air, the Ship shall have run many feet; the Fishes in their water shall not swim with more trouble towards the fore-part, than towards the hinder part of the tub; but shall with equal velocity make to the bait placed on any side of the tub; and lastly, the flies and gnats shall continue their flight indifferently towards all parts; nor shall they ever happen to be driven together towards the side of the Cabbin next the prow, as if they were wearied with following the swift course of the Ship, from which through their suspension in the Air, they had been long separated; and if burning a few graines of incense you make a little smoke, you shall see it ascend on high, and there in manner of a cloud suspend it self, and move indifferently, not inclining more to one side than another: and of this correspondence of effects the cause is for that the Ships motion is common to all the things contained in it, and to the Air also; I mean if those things be shut up in the Cabbin: but in case those things were above deck in the open Air, and not obliged to follow the course of the Ship, differences more or lesse notable would be observed in some of the fore-named effects, and there is no doubt but that the smoke would stay behind as much as the Air it self; the flies also, and the gnats being hindered by the Air would not be able to follow the motion of the Ship, if they were separated at any distance from it. But keeping neer thereto, because the Ship it self as being an unfractuous Fabrick, carrieth along with it part of its neerest Air, they would follow the said Ship without any pains or difficulty. And for the like reason we see sometimes in riding post, that the troublesome flies and * Tafaris, horse-flyes.* hornets do follow the horses flying sometimes to one, sometimes to another part of the body, but in the falling drops the difference would be very small; and in the salts, and projections of grave bodies altogether imperceptible.

Sagr.Though it came not into my thoughts to make triall of these observations, when I was at Sea, yet am I confident that they will succeed in the same manner, as you have related; in confirmation of which I remember that being in my Cabbin I have asked an hundred times whether the Ship moved or stood still; and sometimes I have imagined that it moved one way, when it steered quite another way. I am therefore as hitherto satisfied and convinced of the nullity of all those experiments that have been produced in proof of the negative part. There now remains the objection founded upon that which experience shews us, namely, that a swift Vertigo or whirling about hath a faculty to extrude and disperse the matters adherent to the machine that turns round; whereupon many were of opinion, and Ptolomy amongst the rest, that if the Earth should turn round with so great velocity, the stones and creatures upon it should be tost into the Skie, and that there could not be a morter strong enough to fasten buildings so to their foundations, but that they would likewise suffer a like extrusion.

Salv.Before I come to answer this objection, I cannot but take notice of that which I have an hundred times observed, and not without laughter, to come into the minds of most men so soon as ever they hear mention made of this motion of the Earth, which is believed by them so fixt and immoveable, that they not only never doubted of that rest, but have ever strongly believed that all other men aswell as they, have held it to be created immoveable, and so to have continued through all succeeding ages:The stupidity of some that think the Earth to have begun to move, when Pythagoras began to affirme that it did so. and being setled in this perswasion, they stand amazed to hear that any one should grant it motion, as if, after that he had held it to be immoveable, he had fondly thought it to commence its motion then (and not till then) when Pythagoras (or whoever else was the first hinter of its mobility) said that it did move. Now that such a foolish conceit (I mean of thinking that those who admit the motion of the Earth, have first thought it to stand still from its creation, untill the time of Pythagoras, and have onely made it moveable after that Pythagoras esteemed it so) findeth a place in the mindes of the vulgar, and men of shallow capacities, I do not much wonder; but that such persons as Aristotle and Ptolomy should also run into this childish mistake, is to my thinking a more admirable and unpardonable folly.

Sagr.You believe then, Salviatus, that Ptolomy thought, that in his Disputation he was to maintain the stability of the Earth against such persons, as granting it to have been immoveable, untill the time of Pythagoras, did affirm it to have been but then made moveable, when the said Pythagoras ascribed unto it motion.

Salv.We can think no other, if we do but consider the way he taketh to confute their assertion;Aristotle and Ptolomy seem to confute the mobility of the Earth against those who thought that it having a long time stood still, did begin to move in the time of Pythagoras the confutation of which consists in the demolition of buildings, and the tossing of stones, living creatures and men themselves up into the Air. And because such overthrows and extrusions cannot be made upon buildings and men, which were not before on the Earth, nor can men be placed, nor buildings erected upon the Earth, unlesse when it standeth still; hence therefore it is cleer, that Ptolomy argueth against those, who having granted the stability of the Earth for some time, that is, so long as living creatures, stones, and Masons were able to abide there, and to build Palaces and Cities, make it afterwards precipitately moveable to the overthrow and destructi- of Edifices, and living creatures, &c. For if he had undertook to dispute against such as had ascribed that revolution to the Earth from its first creation, he would have confuted them by saying, that if the Earth had alwayes moved, there could never have been placed upon it either men or stones; much less could buildings have been erected, or Cities founded, &c.

Simpl.I do not well conceive these Aristotelick and Ptolomaick inconveniences.

Salv.Ptolomey either argueth against those who have esteemed the Earth always moveable; or against such as have held that it stood for some time still, and hath since been set on moving. If against the first, he ought to say, that the Earth did not always move, for that then there would never have been men, animals, or edifices on the Earth, its vertigo not permitting them to stay thereon. But in that he arguing, saith that the Earth doth not move, because that beasts, men, and houses before plac'd on the Earth would precipitate, he supposeth the Earth to have been once in such a state, as that it did admit men and beasts to stay, and build thereon; the which draweth on the consequence, that it did for some time stand still, to wit, was apt for the abode of animals and erection of buildings. Do you now conceive what I would say?

Simpl.I do, and I do not: but this little importeth to the merit of the cause; nor can a small mistake of Ptolomey, committed through inadvertencie be sufficient to move the Earth, when it is immoveable. But omitting cavils, let us come to the substance of the argument, which to me seems unanswerable.

Salv.And I, Simplicius, will drive it home, and re-inforce it, by shewing yet more sensibly, that it is true that grave bodies turn'd with velocity about a settled centre, do acquire an impetus of moving, and receding to a distance from that centre, even then when they are in a state of having a propension of moving naturally to the same. Tie a bottle that hath water in it, to the end of a cord, and holding the other end fast in your hand, and making the cord and your arm the semi-diameter, and the knitting of the shoulder the centre, swing the bottle very fast about, so as that it may describe the circumference of a circle, which, whether it be parallel to the Horizon, or perpendicular to it, or any way inclined, it shall in all cases follow, that the water will not fall out of the bottle: nay, he that shall swing it, shall find the cord always draw, and strive to go farther from the shoulder. And if you bore a hole in the bottom of the bottle, you shall see the water spout forth no less upwards into the skie, than laterally, and downwards to the Earth; and if instead of water, you shall put little pebble stones into the bottle, and swing it in the same manner, you shall find that they will strive in the like manner against the cord. And lastly, we see boys throw stones a great way, by swinging round a piece of a stick, at the end of which the stone is let into a slit (which stick is called by them a sling;) all which are arguments of the truth of the conclusion, to wit, that the vertigo or swing conferreth upon the moveable, a motion towards the circumference, in case the motion be swift: and therefore if the Earth revolve about its own centre, the motion of the superficies, and especially towards the great circle, as being incomparably more swift than those before named, ought to extrude all things up into the air.

Simpl.The Argument seemeth to me very well proved and inforced; and I believe it would be an hard matter to answer and overthrow it.

Salv.Its solution dependeth upon certain notions no less known and believed by you, than by my self: but because they come not into your mind, therefore it is that you perceive not the answer; wherefore, without telling you it (for that you know the same already) I shall with onely assisting your memory, make you to refute this argument.

Simpl.I have often thought of your way of arguing, which hath made me almost think that you lean to that opinion of Plato,Our knowledg is a kind of reminiscence according to Plato. Quòd nostrum scire sit quoddam reminisci; therefore I intreat you to free me from this doubt, by letting me know your judgment.

Salv.What I think of the opinion of Plato, you may gather from my words and actions. I have already in the precedent conferences expresly declared my self more than once; I will pursue the same style in the present case, which may hereafter serve you for an example, thereby the more easily to gather what my opinion is touching the attainment of knowledg, when a time shall offer upon some other day: but I would not have Sagredus offended at this digression.

Sagr.I am rather very much pleased with it, for that I remember that when I studied Logick, I could never comprehend that so much cry'd up and most potent demonstration of Aristotle.

Salv.Let us go on therefore; and let Simplicius, tell me what that motion is which the stone maketh that is held fast in the slit of the sling, when the boy swings it about to throw it a great way?

Simpl.The motion of the stone, so long as it is in the slit, is circular, that is, moveth by the arch of a circle, whose stedfast centre is the knitting of the shoulder, and its semi-diameter the arm and stick.

Salv.And when the stone leaveth the sling, what is its motion? Doth it continue to follow its former circle, or doth it go by another line?

Simpl.It will continue no longer to swing round, for then it would not go farther from the arm of the projicient, whereas we see it go a great way off.

Salv.With what motion doth it move then?

Simpl.Give me a little time to think thereof; For I have never considered it before.

Salv.Hark hither, Sagredus; this is the Quoddam reminisci in a subject well understood. You have paused a great while, Simplicius.

Simpl.As far as I can see, the motion received in going out of the sling, can be no other than by a right line; nay, it must necessarily be so, if we speak of the pure adventitious impetus. I was a little puzled to see it make an arch, but because that arch bended all the way upwards, and no other way, I conceive that that incurvation cometh from the gravity of the stone,The motion impressed by the projicient is onely by a right line. which naturally draweth it downwards. The impressed impetus, I say, without respecting the natural, is by a right line.

Salv.But by what right line? Because infinite, and towards every side may be produced from the slit of the sling, and from the point of the stones separation from the sling.

Simpl.It moveth by that line which goeth directly from the motion which the stone made in the sling.

Salv.The motion of the stone whilst it was in the slit, you have affirmed already to be circular; now circularity opposeth directness, there not being in the circular line any part that is direct or streight.

Simpl.I mean not that the projected motion is direct in respect of the whole circle, but in reference to that ultimate point, where the circular motion determineth. I know what I would say, but do not well know how to express my self.

Salv.And I also perceive that you understand the business, but that you have not the proper terms, wherewith to express the same. Now these I can easily teach you; teach you, that is, as to the words, but not as to the truths, which are things. And that you may plainly see that you know the thing I ask you, and onely want language to express it, tell me, when you shoot a bullet out of a gun, towards what part is it, that its acquired impetus carrieth it?

Simpl.Its acquired impetus carrieth it in a right line, which continueth the rectitude of the barrel, that is, which inclineth neither to the right hand nor to the left, nor upwards nor downwards.

Salv.Which in short is asmuch as to say, it maketh no angle with the line of streight motion made by the sling.

Simpl.So I would have said.

Salv.If then the line of the projects motion be to continue without making an angle upon the circular line described by it, whilst it was with the projicient; and if from this circular motion it ought to pass to the right motion, what ought this right line to be?

Simpl.It must needs be that which toucheth the circle in the point of separation, for that all others, in my opinion, being prolonged would intersect the circumference, and by that means make some angle therewith.

Salv.You have argued very well, and shewn your self half a Geometrician. Keep in mind therefore, that your true opinion is exprest in these words, namely, That the project acquireth an impetus of moving by the Tangent, the arch described by the motion of the projicient, in the point of the said projects separation from the projicient.

Simpl.I understand you very well, and this is that which I would say.

Salv.Of a right line which toucheth a circle, which of its points is the nearest to the centre of that circle?

Simpl.That of the contact without doubt: for that is in the circumference of a circle, and the rest without: and the points of the circumference are all equidistant from the centre.

Salv.Therefore a moveable departing from the contact, and moving by the streight Tangent, goeth continually farther and farther from the contact, and also from the centre of the circle.

Simpl.It doth so doubtless.

Salv.Now if you have kept in mind the propositions, which you have told me, lay them together, and tell me what you gather from them.

Simpl.I think I am not so forgetful, but that I do remember them.The project moveth by the Tangent of the circle of the motion precedent in the point of separation. From the things premised I gather that the project swiftly swinged round by the projicient, in its separating from it, doth retain an impetus of continuing its motion by the right line, which toucheth the circle described by the motion of the projicient in the point of separation, by which motion the project goeth continually receding from the centre of the circle described by the motion of the projicient.

Salv.You know then by this time the reason why grave bodies sticking to the rim of a wheele, swiftly moved, are extruded and thrown beyond the circumference to yet a farther distance from the centre.

Simpl.I think I understand this very well; but this new knowledg rather increaseth than lesseneth my incredulity that the Earth can turn round with so great velocity, without extruding up into the sky, stones, animals, &c.

Salv.In the same manner that you have understood all this, you shall, nay you do understand the rest: and with recollecting your self, you may remember the same without the help of others: but that we may lose no time, I will help your memory therein. You do already know of your self, that the circular motion of the projicient impresseth on the project an impetus of moving (when they come to separate) by the right Tangent, the circle of the motion in the point of separation, and continuing along by the same the motion ever goeth receding farther and farther from the projicient: and you have said, that the project would continue to move along by that right line, if there were not by its proper weight an inclination of descent added unto it; from which the incurvation of the line of motion is derived. It seems moreover that you knew of your self, that this incurvation always bended towards the centre of the Earth, for thither do all grave bodies tend. Now I proceed a little farther, and ask you, whether the moveable after its separation, in continuing the right motion goeth always equally receding from the centre, or if you will, from the circumference of that circle, of which the precedent motion was a part; which is as much as to say, Whether a moveable, that forsaking the point of a Tangent, and moving along by the said Tangent, doth equally recede from the point of contact, and from the circumference of the circle?

Simpl.No, Sir: for the Tangent near to the point of contact, recedeth very little from the circumference, wherewith it keepeth a very narrow angle, but in its going farther and farther off, the distance always encreaseth with a greater proportion; so that in a circle that should have v. g. ten yards of diameter, a point of the Tangent that was distant from the contact but two palms, would be three or four times as far distant from the circumference of the circle, as a point that was distant from the contaction one palm, and the point that was distant half a palm, I likewise believe would fearse recede the fourth part of the distance of the second: so that within an inch or two of the contact, the separation of the Tangent from the circumference is scarse discernable.

Salv.So that the recession of the project from the circumference of the precedent circular motion is very small in the begining?

Simpl.Almost insensible.

Salv.Now tell me a little; the project, which from the motion of the projicient receiveth an impetus of moving along the Tangent in a right line, and that would keep unto the same, did not its own weight depress it downwards, how long is it after the separation, ere it begin to decline downwards.

Simpl.I believe that it beginneth presently; for it not having any thing to uphold it, its proper gravity cannot but operate. A grave project, as soon as it is separated from the projicient begineth to decline.

Salv.So that, if that same stone, which being extruded from that wheel turn'd about very fast, had as great a natural propension of moving towards the centre of the said wheel, as it hath to move towards the centre of the Earth, it would be an easie matter for it to return unto the wheel, or rather not to depart from it; in regard that upon the begining of the separation, the recession being so small, by reason of the infinite acuteness of the angle of contact, every very little of inclination that draweth it back towards the centre of the wheel, would be sufficient to retain it upon the rim or circumference.

Simpl.I question not, but that if one suppose that which neither is, nor can be, to wit, that the inclination of those grave bodies was to go towards the centre of the wheel, they would never come to be extruded or shaken off.

Salv.But I neither do, nor need to suppose that which is not; for I will not deny but that the stones are extruded. Yet I speak this by way of supposition, to the end that you might grant me the rest. Now fancy to your self, that the Earth is that great wheel, which moved with so great velocity is to extrude the stones. You could tell me very well even now, that the motion of projection ought to be by that right line which toucheth the Earth in the point of separation: and this Tangent, how doth it notably recede from the superficies of the Terrestrial Globe?

Simpl.I believe, that in a thousand yards, it will not recede from the Earth an inch.

Salv.And did you not say, that the project being drawn by its own weight, declineth from the Tangent towards the centre of the Earth?

Simpl.I said so, and also confesse the rest: and do now plainly understand that the stone will not separate from the Earth, for that its recession in the beginning would be such, and so small, that it is a thousand times exceeded by the inclination which the stone hath to move towards the centre of the Earth, which centre in this case is also the centre of the wheel. And indeed it must be confessed that the stones, the living creatures, and the other grave bodies cannot be extruded; but here again the lighter things beget in me a new doubt, they having but a very weak propension of descent towards the centre; so that there being wanting in them that faculty of withdrawing from the superficies, I see not, but that they may be extruded; and you know the rule, that ad destruendum sufficit unum.

Savl.We will also give you satisfaction in this. Tell me therefore in the first place, what you understand by light matters, that is, whether you thereby mean things really so light, as that they go upwards, or else not absolutely light, but of so small gravity, that though they descend downwards, it is but very slowly; for if you mean the absolutely light, I will be readier than your self to admit their extrusion.

Simpl.I speak of the other sort, such as are feathers, wool, cotton, and the like; to lift up which every small force sufficeth: yet neverthelesse we see they rest on the Earth very quietly.

Salv.This pen, as it hath a natural propension to descend towards the superficies of the Earth, though it be very small, yet I must tell you that it sufficeth to keep it from mounting upwards: and this again is not unknown to you your self; therefore tell me if the pen were extruded by the Vertigo of the Earth, by what line would it move?

Simpl.By the tangent in the point of separation.

Salv.And when it should be to return, and re-unite it self to the Earth, by what line would it then move?

Simpl.By that which goeth from it to the centre of the Earth.

Salv.So then here falls under our consideration two motions; one the motion of projection, which beginneth from the point of contact, and proceedeth along the tangent; and the other the motion of inclination downwards, which beginneth from the project it self, and goeth by the secant towards the centre; and if you desire that the projection follow, it is necessary that the impetus by the tangent overcome the inclination by the secant: is it not so?

Simpl.So it seemeth to me.

Salv.But what is it that you think necessary in the motion of the projicient, to make that it may prevail over that inclination, from which ensueth the separation and elongation of the pen from the Earth?

Simpl.I cannot tell.

Salv.How, do you not know that? The moveable is here the same, that is, the same pen; now how can the same moveable superate and exceed it self in motion?

Simpl.I do not see how it can overcome or yield to it self in motion, unlesse by moving one while faster, and another while slower.

Salv.You see then, that you do know it. If therefore the projection of the pen ought to follow, and its motion by the tangent be to overcome its motion by the secant, what is it requisite that their velocities should be?

Simpl.It is requisite that the motion by the tangent be greater than that other by the secant. But wretch that I am! Is it not only many thousand times greater than the descending motion of the pen, but than that of the stone? And yet like a simple fellow I had suffered my self to be perswaded, that stones could not be extruded by the revolution of the Earth. I do therefore revoke my former sentence, and say, that if the Earth should move, stones, Elephants, Towers, and whole Cities would of necessity be tost up into the Air; and because that that doth not evene, I conclude that the Earth doth not move.

Salv.Softly Simplicius, you go on so fast, that I begin to be more afraid for you, than for the pen. Rest a little, and observe what I am going to speap. If for the reteining of the stone or pen annexed to the Earths surface it were necessary that its motion of descent were greater, or as much as the motion made by the tangent; you would have had reason to say, that it ought of necessity to move as fast, or faster by the secant downwards, than by the tangent Eastwards: But did not you tell me even now, that a thousand yards of distance by the tangent from the contact, do remove hardly an inch from the circumference? It is not sufficient therefore that the motion by the tangent, which is the same with that of the diurnall Vertigo, (or hasty revolution) be simply more swift than the motion by the secant, which is the same with that of the pen in descending; but it is requisite that the same be so much more swift as that the time which sufficeth for the pen to move v. g. a thousand yards by the tangent, be insufficient for it to move one sole inch by the secant. The which I tell you shall never be, though you should make that motion never so swift, and this never so slow.

Simpl.And why might not that by the tangent be so swift, as not to give the pen time to return to the surface of the Earth?

Salv.Try whether you can state the case in proper termes, and I will give you an answer. Tell me therefore, how much do you think sufficeth to make that motion swifter than this?

Simpl.I will say for example, that if that motion by the tangent were a million of times swifter than this by the secant, the pen, yea, and the stone also would come to be extruded.

Salv.You say so, and say that which is false, onely for want, not of Logick, Physicks, or Metaphysicks, but of Geometry; for if you did but understand its first elements, you would know, that from the centre of a circle a right line may be drawn to meet the tangent, which intersecteth it in such a manner, that the part of the tangent between the contact and the secant, may be one, two, or three millions of times greater than that part of the secant which lieth between the tangent and the circumference, and that the neerer and neerer the secant shall be to the contact, this proportion shall grow greater and greater in infinitum; so that it need not be feared, though the vertigo be swift, and the motion downwards slow, that the pen or other lighter matter can begin to rise upwards, for that the inclination downwards always exceedeth the velocity of the projection.

Sagr.I do not perfectly apprehend this businesse.

Salv.I will give you a most universal yet very easie demonstration thereof.A geometrical demonstration to prove the impossibility of extrusion by means of the terrestrial vertigo. Let a proportion be given between BA [in Fig. 3.] and C: And let BA be greater than C at pleasure. And let there be described a circle, whose centre is D. From which it is required to draw a secant, in such manner, that the tangent may be in proportion to the said secant, as BA to C. Let AI be supposed a third proportional to BA and C. And as BI is to IA, so let the diameter FE be to EG; and from the point G, let there be drawn the tangent GH. I say that all this is done as was required; and as BA is to C, so is HG to GE. And in regard that as BI is to IA, so is FE to EG; therefore by composition, as BA is to AI; so shall FG be to GE. And because C is the middle proportion between BA and AI; and GH is a middle term between FG and GE; therefore, as BA is to C, so shall FG be to GH; that is HG to GE, which was to be demonstrated.

Sagr.I apprehend this demonstration; yet neverthelesse, I am not left wholly without haesitation; for I find certain confused scruples role to and again in my mind, which like thick and dark clouds, permit me not to discern the cleernesse and necessity of the conclusion with that perspicuity, which is usual in Mathematical Demonstrations. And that which I stick at is this. It is true that the spaces between the tangent and the circumference do gradually diminish in infinitum towards the contact; but it is also true on the contrary, that the propension of the moveable to descending groweth less & less in it, the nearer it is to the first term of its descent; that is, to the state of rest; as is manifest from that which you declare unto us, demonstrating that the descending grave body departing from rest, ought to passe thorow all the degrees of tardity comprehended between the said rest, & any assigned degree of velocity, the which grow less and in infinitum. To which may be added, that the said velocity and propension to motion, doth for another reason diminish to infinity; and it is because the gravity of the said moveable may infinitely diminish. So that the causes which diminish the propension of ascending, and consequently favour the projection, are two; that is, the levity of the moveable, and its vicinity to the state of rest; both which are augmentable in infinit. and these two on the contrary being to contract but with one sole cause of making the projection, I cannot conceive how it alone, although it also do admit of infinite augmentation, should be able to remain invincible against the union & confederacy of the others, w^ch are two, and are in like manner capable of infinite augmentation.

Salv.This is a doubt worthy of Sagredus; and to explain it so as that we may more cleerly apprehend it, for that you say that you your self have but a confused Idea of it, we will distinguish of the same by reducing it into figure; which may also perhaps afford us some ease in resolving the same. Let us therefore [in Fig. 4.] draw a perpendicular line towards the centre, and let it be AC, and to it at right angles let there be drawn the Horizontal line AB, upon which the motion of the projection ought to be made; now the project would continue to move along the same with an even motion, if so be its gravity did not incline it downwards. Let us suppose from the point A a right line to be drawn, that may make any angle at pleasure with the line AB; which let be AE, and upon AB let us mark some equal spaces AF, FH, HK, and from them let us let fall the perpendiculars FG, HI, KL, as far as AE. And because, as already hath been said, the descending grave body departing from rest, goeth from time to time acquiring a greater degrees of velocity, according as the said time doth successively encrease; we may conceive the spaces AF, FH, HK, to represent unto us equal times; and the perpendiculars FG, HI, KL, degrees of velocity acquired in the said times; so that the degree of velocity acquired in the whole time AK, is as the line KL, in respect to the degree HI, acquired in the time AH, and the degree FG in the time AF; the which degrees KL, HI, FG, are (as is manifest) the same in proportion, as the times KA, HA, FA, and if other perpendiculars were drawn from the points marked at pleasure in the line FA, one might successively find degrees lesse and lesse in infinitum, proceeding towards the point A, representing the first instant of time, and the first state of rest. And this retreat towards A, representeth the first propension to the motion of descent, diminished in infinitum by the approach of the moveable to the first state of rest, which approximation is augmentable in infinitum. Now let us find the other diminution of velocity, which likewise may proceed to infinity, by the diminution of the gravity of the moveable, and this shall be represented by drawing other lines from the point A, which contein angles lesse than the angle BAE, which would be this line AD, the which intersecting the parallels KL, HI, FG, in the points M, N, and O, represent unto us the degrees FO, HN, KM, acquired in the times AF, AH, AK, lesse than the other degrees FG, HI, KL, acquired in the same times; but these latter by a moveable more ponderous, and those other by a moveable more light. And it is manifest, that by the retreat of the line EA towards AB, contracting the angle EAB (the which may be done in infinitum, like as the gravity may in infinitum be diminished) the velocity of the cadent moveable may in like manner be diminished in infinitum, and so consequently the cause that impeded the projection; and therefore my thinks that the union of these two reasons against the projection, diminished to infinity, cannot be any impediment to the said projection. And couching the whole argument in its shortest terms, we will say, that by contracting the angle EAB, the degrees of velocity LK, IH, GF, are diminished; and moreover by the retreat of the parallels KL, HI, FG, towards the angle A, the same degrees are again diminished; and both these diminutions extend to infinity: Therefore the velocity of the motion of descent may very well diminish so much, (it admitting of a twofold diminution in infinitum) as that it may not suffice to restore the moveable to the circumference of the wheel, and thereupon may occasion the projection to be hindered and wholly obviated.

Again on the contrary, to impede the projection, it is necessary that the spaces by which the project is to descend for the reuniting it self to the Wheel, be made so short and close together, that though the descent of the moveable be retarded, yea more, diminished in infinitum, yet it sufficeth to reconduct it thither: and therefore it would be requisite, that you find out a diminution of the said spaces, not only produced to infinity, but to such an infinity, as that it may superate the double infinity that is made in the diminution of the velocity of the descending moveable. But how can a magnitude be diminished more than another, which hath a twofold diminution in infinitum? Now let Simplicius observe how hard it is to philosophate well in nature, without Geometry. The degrees of velocity diminished in infinitum, as well by the diminution of the gravity of the moveable, as by the approxination to the first term of the motion, that is, to the state of rest, are alwayes determinate, and answer in proportion to the parallels comprehended between two right lines that concur in an angle, like to the angle BAE, or BAD, or any other infinitely more acute, alwayes provided it be rectilineall. But the diminution of the spaces thorow which the moveable is to be conducted along the circumference of the wheel, is proportionate to another kind of diminution, comprehended between lines that contain an angle infinitely more narrow and acute, than any rectilineal angle, how acute soever, which is that in our present case. Let any point be taken in the perpendicular AC, and making it the centre, describe at the distance CA, an arch AMP, the which shall intersect the parallels that determine the degrees of velocity, though they be very minute, and comprehended within a most acute rectilineal angle; of which parallels the parts that lie between the arch and the tangent AB, are the quantities of the spaces, and of the returns upon the wheel, alwayes lesser (and with greater proportion lesser, by how much neerer they approach to the contact) than the said parallels of which they are parts. The parallels comprehended between the right lines in retiring towards the angle diminish alwayes at the same rate, as v. g. AH being divided in two equal parts in F, the parallel HI shall be double to FG, and sub-dividing FA, in two equal parts, the parallel produced from the point of the division shall be the half of FG; and continuing the sub-division in infinitum, the subsequent parallels shall be alwayes half of the next preceding; but it doth not so fall out in the lines intercepted between the tangent and the circumference of the circle: For if the same sub-division be made in FA; and supposing for example, that the parallel which cometh from the point H, were double unto that which commeth from F, this shall be more then double to the next following, and continually the neerer we come towards the contact A, we shall find the precedent lines contein the next following three, four, ten, an hundred, a thousand, an hundred thousand, an hundred millions of times, and more in infinitum. The brevity therefore of such lines is so reduced, that it far exceeds what is requisite to make the project, though never so light, return, nay more, continue unremoveable upon the circumference.

Sagr.I very well comprehend the whole discourse, and upon what it layeth all its stresse, yet neverthelesse methinks that he that would take pains to pursue it, might yet start some further questions, by saying, that of those two causes which render the descent of the moveable slower and slower in infinitum, it is manifest, that that which dependeth on the vicinity to the first term of the descent, increaseth alwayes in the same proportion, like as the parallels alwayes retain the same proportion to each other, &c. Page 180 but that the diminution of the same velocity, dependent on the diminution of the gravity of the moveable (which vvas the second cause) doth also observe the same proportion, doth not so plainly appear, And vvho shall assure us that it doth not proceed according to the proportion of the lines intercepted between the secant, and the circumference; or vvhether vvith a greater proportion?

Salv.I have assumed for a truth, that the velocities of moveables descending naturally, will follow the proportion of their gravities, with the favour of Simplicius, and of Aristotle, who doth in many places affirm the same, as a proposition manifest: You, in favour of my adversary, bring the same into question, and say that its possible that the velocity increaseth with greater proportion, yea and greater in infinitum than that of the gravity; so that all that hath been said falleth to the ground: For maintaining whereof, I say, that the proportion of the velocities is much lesse than that of the gravities; and thereby I do not onely support but confirme the premises. And for proof of this I appeal unto experience, which will shew us, that a grave body, howbeit thirty or fourty times bigger then another; as for example, a ball of lead, and another of sugar, will not move much more than twice as fast. Now if the projection would not be made, albeit the velocity of the cadent body should diminish according to the proportion of the gravity, much lesse would it be made so long as the velocity is but little diminished, by abating much from the gravity. But yet supposing that the velocity diminisheth with a proportion much greater than that wherewith the gravity decreaseth, nay though it were the self-same wherewith those parallels conteined between the tangent and circumference do decrease, yet cannot I see any necessity why I should grant the projection of matters of never so great levity; yea I farther averre, that there could no such projection follow, meaning alwayes of matters not properly and absolutely light, that is, void of all gravity, and that of their own natures move upwards, but that descend very slowly, and have very small gravity. And that which moveth me so to think is, that the diminution of gravity, made according to the proportion of the parallels between the tangent and the circumference, hath for its ultimate and highest term the nullity of weight, as those parallels have for their last term of their diminution the contact it self, which is an indivisible point: Now gravity never diminisheth so far as to its last term, for then the moveable would cease to be grave; but yet the space of the reversion of the project to the circumference is reduced to the ultimate minuity, which is when the moveable resteth upon the circumference in the very point of contact; so as that to return thither it hath no need of space: and therefore let the propension to the motion of descent be never so small, yet is it alwayes more than sufficient to reconduct the moveable to the circumference, from which it is distant but its least space, that is, nothing at all.

Sagr.Your discourse, I must confess, is very accurate; and yet no less concluding than it is ingenuous; and it must be granted that to go about to handle natural questions, without Geometry, is to attempt an impossibility.

Salv.But Simplicius will not say so; and yet I do not think that he is one of those Peripateticks that disswade their Disciples from studying the Mathematicks, as Sciences that vitiate the reason, and render it lesse apt for contemplation.

Simpl.I would not do so much wrong to Plato, but yet I may truly say with Aristotle, that he too much lost himself in, and too much doted upon that his Geometry: for that in conclusion these Mathematical subtilties Salviatus are true in abstract, but applied to sensible and Physical matter, they hold not good. For the Mathematicians will very well demonstrate for example, that Sphæra tangit planum in puncto; a position like to that in dispute, but when one cometh to the matter, things succeed quite another way. And so I may say of these angles of contact, and these proportions; which all evaporate into Air, when they are applied to things material and sensible.

Salv.You do not think then, that the tangent toucheth the superficies of the terrestrial Globe in one point only?

Simpl.No, not in one sole point; but I believe that a right line goeth many tens and hundreds of yards touching the surface not onely of the Earth, but of the water, before it separate from the same.

Salv.But if I grant you this, do not you perceive that it maketh so much the more against your cause? For if it be supposed that the tangent was separated from the terrestrial superficies, yet it hath been however demonstrated that by reason of the great acuity of the angle of contingence (if happily it may be call'd an angle) the project would not separate from the same; how much lesse cause of separation would it have, if that angle should be wholly closed,The truth sometimes gaines strength by contradiction. and the superficies and the tangent become all one? Perceive you not that the Projection would do the same thing upon the surface of the Earth, which is asmuch as to say, it would do just nothing at all? You see then the power of truth, which while you strive to oppose it, your own assaults themselves uphold and defend it. But in regard that you have retracted this errour, I would be loth to leave you in that other which you hold, namely, that a material Sphere doth not touch a plain in one sole point: and I could wish some few hours conversation with some persons conversant in Geometry, might make you a little more intelligent amongst those who know nothing thereof. Now to shew you how great their errour is who say, that a Sphere v. g. of brasse, doth not touch a plain v. g. of steel in one sole point, Tell me what conceipt you would entertain of one that should constantly aver, that the Sphere is not truly a Sphere.

Simpl.I would esteem him wholly devoid of reason.

The sphere although material, toucheth the material plane but in one point onely.Salv.He is in the same case who saith that the material Sphere doth not touch a plain, also material, in one onely point; for to say this is the same, as to affirm that the Sphere is not a Sphere. And that this is true, tell me in what it is that you constitute the Sphere to consist, that is, what it is that maketh the Sphere differ from all other solid bodies.

The definition of the sphere.Simpl.I believe that the essence of a Sphere consisteth in having all the right lines produced from its centre to the circumference, equal.

Salv.So that, if those lines should not be equal, that same solidity would be no longer a sphere?

Simpl.True.

Salv.Go to; tell me whether you believe that amongst the many lines that may be drawn between two points, there may be more than one right line onely.

Simpl.There can be but one.

Salv.But yet you understand that this onely right line shall again of necessity be the shortest of them all?

Simpl.I know it, and also have a demonstration thereof, produced by a great Peripatetick Philosopher, and as I take it, if my memory do not deceive me, he alledgeth it by way of reprehending Archimedes, that supposeth it as known, when it may be demonstrated.

Salv.This must needs be a great Mathematician, that knew how to demonstrate that which Archimedes neither did, nor could demonstrate. And if you remember his demonstration, I would gladly hear it: for I remember very well, that Archimedes in his Books, de Sphæra & Cylindro, placeth this Proposition amongst the Postulata; and I verily believe that he thought it demonstrated.

Simpl.I think I shall remember it, for it is very easie and short.

Salv.The disgrace of Archimedes, and the honour of this Philosopher shall be so much the greater.

Simpl.I will describe the Figure of it. Between the points A and B,The demonstration of a Peripatetick, to prove the right line to be the shortest of all lines. [in Fig. 5.] draw the right line AB, and the curve line ACB, of which we will prove the right to be the shorter: and the proof is this; take a point in the curve-line, which let be C, and draw two other lines, AC and CB, which two lines together, are longer than the sole line AB, for so demonstrateth Euclid. But the curve-line ACB, is greater than the two right-lines AC, and CB; therefore, à fortiori, the curve-line ACB, is much greater than the right line AB, which was to be demonstrated.

The Paralogism of the same Peripatetick, which proveth ignotum pe ignotius.Salv.I do not think that if one should ransack all the Paralogisms of the world, there could be found one more commodious than this, to give an example of the most solemn fallacy of all fallacies, namely, than that which proveth ignotum per ignotius.

Simpl.How so?

Salv.Do you ask me how so? The unknown conclusion which you desire to prove, is it not, that the curved line ACB, is longer than the right line AB; the middle term which is taken for known, is that the curve-line ACB, is greater than the two lines AC and CB, the which are known to be greater than AB; And if it be unknown whether the curve-line be greater than the single right-line AB, shall it not be much more unknown whether it be greater than the two right lines AC & CB, which are known to be greater than the sole line AB, & yet you assume it as known?

Simpl.I do not yet very well perceive wherein lyeth the fallacy.

Salv.As the two right lines are greater than AB, (as may be known by Euclid) and in as much as the curve line is longer than the two right lines AC and BC, shall it not not be much greater than the sole right line AB?

Simpl.It shall so.

Salv.That the curve-line ACB, is greater than the right line AB, is the conclusion more known than the middle term, which is, that the same curve-line is greater than the two right-lines AC and CB. Now when the middle term is less known than the conclusion, it is called a proving ignotum per ignotius. But to return to our purpose, it is sufficient that you know the right line to be the shortest of all the lines that can be drawn between two points. And as to the principal conclusion, you say, that the material sphere doth not touch the sphere in one sole point. What then is its contact?

Simpl.It shall be a part of its superficies.

Salv.And the contact likewise of another sphere equal to the first, shall be also a like particle of its superficies?

Simpl.There is no reason why it should be otherwise.

Salv.Then the two spheres which touch each other, shall touch with the two same particles of a superficies, for each of them agreeing to one and the same plane, they must of necessity agree in like manner to each other.A demonstration that the sphere toucheth the plane but in one point. Imagine now that the two spheres [in Fig. 6.] whose centres are A and B, do touch one another: and let their centres be conjoyned by the right line AB, which passeth through the contact. It passeth thorow the point C, and another point in the contact being taken as D, conjoyn the two right lines AD and BD, so as that they make the triangle ADB; of which the two sides AD and DB shall be equal to the other one ACB, both those and this containing two semidiameters, which by the definition of the sphere are all equal: and thus the right line AB, drawn between the two centres A and B, shall not be the shortest of all, the two lines AD and DB being equal to it: which by your own concession is absurd.

Simpl.This demonstration holdeth in the abstracted, but not in the material spheres.

Salv.Instance then wherein the fallacy of my argument consisteth, if as you say it is not concluding in the material spheres, but holdeth good in the immaterial and abstracted.

Simpl.The material spheres are subject to many accidents,Why the sphere in abstract, toucheth the plane onely in one point, and not the material in concrete. which the immaterial are free from. And because it cannot be, that a sphere of metal passing along a plane, its own weight should not so depress it, as that the plain should yield somewhat, or that the sphere it self should not in the contact admit of some impression. Moreover, it is very hard for that plane to be perfect, if for nothing else, yet at least for that its matter is porous: and perhaps it will be no less difficult to find a sphere so perfect, as that it hath all the lines from the centre to the superficies, exactly equal.

Salv.I very readily grant you all this that you have said; but it is very much beside our purpose: for whilst you go about to shew me that a material sphere toucheth not a material plane in one point alone, you make use of a sphere that is not a sphere, and of a plane that is not a plane; for that, according to what you say, either these things cannot be found in the world, or if they may be found, they are spoiled in applying them to work the effect. It had been therefore a less evil, for you to have granted the conclusion, but conditionally, to wit, that if there could be made of matter a sphere and a plane that were and could continue perfect, they would touch in one sole point, and then to have denied that any such could be made.

Simpl.I believe that the proposition of Philosophers is to be understood in this sense; for it is not to be doubted, but that the imperfection of the matter, maketh the matters taken in concrete, to disagree with those taken in abstract.

Salv.What, do they not agree? Why, that which you your self say at this instant, proveth that they punctually agree.

Simpl.How can that be?

Salv.Do you not say, that through the imperfection of the matter, that body which ought to be perfectly spherical, and that plane which ought to be perfectly level, do not prove to be the same in concrete, as they are imagined to be in abstract?

Simpl.This I do affirm.

Salv.Then when ever in concrete you do apply a material Sphere to a material plane,Things are exactly the same in abstract as in concrete. you apply an imperfect Sphere to an imperfect plane, & these you say do not touch only in one point. But I must tell you, that even in abstract an immaterial Sphere, that is, not a perfect Sphere, may touch an immaterial plane, that is, not a perfect plane, not in one point, but with part of its superficies, so that hitherto that which falleth out in concrete, doth in like manner hold true in abstract. And it would be a new thing that the computations and rates made in abstract numbers, should not afterwards answer to the Coines of Gold and Silver, and to the merchandizes in concrete. But do you know Simplicius, how this commeth to passe? Like as to make that the computations agree with the Sugars, the Silks, the Wools, it is necessary that the accomptant reckon his tares of chests, bags, and such other things: So when the Geometricall Philosopher would observe in concrete the effects demonstrated in abstract, he must defalke the impediments of the matter, and if he know how to do that, I do assure you, the things shall jump no lesse exactly, than Arithmetical computations. The errours therefore lyeth neither in abstract, nor in concrete, nor in Geometry, nor in Physicks, but in the Calculator, that knoweth not how to adjust his accompts. Therefore if you had a perfect Sphere and plane, though they were material, you need not doubt but that they would touch onely in one point. And if such a Sphere was and is impossible to be procured, it was much besides the purpose to say, Quod Sphæra ænea non tangit in puncto. Furthermore, if I grant you Simplicius, that in matter a figure cannot be procured that is perfectly spherical, or perfectly level: Do you think there may be had two materiall bodies, whose superficies in some part, and in some sort are incurvated as irregularly as can be desired?

Simpl.Of these I believe that there is no want.

Contact in a single point is not peculiar to the perfect Spheres onely, but belongeth to all curved figures.Salv.If such there be, then they also will touch in one sole point; for this contact in but one point alone is not the sole and peculiar priviledge of the perfect Sphere and perfect plane. Nay, he that should prosecute this point with more subtil contemplations would finde that it is much harder to procure two bodies that touch with part of their snperficies,It is more difficult to find Figures that touch with a part of their surface, than in one sole point. than with one point onely. For if two superficies be required to combine well together, it is necessary either, that they be both exactly plane, or that if one be convex, the other be concave; but in such a manner concave, that the concavity do exactly answer to the convexity of the other: the which conditions are much harder to be found, in regard of their too narrow determination, than those others, which in their casuall latitude are infinite.

Simpl.You believe then, that two stones, or two pieces of Iron taken at chance, and put together, do for the most part touch in one sole point?

Salv.In casual encounters, I do not think they do; as well because for the most part there will be some small yielding filth upon them, as because that no diligence is used in applying them without striking one another; and every small matter sufficeth to make the one superficies yield somewhat to the other; so that they interchangeably, at least in some small particle, receive figure from the impression of each other. But in case their superficies were very terse and polite, and that they were both laid upon a table, that so one might not presse upon the other, and gently put towards one another, I question not, but that they might be brought to the simple contact in one onely point.

Sagr.It is requisite, with your permission, that I propound a certain scruple of mine, which came into my minde, whil'st I heard proposed by Simplicius, the impossibility of finding a materiall and solid body, that is, perfectly of a Spherical figure, and whil'st I saw Salviatus in a certain manner, not gainsaying, to give his consent thereto; therefore I would know, whether there would be the same difficulty in forming a solid of some other figure, that is, to expresse my self better, whether there is more difficulty in reducing a piece of Marble into the figure of a perfect Sphere, than into a perfect Pyramid, or into a perfect Horse, or into a perfect Grasse-hopper?

Salv.To this I will make you the first answer: and in the first place, I will acquit my self of the assent which you think I gave to Simplicius, which was only for a time; for I had it also in my thoughts, before I intended to enter upon any other matter, to speak that, which, it may be, is the same, or very like to that which you are about to say;The Sphericall Figure is easier to be made than any other. And answering to your first question, I say, that if any figure can be given to a Solid, the Spherical is the easiest of all others, as it is likewise the most simple, and holdeth the same place amongst solid figures,The circular Figure only is placed amongst the postulata of Mathematicians. as the Circle holdeth amongst the superficial. The description of which Circle, as being more easie than all the rest, hath alone been judged by Mathematicians worthy to be put amongst the ** Demands or Petitions. postulata belonging to the description of all other figures. And the formation of the Sphere is so very easie, that if in a plain plate of hard metal you take an empty or hollow circle, within which any Solid goeth casually revolving that was before but grosly rounded, it shall, without any other artifice be reduced to a Spherical figure, as perfect as is possible for it to be; provided, that that same Solid be not lesse than the Sphere that would passe thorow that Circle. And that which is yet more worthy of our consideration is, that within the self-same incavity one may form Spheres of several magnitudes.Sphericall Figures of sundry magnitudes may be made with one onely instrument. But what is required to the making of an Horse, or (as you say) of a Grass-hopper, I leave to you to judge, who know that there are but few statuaries in the world able to undertake such a piece of work. And I think that herein Simplicius will not dissent from me.

Simpl.I know not whether I do at all dissent from you; my opinion is this, that none of the afore-named figures can be perfectly obteined; but for the approaching as neer as is possible to the most perfect degree, I believe that it is incomparably more easie to reduce the Solid into a Spherical figure, than into the shape of an Horse, or Grasse-hopper?

Sagr.And this greater difficulty, wherein think you doth it depend?

Simpl.Like as the great facility in forming the Sphere ariseth from its absolute simplicity and uniformity so the great irregularity rendereth the construction of all other figures difficult.Irregular forms difficult to be introduced.

Sagr.Therefore the irregularity being the cause of the difficulty, than the figure of a stone broken with an hammer by chance, shall be one of the figures that are difficult to be introduced, it being perhaps more irregular than that of the horse?

Simpl.So it should be.

Sagr.But tell me; that figure what ever it is which the stone hath, hath it the same in perfection, or no?

Simpl.What it hath, it hath so perfectly, that nothing can be more exact.

Sagr.Then, if of figures that are irregular, and consequently hard to be procured, there are yet infinite which are most perfectly obteined, with what reason can it be said, that the most simple, and consequently the most easie of all, is impossible to be procured?

Salv.Gentlemen, with your favour, I may say that we have sallied out into a dispute not much more worth than the wool of a goat; and whereas our argumentations should continually be conversant about serious and weighty points, we consume our time in frivolous and impertinent wranglings.The constitution of the Universe is one of the most noble Problems. Let us call to minde, I pray you, that the search of the worlds constitution, is one of the greatest and noblest Problems that are in nature; and so much the greater, inasmuch as it is directed to the resolving of that other; to wit, of the cause of the Seas ebbing and flowing, enquired into by all the famous men, that have hitherto been in the world, and possibly found out by none of them. Therefore if we have nothing more remaining for the full confutation of the argument taken from the Earths vertigo, which was the last, alledged to prove its immobility upon its own centre, let us passe to the examination of those things that are alledged for, and against the Annual Motion.

Sagr.I would not have you, Salviatus, measure our wits by the scale of yours: you, who use to be continually busied about the sublimest contemplations, esteem those notions frivolous and below you, which we think matters worthy of our profoundest thoughts: yet sometimes for our satisfaction do not disdain to stoop so low as to give way a little to our curiosity. As to the refutation of the last argument, taken from the extrusions of the diurnal vertigo, far less than what hath been said, would have given me satisfaction: and yet the things superfluously spoken, seemed to me so ingenious, that they have been so far from wearying my fancy, as that they have, by reason of their novelty, entertained me all along with so great delight, that I know not how to desire greater: Therefore, if you have any other speculation to add, produce it, for I, as to my own particular, shall gladly hearken to it.

Salv.I have always taken great delight in those things which I have had the fortune to discover, and next to that, which is my chief content, I find great pleasure in imparting them to some friends, that apprehendeth and seemeth to like them: Now, in regard you are one of these, slacking a little the reins of my ambition, which is much pleased when I shew my self more perspicacious, than some other that hath the reputation of a sharp sight, I will for a full and true measure of the past dispute, produce another fallacy of the Sectators of Ptolomey and Aristotle, which I take from the argument alledged.

Sagr.See how greedily I wait to hear it.

Salv.We have hitherto over-passed, and granted to Ptolomey, as an effect indubitable, that the extrusion of the stone proceeding from the velocity of the wheel turn'd round upon its centre, the cause of the said extrusion encreaseth in proportion, as the velocity of the vertigo (or whirling) is augmented: from whence it was inferred, that the velocity of the Earth's vertigo being very much greater than that of any machin whatsoever, that we can make to turn round artificially; the extrusion of stones, of animals, &c. would consequently be far more violent. Now, I observe that there is a great fallacy in this discourse, in that we do compare these velocities indifferently and absolutely to one another. It's true, that if I compare the velocities of the same wheel, or of two wheels equal to each other, that which shall be more swiftly turn'd round, shall extrude the stone with greater violence; and the velocity encreasing, the cause of the projection shall likewise encrease: but when the velocity is augmented, not by encreasing the velocity in the same wheel, which would be by causing it to make a greater number of revolutions in equal times; but by encreasing the diameter, and making the wheel greater, so as that the conversion taking up the same time in the lesser wheel, as in the greater,The cause of the projection increaseth not according to the proportion of the velocity, increased by making the wheel bigger. the velocity is greater onely in the bigger wheel, for that its circumference is bigger; there is no man that thinketh that the cause of the extrusion in the great wheel will encrease according to the proportion of the velocity of its circumference, to the velocity of the circumference of the other lesser wheel; for that this is most false, as by a most expeditious experiment I shall thus grosly declare: We may sling a stone with a stick of a yard long, farther than we can do with a stick six yards long, though the motion of the end of the long stick, that is of the stone placed in the slit thereof, were more than double as swift as the motion of the end of the other shorter stick, as it would be if the velocities were such that the lesser stick should turn thrice round in the time whilst the greater is making one onely conversion.

Sagr.This which you tell me, Salviatus, must, I see, needs succeed in this very manner; but I do not so readily apprehend the cause why equal velocities should not operate equally in extruding projects, but that of the lesser wheel much more than the other of the greater wheel; therefore I intreat you to tell me how this cometh to pass?

Simpl.Herein, Sagredus, you seem to differ much from your self, for that you were wont to penetrate all things in an instant, and now you have overlook'd a fallacy couched in the experiment of the stick, which I my self have been able to discover: and this is the different manner of operating, in making the projection one while with the short sling and another while with the long one, for if you will have the stone fly out of the slit, you need not continue its motion uniformly, but at such time as it is at the swiftest, you are to stay your arm, and stop the velocity of the stick; whereupon the stone which was in its swiftest motion, flyeth out, and moveth with impetuosity: but now that stop cannot be made in the great stick, which by reason of its length and flexibility, doth not entirely obey the check of the arm, but continueth to accompany the stone for some space, and holdeth it in with so much less force, and not as if you had with a stiff sling sent it going with a jerk: for if both the sticks or slings should be check'd by one and the same obstacle, I do believe they would fly aswell out of the one, as out of the other, howbeit their motions were equally swift.

Sagr.With the permission of Salviatus, I will answer something to Simplicius, in regard he hath addressed himself to me; and I say, that in his discourse there is somewhat good and somewhat bad: good, because it is almost all true; bad, because it doth not agree with our case: Truth is, that when that which carrieth the stones with velocity, shall meet with a check that is immoveable, they shall fly out with great impetuosity: the same effect following in that case, which we see dayly to fall out in a boat that running a swift course, runs a-ground, or meets with some sudden stop, for all those in the boat, being surprized, Granting the diurnal vertigo of the Earth, & that by some sudden stop or obstacle it were arrested, houses, mountains themselves, and perhaps the whole Globe would be shaken in pieces. stumble forwards, and fall towards the part whither the boat steered. And in case the Earth should meet with such a check, as should be able to resist and arrest its vertigo, then indeed I do believe that not onely beasts, buildings and cities, but mountains, lakes and seas would overturn, and the globe it self would go near to shake in pieces; but nothing of all this concerns our present purpose, for we speak of what may follow to the motion of the Earth, it being turn'd round uniformly, and quietly about its own centre, howbeit with a great velocity. That likewise which you say of the slings, is true in part; but was not alledged by Salviatus, as a thing that punctually agreed with the matter whereof we treat, but onely, as an example, for so in gross it may prompt us in the more accurate consideration of that point, whether, the velocity increasing at any rate, the cause of the projection doth increase at the same rate: so that v. g. if a wheel of ten yards diameter, moving in such a manner that a point of its circumference will pass an hundred yards in a minute of an hour, and so hath an impetus able to extrude a stone, that same impetus shall be increased an hundred thousand times in a wheel of a million of yards diameter; the which Salviatus denieth, and I incline to his opinion; but not knowing the reason thereof, I have requested it of him, and stand impatiently expecting it.

Salv.I am ready to give you the best satisfaction, that my abilities will give leave: And though in my first discourse you thought that I had enquired into things estranged from our purpose, yet neverthelesse I believe that in the sequel of the dispute, you will find that they do not prove so. Therefore let Sagredus tell me wherein he hath observed that the resistance of any moveable to motion doth consist.

Sagr.I see not for the present that the moveable hath any internal resistance to motion, unlesse it be its natural inclination and propension to the contrary motion, as in grave bodies, that have a propension to the motion downwards, the resistance is to the motion upwards; and I said an internal resistance, because of this, I think, it is you intend to speak, and not of the external resistances, which are many and accidental.

Salv.It is that indeed I mean, and your nimblenesse of wit hath been too hard for my craftinesse, but if I have been too short in asking the question, I doubt whether Sagredus hath been full enough in his answer to satisfie the demand; and whether there be not in the moveable, besides the natural inclination to the contrary term, another intrinsick and natural quality,The inclination of grave bodies to the motion downwards, is equal to their resistance to the motion upwards. which maketh it averse to motion. Therefore tell me again; do you not think that the inclination v. g. of grave bodies to move downwards, is equal to the resistance of the same to the motion of projection upwards?

Sagr.I believe that it is exactly the same. And for this reason I see that two equal weights being put into a ballance, they do stand still in equilibrium, the gravity of the one resisting its being raised by the gravity wherewith the other pressing downwards would raise it.

Salv.Very well; so that if you would have one raise up the other, you must encrease the weight of that which depresseth, or lessen the weight of the other. But if the resistance to ascending motion cunsist onely in gravity, how cometh it to passe, that in ballances of unequal arms, to wit in the * A portable ballance wherewith market-people weigh their commodities, giving it gravity by removing the weight farther from the cock: call'd by the Latines, Campana trutina.* Stiliard, a weight sometimes of an hundred pounds, with its pression downwards, doth not suffice to raise up on of four pounds; that shall counterpoise with it, nay this of four, descending shall raise up that of an hundred; for such is the effect of the pendant weight upon the weight which we would weigh? If the resistance to motion resideth onely in the gravity, how can the arm with its weight of four pounds onely, resist the weight of a sack of wool, or bale of silk, which shall be eight hundred, or a thousand weight; yea more, how can it overcome the sack with its moment, and raise it up? It must therefore be confest Sagredus, that here it maketh use of some other resistance, and other force, besides that of simple gravity.

Sagr.It must needs be so; therefore tell me what this second virtue should be.

Salv.It is that which was not in the ballance of equal arms; you see then what variety there is in the Stiliard; and upon this doubtlesse dependeth the cause of the new effect.

Sagr.I think that your putting me to it a second time, hath made me remember something that may be to the purpose. In both these beams the business is done by the weight, and by the motion; in the ballance, the motions are equal, and therefore the one weight must exceed it in gravity before it can move it; in the stiliard, the lesser weight will not move the greater, unless when this latter moveth little, as being hung at a lesser distance, and the other much, as hanging at a greater distance from the lacquet or cock. It is necessary therefore to conclude, that the lesser weight overcometh the resistance of the greater, by moving much, whilst the other is moved but little.

Salv.Which is as much as to say, that the velocity of the moveable less grave, compensateth the gravity of the moveable more grave and less swift.

Sagr.But do you think that the velocity doth fully make good the gravity?The greater velocity exactly compensates the greater gravity. that is, that the moment and force of a moveable of v. g. four pounds weight, is as great as that of one of an hundred weight, whensoever that the first hath an hundred degrees of velocity, and the later but four onely?

Salv.Yes doubtless, as I am able by many experiments to demonstrate: but for the present, let this onely of the stiliard suffice: in which you see that the light end of the beam is then able to sustain and equilibrate the great Wool-sack, when its distance from the centre, upon which the stiliard resteth and turneth, shall so much exceed the lesser distance, by how much the absolute gravity of the Wool-sack exceedeth that of the pendent weight. And we see nothing that can cause this insufficiencie in the great sack of Wool, to raise with its weight the pendent weight so much less grave, save the disparity of the motions which the one and the other should make, whilst that the Wool-sack by descending but one inch onely, will raise the pendent weight an hundred inches: (supposing that the sack did weigh an hundred times as much, and that the distance of the small weight from the centre of the beam were an hundred times greater, than the distance between the said centre and the point of the sacks suspension.) And again, the pendent weight its moving the space of an hundred inches, in the time that the sack moveth but one inch onely, is the same as to say, that the velocity of the motion of the little pendent weight, is an hundred times greater than the velocity of the motion of the sack. Now fix it in your belief, as a true and manifest axiom, that the resistance which proceedeth from the velocity of motion, compensateth that which dependeth on the gravity of another moveable: So that consequently, a moveable of one pound, that moveth with an hundred degrees of velocity, doth as much resist all obstruction, as another moveable of an hundred weight, whose velocity is but one degree onely. And two equal moveables will equally resist their being moved, if that they shall be moved with equal velocity: but if one be to be moved more swiftly than the other, it shall make greater resistance, according to the greater velocity that shall be conferred on it. These things being premised, let us proceed to the explanation of our Problem; and for the better understanding of things, let us make a short Scheme thereof. Let two unequal wheels be described about this centre A, [in Fig. 7.] and let the circumference of the lesser be BG, and of the greater CEH, and let the semidiameter ABC, be perpendicular to the Horizon; and by the points B and C, let us draw the right lined Tangents BF and CD; and in the arches BG and CE, take two equal parts BG and CE: and let the two wheels be supposed to be turn'd round upon their centres with equal velocities, so as that two moveables, which suppose for example to be two stones placed in the points B and C, come to be carried along the circumferences BG and CE, with equal velocities; so that in the same time that the stone B shall have run the arch BG, the stone C will have past the arch CE. I say now, that the whirl or vertigo of the lesser wheel is much more potent to make the projection of the stone B, than the vertigo of the bigger wheel to make that of the stone C. Therefore the projection, as we have already declared, being to be made along the tangent, when the stones B and C are to separate from their wheel, and to begin the motion of projection from the points B and C, then shall they be extruded by the impetus conceived from the vertigo by (or along) the tangents BF and CD. The two stones therefore have equal impetuosities of running along the tangents BF and CD, and would run along the same, if they were not turn'd aside by some other force: is it not so Sagredus?

Sagr.In my opinion the businesse is as you say.

Salv.But what force, think you, should that be which averts the stones from moving by the tangents, along which they are certainly driven by the impetus of the vertigo.

Sagr.It is either their own gravity, or else some glutinous matter that holdeth them fast and close to the wheels.

Salv.But for the diverting of a moveable from the motion to which nature inciteth it, is there not required greater or lesser force, according as the deviation is intended to be greater or lesser? that is, according as the said moveable in its deviation hath a greater or lesser space to move in the same time?

Sagr.Yes certainly: for it was concluded even now, that to make a moveable to move; the movent vertue must be increased in proportion to the velocity wherewith it is to move.

Salv.Now consider, that for the deviating the stone upon the lesse wheel from the motion of projection, which it would make by the tangent BF, and for the holding of it fast to the wheel, it is required, that its own gravity draw it back the whole length of the secant FG, or of the perpendicular raised from the point G, to the line BF, whereas in the greater wheel the retraction needs to be no more than the secant DE, or the perpendicular let fall from the tangent DC to the point E, lesse by much than FG, and alwayes lesser and lesser according as the wheel is made bigger. And forasmuch as these retractions (as I may call them) are required to be made in equal times, that is, whil'st the wheels passe the two equal arches BG and CE, that of the stone B, that is, the retraction FG ought to be more swift than the other DE; and therefore much greater force will be required for holding fast the stone B to its little wheel, than for the holding the stone C to its great one, which is as much as to say, that such a small thing will impede the extrusion in the great wheel, as will not at all hinder it in the little one. It is manifest therefore that the more the wheel augmenteth, the more the cause of the projection diminisheth.

Sagr.From this which I now understand, by help of your minute dissertation, I am induced to think, that I am able to satisfie my judgment in a very few words. For equal impetus being impressed on both the stones that move along the tangents, by the equal velocity of the two wheels, we see the great circumference, by means of its small deviation from the tangent, to go seconding, as it were, and in a fair way refraining in the stone the appetite, if I may so say, of separating from the circumference; so that any small retention, either of its own inclination, or of some glutination sufficeth to hold it fast to the wheel. Which, again, is not able to work the like effect in the little wheel, which but little prosecuting the direction of the tangent, seeketh with too much eagernesse to hold fast the stone; and the restriction and glutination not being stronger than that which holdeth the other stone fast to the greater wheel, it ** Strappar la cavezza, is to break the bridle. breaks loose, and runneth along the tangent. Therefore I do not only finde that all those have erred, who have believed the cause of the projection to increase according to the augmentation of the vertigo's velocity; but I am further thinking, that the projection diminishing in the inlarging of the wheel, so long as the same velocity is reteined in those wheels; it may possibly be true, that he that would make the great wheel extrude things like the little one, would be forced to increase them as much in velocity; as they increase in diameter, which he might do, by making them to finish their conversions in equal times; and thus we may conclude, that the Earths revolution or vertigo would be no more able to extrude stones, than any little wheel that goeth so slowly, as that it maketh but one turn in twenty four hours.

Salv.We will enquire no further into this point for the present: let it suffice that we have abundantly (if I deceive not my self) demonstrated the invalidity of the argument, which at first sight seemed very concluding, and was so held by very famous men: and I shall think my time and words well bestowed, if I have but gained some belief in the opinion of Simplicius, I will not say of the Earths mobility, but only that the opinion of those that believe it, is not so ridiculous and fond, as the rout of vulgar Philosophers esteem it.

Simpl.The answers hitherto produced against the arguments brought against this Diurnal Revolution of the Earth taken from grave bodies falling from the top of a Tower, and from projections made perpendicularly upwards, or according to any inclination sidewayes towards the East, West, North, South, &c. have somewhat abated in me the antiquated incredulity I had conceived against that opinion: but other greater doubts run in my mind at this very instant, which I know not in the least how to free my self of, and haply you your self will not be able to resolve them; nay, its possible you may not have heard them, for they are very modern. And these are the objections of two Authours, that ex professo write against Copernicus.Other objections of two modern Authors against Copernicus. Some of which are read in a little Tract of natural conclusions; The rest are by a great both Philosopher and Mathematician, inserted in a Treatise which he hath written in favour of Aristotle, and his opinion touching the inalterability of the Heavens, where he proveth, that not onely the Comets, but also the new stars, namely, that anno 1572. in Cassiopeia, and that anno 1604. in Sagittarius were not above the Spheres of the Planets, but absolutely beneath the concave of the Moon in the Elementary Sphere, and this he demonstrateth against Tycho, Kepler, and many other Astronomical Observators, and beateth them at their own weapon; to wit, the Doctrine of Parallaxes. If you like thereof, I will give you the reasons of both these Authours, for I have read them more than once, with attention; and you may examine their strength, and give your opinion thereon.

Salv.In regard that our principal end is to bring upon the stage, and to consider what ever hath been said for, or against the two Systemes, Ptolomaick, and Copernican, it is not good to omit any thing that hath been written on this subject.

Simpl.I will begin therefore with the objections which I finde in the Treatise of Conclusions, and afterwards proceed to the rest.The first objection of the modern Author of the little tract of Conclusions. In the first place then, he bestoweth much paines in calculating exactly how many miles an hour a point of the terrestrial Globe situate under the Equinoctial, goeth, and how many miles are past by other points situate in other parallels: and not being content with finding out such motions in horary times, he findeth them also in a minute of an hour; and not contenting himself with a minute, he findes them also in a second minute; yea more, he goeth on to shew plainly, how many miles a Cannon bullet would go in the same time,A Cannon bullet would spend more than six days in falling from the Concave of the Moon to the centre of the Earth, according to the opinion of that modern Author of the Conclusions. being placed in the concave of the Lunar Orb, supposing it also as big as Copernicus himself representeth it, to take away all subterfuges from his adversary. And having made this most ingenious and exquisite supputation, he sheweth, that a grave body falling from thence above would consume more than six dayes in attaining to the centre of the Earth, to which all grave bodies naturally move. Now if by the absolute Divine Power, or by some Angel, a very great Cannon bullet were carried up thither, and placed in our Zenith or vertical point, and from thence let go at liberty, it is in his, and also in my opinion, a most incredible thing that it, in descending downwards, should all the way maintain it self in our vertical line, continuing to turn round with the Earth, about its centre, for so many dayes, describing under the Equinoctial a Spiral line in the plain of the great circle it self; and under other Parallels, Spiral lines about Cones, and under the Poles falling by a simple right line. He, in the next place, stablisheth and confirmeth this great improbability by proving, in the way of interrogations, many difficulties impossible to be removed by the followers of Copernicus; and they are, if I do well remember———.

Salv.Take up a little, good Simplicius, and do not load me with so many novelties at once: I have but a bad memory, and therefore I must not go too fast. And in regard it cometh into my minde, that I once undertook to calculate how long time such a grave body falling from the concave of the Moon, would be in passing to the centre of the Earth, and that I think I remember that the time would not be so long; it would be fit that you shew us by what rule this Author made his calculation.

Simpl.He hath done it by proving his intent à fortiori, a sufficient advantage for his adversaries, supposing that the velocity of the body falling along the vertical line, towards the centre of the Earth, were equal to the velocity of its circular motion, which it made in the grand circle of the concave of the Lunar Orb. Which by equation would come to passe in an hour, twelve thousand six hundred German miles, a thing which indeed savours of impossibility: Yet neverthelesse, to shew his abundant caution, and to give all advantages to his adversaries, he supposeth it for true, and concludeth, that the time of the fall ought however to be more than six dayes.

Salv.And is this the sum of his method? And doth he by this demonstration prove the time of the fall to be above six dayes?

Sagr.Me thinks that he hath behaved himself too modestly, for that having it in the power of his will to give what velocity he pleased to such a descending body, and might aswell have made it six moneths, nay, six years in falling to the Earth, he is content with six dayes. But, good Salviatus, sharpen my appetite a little, by telling me in what manner you made your computation, in regard you say, that you have heretofore cast it up: for I am confident that if the question had not required some ingenuity in working it, you would never have applied your minde unto it.

Salv.It is not enough, Sagredus, that the subjects be noble and great, but the businesse consists in handling it nobly. And who knoweth not, that in the dissection of the members of a beast, there may be discovered infinite wonders of provident and prudent Nature; and yet for one, that the Anatomist dissects, the butcher cuts up a thousand. Thus I, who am now seeking how to satisfie your demand, cannot tell with which of the two shapes I had best to appear on the Stage; but yet, taking heart from the example of Simplicius, his Authour, I will, without more delays, give you an account (if I have not forgot) how I proceeded. But before I go any further, I must not omit to tell you, that I much fear that Simplicius hath not faithfully related the manner how this his Authour found, that the Cannon bullet in coming from the concave of the Moon to the centre of the Earth, would spend more than six dayes: for if he had supposed that its velocity in descending was equal to that of the concave (as Simplicius saith he doth suppose) he would have shewn himself ignorant of the first, and more simple principles of Geometry; yea, I admire that Simplicius, in admitting the supposition which he speaketh of, doth not see the monstrous absurdity that is couched in it.

Simpl.Its possible that I may have erred in relating it; but that I see any fallacy in it, I am sure is not true.

Salv.Perhaps I did not rightly apprehend that which you said, Do you not say, that this Authour maketh the velocity of the bullet in descending equall to that which it had in turning round, being in the concave of the Moon, and that comming down with the same velocity, it would reach to the centre in six dayes?

Simpl.So, as I think, he writeth.

Salv.And do not you perceive a shamefull errour therein? But questionlesse you dissemble it: For it cannot be, but that you should know that the semidiameter of the Circle is lesse than the sixth part of the circumference;A shamefull errour in the Argument taken from the bullets falling out of the Moons concave. and that consequently, the time in which the moveable shall passe the semidiameter, shall be lesse than the sixth part of the time; in which, being moved with the same velocity, it would passe the circumference; and that therefore the bullet descending with the velocity, wherewith it moved in the concave, will arrive in lesse than four hours at the centre, supposing that in the concave one revolution should be consummate in twenty four hours, as he must of necessity have supposed it, for to keep it all the way in the same vertical line.

Simpl.Now I thorowly perceive the mistake: but yet I would not lay it upon him undeservedly, for it's possible that I may have erred in rehearsing his Argument, and to avoid running into the same mistakes for the future, I could wish I had his Book; and if you had any body to send for it, I would take it for a great favour.

Sagr.You shall not want a Lacquey that will runne for it with all speed: and he shall do it presently, without losing any time; in the mean time Salviatus may please to oblige us with his computation.

Simpl.If he go, he shall finde it lie open upon my Desk, together with that of the other Author, who also argueth against Copernicus.

Sagr.We will make him bring that also for the more certainty: and in the interim Salviatus shall make his calculation: I have dispatch't away a messenger.

Salv.Above all things it must be considered, that the motion of descending grave bodies is not uniform, but departing from rest they go continually accelerating:An exact compute of the time of the fall of the Canon bullet from the Moons concave to the Earths centre. An effect known and observed by all men, unlesse it be by the forementioned modern Authour, who not speaking of acceleration, maketh it even and uniforme. But this general notion is of no avail, if it be not known according to what proportion this increase of velocity is made; a conclusion that hath been until our times unknown to all Philosophers; and was first found out & demonstrated by the ** The Author. Academick, our common friend, who in some of his ** By these Writings, he every where meanes his Dialogues, De motu, which I promise to give you in my second Volume. writings not yet published, but in familiarity shewn to me, and some others of his acquaintance he proveth, how that the acceleration of the right motion of grave bodies, is made according to the numbers uneven beginning ab unitate, that is, any number of equal times being assigned, if in the first time the moveable departing from rest shall have passed such a certain space,Acceleration of the natural motion of grave bodies is made according to the odde numbers beginning at unity. as for example, an ell, in the second time it shall have passed three ells, in the third five, in the fourth seven, and so progressively, according to the following odd numbers; which in short is the same, as if I should say, that the spaces passed by the moveable departing from its rest,The spaces past by the falling grave body are as the squares of their times. are unto each other in proportion double to the proportion of the times, in which those spaces are measured; or we will say, that the spaces passed are to each other, as the squares of their times.

Sagr.This is truly admirable: and do you say that there is a Mathematical demonstration for it?

Salv.Yes, purely Mathematical; and not onely for this, but for many other very admirable passions, pertaining to natural motions, An intire and new Science of the Academick concerning local motion. and to projects also, all invented, and demonstrated by Our Friend, and I have seen and considered them all to my very great content and admiration, seeing a new compleat Doctrine to spring up touching a subject, upon which have been written hundreds of Volumes; and yet not so much as one of the infinite admirable conclusions that those his writings contain, hath ever been observed, or understood by any one, before Our Friend made them out.

Sagr.You make me lose the desire I had to understand more in our disputes in hand, onely that I may hear some of those demonstrations which you speak of; therefore either give them me presently, or at least promise me upon your word, to appoint a particular conference concerning them, at which Simplicius also may be present, if he shall have a mind to hear the passions and accidents of the primary effect in Nature.

Simpl.I shall undoubtedly be much pleased therewith, though indeed, as to what concerneth Natural Philosophy, I do not think that it is necessary to descend unto minute particularities, a general knowledg of the definition of motion, and of the distinction of natural and violent, even and accelerate, and the like, sufficing: For if this were not sufficient, I do not think that Aristotle would have omitted to have taught us what ever more was necessary.

Salv.It may be so. But let us not lose more time about this, which I promise to spend half a day apart in, for your satisfaction; nay, now I remember, I did promise you once before to satisfie you herein. Returning therefore to our begun calculation of the time, wherein the grave cadent body would pass from the concave of the Moon to the centre of the earth, that we may not proceed arbitrarily and at randon, but with a Logical method, we will first attempt to ascertain our selves by experiments often repeated, in how long time a ball v. g. of Iron descendeth to the Earth from an altitude of an hundred yards.

Sagr.Let us therefore take a ball of such a determinate weight, and let it be the same wherewith we intend to make the computation of the time of descent from the Moon.

Salv.This is not material, for that a ball of one, of ten, of an hundred, of a thousand pounds, will all measure the same hundred yards in the same time.

Simpl.But this I cannot believe, nor much less doth Aristotle think so, who writeth, that the velocities of descending grave bodies, are in the same proportion to one another, as their gravities.

Salv.If you will admit this for true,The error of Aristotle in affirming, falling grave bodies to move according to the proportion of their gravities. you must believe also, that two balls of the same matter, being let fall in the same moment, one of an hundred pounds, and another of one, from an altitude of an hundred yards, the great one arriveth at the ground, before the other is descended but one yard onely: Now bring your fancy, if you can, to imagine, that you see the great ball got to the ground, when the little one is still within less than a yard of the top of the Tower.

Sagr.That this proposition is most false, I make no doubt in the world; but yet that yours is absolutely true, I cannot well assure my self: nevertheless, I believe it, seeing that you so resolutely affirm it; which I am sure you would not do, if you had not certain experience, or some clear demonstration thereof.

Salv.I have both: and when we shall handle the business of motions apart, I will communicate them: in the interim, that we may have no more occasions of interrupting our discourse, we will suppose, that we are to make our computation upon a ball of Iron of an hundred (a) pounds, the which by (a) (b) Note that these Calculations are made in Italian weights and measures. And 100 pounds Haverdupoise make 131 l. Florentine. And 100 English yards makes 1502/5 Braces Florent. so that the brace or yard of our Author is 3/4 of our yard.reiterated experiments descendeth from the altitude of an hundred (b) yards, in five second-minutes of an hour. And because, as we have said, the spaces that are measured by the cadent moveable, increase in double proportion; that is, according to the squares of the times, being that the time of one first-minute is duodecuple to the time of five seconds, if we multiply the hundred yards by the square of 12, that is by 144, we shall have 14400, which shall be the number of yards that the same moveable shall pass in one first-minute of an hour: and following the same rule because one hour is 60 minutes, multiplying 14400, the number of yards past in one minute, by the square of 60, that is, by 3600, there shall come forth 51840000, the number of yards to be passed in an hour, which make 17280 miles. And desiring to know the space that the said ball would pass in 4 hours, let us multiply 17280 by 16, (which is the square of 4) and the product will be 276480 miles: which number is much greater than the distance from the Lunar concave to the centre of the Earth, which is but 196000 miles, making the distance of the concave 56 semidiameters of the Earth, as that modern Author doth; and the semidiameter of the Earth 3500 miles, of 3000 ** The Italian measure which I commonly translate yards. Braces to a †† The Italian mile is 1000/1056 of our mile. mile, which are our Italian miles.

Therefore, Simplicius, that space from the concave of the Moon to the centre of the Earth, which your Accomptant said could not be passed under more than six days, you see that (computing by experience, and not upon the fingers ends) that it shall be passed in much less than four hours; and making the computation exact, it shall be passed by the moveable in 3 hours, 22 min. prim. and 4 seconds.

Sagr.I beseech you, dear Sir, do not defraud me of this exact calculation, for it must needs be very excellent.

Salv.So indeed it is: therefore having (as I have said) by diligent tryal observed, that such a moveable passeth in its descent, the height of 100 yards in 5 seconds of an hour, we will say, if 100 yards are passed in 5 seconds; in how many seconds shall 588000000 yards (for so many are in 56 diameters of the Earth) be passed? The rule for this work is, that the third number must be multiplied by the square of the second, of which doth come 14700000000, which ought to be divided by the first, that is, by 100, and the root square of the quotient, that is, 12124 is the number sought, namely 12124 min. secun. of an hour, which are 3 hours, 22 min. prim. and 4 seconds.

Sagr.I have seen the working, but I know nothing of the reason for so working, nor do I now think it a time to ask it.

Salv.Yet I will give it, though you do not ask it, because it is very easie. Let us mark these three numbers with the Letters A first, B second, C third. A and C are the numbers of the spaces, B is the number of the time; the fourth number is sought, of the time also. And because we know, that look what proportion the space A, hath to the spuace C, the same proportion shall the square of the time B have to the sqare of the time, which is sought.

100.	5.	588000000.
A	B	C	25
1		14700000000 35956 10
22
241	60	12124 202 3
2422
24240

Therefore by the Golden Rule, let the number C be multiplied by the square of the number B, and let the product be divided by the number A, and the quotient shall be the square of the number sought, and its square root shall be the number it self that is sought. Now you see how easie it is to be understood.

Sagr.So are all truths, when once they are found out, but the difficulty lyeth in finding them I very well apprehend it, and kindly thank you. And if there remain any other curiosity touching this point, I pray you let us hear it; for if I may speak my mind, I will with the favour of Simplicius, that from your discourses I alwayes learn some new motion, but from those of his Philosophers, I do not remember that I have learn't any thing of moment.

Salv.There might be much more said touching these local motions; but according to agreement, we will reserve it to a particular conference; and for the present I will speak something touching the Author named by Simplicius, who thinketh he hath given a great advantage to the adverse party in granting that, that Canon bullet in falling from the concave of the Moon may descend with a velocity equal to the velocity wherewith it would turn round, staying there above, and moving along with the diurnal conversion. Now I tell him, that that same ball falling from the concave unto the centre, will acquire a degree of velocity much more than double the velocity of the diurnal motion of the Lunar concave;The falling moveable if it move with a degree of velocity acquired in a like time with an uniform motion, it shall paß a space double to that passed with the accelerated motion. and this I will make out by solid and not impertinent suppositions. You must know therefore that the grave body falling and acquiring all the way new velocity according to the proportion already mentioned, hath in any whatsoever place of the line of its motion such a degree of velocity, that if it should continue to move therewith, uniformly without farther encreasing it; in another time like to that of its descent, it would passe a space double to that passed in the line of the precedent motion of descent. And thus for example, if that ball in coming from the concave of the Moon to its centre hath spent three hours, 22 min. prim. and 4 seconds, I say, that being arrived at the centre, it shall find it self constituted in such a degree of velocity, that if with that, without farther encreasing it, it should continue to move uniformly, it would in other 3 hours, 22 min. prim. and 4 seconds, passe double that space, namely as much as the whole diameter of the Lunar Orb; and because from the Moons concave to the centre are 196000 miles, which the ball passeth in 3 hours 22 prim. min. and 4 seconds, therefore (according to what hath been said) the ball continuing to move with the velocity which it is found to have in its arrival at the centre, it would passe in other 3 hours 22 min. prim. and 4 seconds, a space double to that, namely 392000 miles; but the same continuing in the concave of the Moon, which is in circuit 1232000 miles, and moving therewith in a diurnal motion, it would make in the same time, that is in 3 hours 22 min. prim. and 4 seconds, 172880 miles, which are fewer by many than the half of the 392000 miles. You see then that the motion in the concave is not as the modern Author saith, that is, of a velocity impossible for the falling ball to partake of, &c.

Sagr.The discourse would pass for current, and would give me full satisfaction, if that particular was but salved, ofroof the moving of the moveable by a double space to that passed in falling in another time equal to that of the descent, in case it doth continue to move uniformly with the greatest degree of velocity acquired in descending. A proposition which you also once before supposed as true, but never demonstrated.

Salv.This is one of the demonstrations of Our Friend, and you shall see it in due time; but for the present, I will with some conjectures (not teach you any thing that is new, but) remember you of a certain contrary opinion, and shew you, that it may haply so be. A bullet of lead hanging in a long and fine thread fastened to the roof, if we remove it far from perpendicularity, and then let it go, have you not observed that, it declining, will pass freely, and well near as far to the other side of the perpendicular?

Sagr.I have observed it very well, and find (especially if the plummet be of any considerable weight) that it riseth so little less than it descended, so that I have sometimes thought, that the ascending arch is equal to that descending, and thereupon made it a question whether the vibrations might not perpetuate themselves; and I believe that they might,The motion of grave penduli might be perpetuated, impediments being removed. if that it were possible to remove the impediment of the Air, which resisting penetration, doth some small matter retard and impede the motion of the pendulum, though indeed that impediment is but small: in favour of which opinion the great number of vibrations that are made before the moveable wholly ceaseth to move, seems to plead.

Salv.The motion would not be perpetual, Sagredus, although the impediment of the Air were totally removed, because there is another much more abstruse.

Sagr.And what is that? as for my part I can think of no other?

Salv.You will be pleased when you hear it, but I shall not tell it you till anon: in the mean time, let us proceed. I have proposed the observation of this Pendulum, to the intent, that you should understand, that the impetus acquired in the descending arch, where the motion is natural, is of it self able to drive the said ball with a violent motion, as far on the other side in the like ascending arch; if so, I say, of it self, all external impediments being removed: I believe also that every one takes it for granted, that as in the descending arch the velocity all the way increaseth, till it come to the lowest point, or its perpendicularity; so from this point, by the other ascending arch, it all the way diminisheth, untill it come to its extreme and highest point: and diminishing with the same proportions, wherewith it did before increase, so that the dgrees of the velocities in the points equidistant from the point of perpendicularity, are equal to each other. Hence it seemeth to me (arguing with all due modesty) that I might easily be induced to believe,If the Terrestrial Globe were perforated, a grave body descending by that bore, would paß and ascend as far beyond the centre, as it did descend. that if the Terrestrial Globe were bored thorow the centre, a Canon bullet descending through that Well, would acquire by that time it came to the centre, such an impulse of velocity, that, it having passed beyond the centre, would spring it upwards the other way, as great a space, as that was wherewith it had descended, all the way beyond the centre diminishing the velocity with decreasements like to the increasements acquired in the descent: and the time spent in this second motion of ascent, I believe, would be equal to the time of descent. Now if the moveable by diminishing that its greatest degree of velocity which it 1
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1had in the centre, successively until it come to total extinction, do carry the moveable in such a time such a certain space, as it had gone in such a like quantity of time, by the acquist of velocity from the total privation of it until it came to that its greatest degree; it seemeth very reasonable, that if it should move always with the said greatest degree of velocity it would pass, in such another quantity of time, both those spaces: For if we do but in our mind successively divide those velocities into rising and falling degrees, as v. g. these numbers in the margine; so that the first sort unto 10 be supposed the increasing velocities, and the others unto one 1, be the increasing; and let those of the time of the descent, and the others of the time of the ascent being added all together, make as many, as if one of the two sums of them had been all of the greatest degrees, and therefore the whole space passed by all the degrees of the increasing velocities, and decreasing, (which put together is the whole diameter) ought to be equal to the space passed by the greatest velocities, that are in number half the aggregate of the increasing and decreasing velocities. I know that I have but obscurely expressed my self, and I wish I may be understood.

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5Sagr.I think I understand you very well; and also that I can in a few words shew, that I do understand you. You had a mind to say, that the motion begining from rest, and all the way increasing the velocity with equal augmentations, such as are those of continuate numbers beginning at 1, rather at 0, which representeth the state of rest, disposed as in the margine: and continued at pleasure, so as that the least degree may be 0, and the greatest v. g. 5, all these degrees of velocity wherewith the moveable is moved, make the sum of 15;but if the moveable should move with as many degrees in number as these are, and each of them equal to the biggest, which is 5, the aggregate of all these last velocities would be double to the others, namely 30. And therefore the moveable moving with a like time, but with uniform velocity, which is that of the highest degree 5, ought to pass a space double to that which it passeth in the accelerate time, which beginneth at the state of rest.

Salv.According to your quick and piercing way of apprehending things, you have explained the whole business with more plainness than I my self; and put me also in mind of adding something more: for in the accelerate motion, the augmentation being continual, you cannot divide the degrees of velocity, which continually increase, into any determinate number, because changing every moment, they are evermore infinite. Therefore we shall be the better able to exemplifie our intentions by describing a Triangle, which let be this ABC, [in Fig. 8.] taking in the Page 205 side AC, as many equal parts as we please, AD, DE, EF, FG, and drawing by the points D, E, F, G, right lines parallel to the 〈◊〉 BC. Now let us imagine the parts marked in the line AC, to be equal times, and let the parallels drawn by the points D, E, F, G, represent unto us the degrees of velocity accelerated, and increasing equally in equal times; and let the Point A be the state of rest, from which the moveable departing, hath v. g. in the time AD, acquired the degree of velocity DH, in the second time we will suppose, that it hath increased the velocity from DH, as far as to EI, and so supposing it to have grown greater in the succeeding times,The acceleration of grave bodies naturally descendent, increaseth from moment to moment. according to the increase of the lines FK, GL, &c. but because the acceleration is made continually from moment to moment, and not disjunctly from one certain part of time to another; the point A being put for the lowest moment of velocity, that is, for the state of rest, and AD for the first instant of time following; it is manifest, that before the acquist of the degree of velocity DH, made in the time AD, the moveable must have past by infinite other lesser and lesser degrees gained in the infinite instants that are in the time DA, answering the infinite points that are in the line DA; therefore to represent unto us the infinite degrees of velocity that precede the degree DH, it is necessary to imagine infinite lines successively lesser and lesser, which are supposed to be drawn by the infinite points of the line DA, and parallels to DH, the which infinite lines represent unto us the superficies of the Triangle AHD, and thus we may imagine any space passed by the moveable, with a motion which begining at rest, goeth uniformly accelerating, to have spent and made use of infinite degrees of velocity, increasing according to the infinite lines that begining from the point A, are supposed to be drawn parallel to the line HD, and to the rest IE, KF, LG, the motion continuing as far as one will.

Now let us compleat the whole Parallelogram AMBC, and let us prolong as far as to the side thereof BM, not onely the Parallels marked in the Triangle, but those infinite others imagined to be drawn from all the points of the side AC; and like as BC, was the greatest of those infinite parallels of the Triangle, representing unto us the greatest degree of velocity acquired by the moveable in the accelerate motion, and the whole superficies of the said Triangle, was the mass and sum of the whole velocity, wherewith in the time AC it passed such a certain space, so the parallelogram is now a mass and aggregate of a like number of degrees of velocity, but each equal to the greatest BC, the which mass of velocities will be double to the mass of the increasing velocities in the Triangle, like as the said Parallelogram is double to the Triangle: and therefore if the moveable, that falling did make use of the accelerated degrees of velocity, answering to the triangle ABC, hath passed in such a time such a space, it is very reasonable and probable, that making use of the uniform velocities answering to the parallelogram, it shall passe with an even motion in the same time a space double to that passed by the accelerate motion.

Sagr.I am entirely satisfied. And if you call this a probable Discourse, what shall the necessary demonstrations be? I wish that in the whole body of common Philosophy, I could find one that was but thus concludent.

In natural Sciences it is not necessary to seek Mathematicall evidence.Simpl.It is not necessary in natural Philosophy to seek exquisite Mathematical evidence.

Sagr.But this point of motion, is it not a natural question? and yet I cannot find that Aristotle hath demonstrated any the least accident of it. But let us no longer divert our intended Theme, nor do you fail, I pray you Salviatus, to tell me that which you hinted to me to be the cause of the Pendulum's quiescence, besides the resistance of the Medium ro penetration.

Salv.Tell me; of two penduli hanging at unequal distances, doth not that which is fastned to the longer threed make its vibrations more seldome?

The pendulum hanging at a longer threed, maketh its vibrations more seldome than the pendulum hanging at a shorter threed.Sagr.Yes, if they be moved to equall distances from their perpendicularity.

Salv.This greater or lesse elongation importeth nothing at all, for the same pendulum alwayes maketh its reciprocations in equall times, be they longer or shorter, that is, though the pendulum be little or much removed from its perpendicularity,The vibrations of the same pendulum are made with the same frequency, whether they be small or great. and if they are not absolutely equal, they are insensibly different, as experience may shew you: and though they were very unequal, yet would they not discountenance, but favour our cause. Therefore let us draw the perpendicular AB [in Fig. 9.] and hang from the point A, upon the threed AC, a plummet C, and another upon the same threed also, which let be E, and the threed AC, being removed from its perpendicularity, and then letting go the plummets C and E, they shall move by the arches CBD, EGF, and the plummet E, as hanging at a lesser distance, and withall, as (by what you said) lesse removed, will return back again faster, and make its vibrations more frequent than the plummet C, and therefore shall hinder the said plummet C, from running so much farther towards the term D, as it would do, if it were free: and thus the plummet E bringing unto it in every vibration continuall impediment,The cause which impedeth the pendulum, and reduceth it to rest. it shall finally reduce it to quiescence. Now the same threed, (raking away the middle plummet) is a composition of many grave penduli, that is, each of its parts is such a pendulum fastned neerer and neerer to the point A, and therefore disposed to make it, vibrations successively more and more frequent; and consequently is able to bring a continual impediment to the plummet C; and for a proof that this is so, if we do but observe the thread AC, we shall see it distended not directly, but in an arch; and if instead of the thread we take a chain, we shall discern the effect more perfectly;The thread or chain to which a pendulum is fastned, maketh an arch, and doth not stretch it selfe streight out in its vibrations. and especially removing the gravity C, to a considerable distance from the perpendicular AB, for that the chain being composed of many loose particles, and each of them of some weight, the arches AEC, and AFD, will appear notably incurvated. By reason therefore, that the parts of the chain, according as they are neerer to the point A, desire to make their vibrations more frequent, they permit not the lower parts of the said chain to swing so far as naturally they would: and by continual detracting from the vibrations of the plummet C, they finally make it cease to move, although the impediment of the air might be removed.

Sagr.The books are now come; here take them Simplicius, and find the place you are in doubt of.

Simpl.See, here it is where he beginneth to argue against the diurnal motion of the Earth, he having first confuted the annual. Motus terræ annuus asserere Copernicanos cogit conversionem ejusdem quotidianam; alias idem terræ Hemisphærium continenter ad Solem esset conversum obumbrato semper averso. [In English thus:] The annual motion of the Earth doth compell the Copernicans to assert the daily conversion thereof; otherwise the same Hemisphere of the Earth would be continually turned towards the Sun, the shady side being always averse. And so one half of the Earth would never come to see the Sun.

Salv.I find at the very first sight, that this man hath not rightly apprehended the Copernican Hypothesis, for if he had but taken notice how he alwayes makes the Axis of the terrestrial Globe perpetually parallel to it self, he would not have said, that one half of the Earth would never see the Sun, but that the year would be one entire natural day, that is, that thorow all parts of the Earth there would be six moneths day, and six moneths night, as it now befalleth to the inhabitants under the Pole, but let this mistake be forgiven him, and let us come to what remaineth.

Simpl.It followeth, Hanc autem gyrationem Terræ impossibilem esse sic demonstramus. Which speaks in English thus: That this gyration of the Earth is impossible we thus demonstrate. That which ensueth is the declaration of the following figure, wherein is delineated many descending grave bodies, and ascending light bodies, and birds that fly to and again in the air, &c.

Sagr.Let us see them, I pray you. Oh! what fine figures, what birds, what balls, and what other pretty things are here?

Simpl.These are balls which come from the concave of the Moon.

Sagr.and what is this?

Simpl.This is a kind of Shell-fish, which here at Venice they call buovoli; and this also came from the Moons concave.

Sagr.Indeed, it seems then, that the Moon hath a great power over these Oyster-fishes, which we call ** Pesci armai, or armati. armed sishes.

Simpl.And this is that calculation, which I mentioned▪ of this Journey in a natural day, in an hour, in a first minute, and in a second, which a point of the Earth would make placed under the Equinoctial, and also in the parallel of 48 gr. And then followeth this, which I doubted I had committed some mistake in reciting, therefore let us read it. His positis, necesse est, terra circulariter mota, omnia ex aëre eidem, &c. Quod si hasce pilas æquales ponemus pondere, magnitudine, gravitate, & in concavo Sphæræ Lunaris positas libero descensui permittamus, si motum deorsum æquemus celeritate motui circum, (quod tamen secus est, cum pila A, &c.) elabentur minimum (ut multum cedamus adversariis) dies sex: quo tempore sexies circa terram, &c. [In English thus.] These things being supposed, it is necessary, the Earth being circularly moved, that all things from the air to the same, &c. So that if we suppose these balls to be equal in magnitude and gravity, and being placed in the concave of the Lunar Sphere, we permit them a free descent, and if we make the motion downwards equal in velocity to the motion about, (which nevertheless is otherwise, if the ball A, &c.) they shall be falling at least (that we may grant much to our adversaries) six dayes; in which time they shall be turned six times about the Earth, &c.

Salv.You have but too faithfully cited the argument of this person. From hence you may collect Simplicius, with what caution they ought to proceed, who would give themselves up to believe others in those things, which perhaps they do not believe themselves. For me thinks it a thing impossible, but that this Author was advised, that he did design to himself a circle, whose diameter (which amongst Mathematicians, is lesse than one third part of the circumference) is above 72 times bigger than it self: an errour that affirmeth that to be considerably more than 200 which is lesse than one.

Sagr.It may be, that these Mathematical proportions, which are true in abstract, being once applied in concrete to Physical and Elementary circles, do not so exactly agree: And yet, I think, that the Cooper, to find the semidiameter of the bottom, which he is to fit to the Cask, doth make use of the rule of Mathematicians in abstract, although such bottomes be things meerly material, and concrete: therefore let Simplicius plead in excuse of this Author; and whether he thinks that the Physicks can differ so very much from the Mathematicks.

Simpl.The substractions are in my opinion insufficient to salve this difference, which is so extreamly too great to be reconciled: and in this case I have no more to say but that, Quandoque bonus dormitet Homerus. But supposing the calculation of ** Not Sagredus, as the Latine ha h it.Salviatus to be more exact, and that the time of the descent of the ball were no more than three hours; yet me thinks, that coming from the concave of the Moon, which is so great a distance off, it would be an admirable thing, that it should have an instinct of maintaining it self all the way over the self-same point of the Earth, over which it did hang in its departure thence, and not rather be left a very great way behind.

Salv.The effect may be admirable, and not admirable, but natural and ordinary, according as the things precedent may fall out. For if the ball (according to the Authors suppositions) whilst it staid in the concave of the Moon, had the circular motion of twenty four hours together with the Earth, and with the rest of the things contained within the said Concave; that very vertue which made it turn round before its descent, will continue it in the same motion in its descending. And so far it is from not keeping pace with the motion of the Earth, and from staying behind, that it is more likely to out-go it; being that in its approaches to the Earth, the motion of gyration is to be made with circles continually lesser and lesser; so that the ball retaining in it self that self-same velocity which it had in the concave, it ought to anticipate, as I have said, the vertigo or conversion of the Earth. But if the ball in the concave did want that circulation, it is not obliged in descending to maintain it self perpendicularly over that point of the Earth, which was just under it when the descent began. Nor will. Copernicus, or any of his followers affirm the same.

Simpl.But the Author maketh an objection, as you see, demanding on what principle this circular motion of grave and light bodies, doth depend: that is, whether upon an internal or an external principle.

Salv.Keeping to the Probleme of which we speak, I say, that that very principle which made the ball turn round, whil'st it was in the Lunar concave, is the same that maintaineth also the circulation in the descent: yet I leave the Author at liberty to make it internal or external at his pleasure.

Simpl.The Author proveth, that it can neither be inward nor outward.

Salv.And I will say then, that the ball in the concave did not move, and so he shall not be bound to shew how that in descending it continueth all the way vertically over one point, for that it will not do any such thing.

Simpl.Very well; But if grave bodies, and light can have no principle, either internal or external of moving circularly, than neither can the terrestrial Globe move with a circular motion: and thus you have the intent of the Author.

Salv.I did not say, that the Earth had no principle, either interne, or externe to the motion of gyration, but I say, that I do not know which of the two it hath; and yet my not knowing it hath not a power to deprive it of the same; but if this Author can tell by what principle other mundane bodies are moved round, of whose motion there is no doubt; I say, that that which maketh the Earth to move, is a vertue, like to that, by which Mars and Jupiter are moved, and wherewith he believes that the starry Sphere it self also doth move; and if he will but assure me, who is the mover of one of these moveables, I will undertake to be able to tell him who maketh the Earth to move. Nay more; I will undertake to do the same, if he can but tell me, who moveth the parts of the Earth downwards.

Simpl.The cause of this is most manifest, and every one knows that it is gravity.

Salv.You are out, Simplicius, you should say, that every one knowes, that it is called Gravity: but I do not question you about the name, but the essence of the thing, of which essence you know not a tittle more than you know the essence of the mover of the stars in gyration; unlesse it be the name that hath been put to this, and made familiar, and domestical, by the many experiences which we see thereof every hour in the day,:We know no more who moveth grave bodies downwards; than who moveth the Stars round, nor know we any thing of these causes, more than the names imposed on them by us. but not as if we really understand any more, what principle or vertue that is which moveth a stone downwards, than we know who moveth it upwards, when it is separated from the projicient, or who moveth the Moon round, except (as I have said) onely the name, which more particularly and properly we have assigned to the motion of descent, namely, Gravity; whereas for the cause of circular motion, in more general termes, we assign the Vertue impressed, and call the same an Intelligence, either assisting, or informing; and to infinite other motions we ascribe Nature for their cause.

Simpl.It is my opinion, that this Author asketh far lesse than that, to which you deny to make answer; for he doth not ask what is nominally and particularly the principle that moveth grave and light bodies circularly, but whatsoever it be, he desireth to know, whether you think it intrinsecal, or extrinsecal: For howbeit, v.gr. I do not know, what kind of thing that gravity is, by which the Earth descendeth; yet I know that it is an intern principle, seeing that if it be not hindered, it moveth spontaneously: and on the contrary, I know that the principle which moveth it upwards, is external; although that I do not know, what thing that vertue is, impressed on it by the projicient.

Salv.Into how many questions must we excurre, if we would decide all the difficulties, which successively have dependance one upon another! You call that an external (and you also call it a preternatural and violent) principle, which moveth the grave project upwards; but its possible that it may be no lesse interne and natural, than that which moveth it downwards; it may peradventure be called external and violent,The vertue which carrieth grave projects upwards, is no lesse natural to them, than the gravity which moveth them downwards. so long as the moveable is joyned to the projicient; but being separated, what external thing remaineth for a mover of the arrow, or ball? In summe, it must necessarliy be granted, that that vertue which carrieth such a moveable upwards, is no lesse interne, than that which moveth it downwards; and I think the motion of grave bodies ascending by the impetus conceived, to be altogether as natural, as the motion of descent depending on gravity.

Simpl.I will never grant this; for the motion of descent hath its principle internal, natural, and perpetual, and the motion of ascent hath its principle externe, violent, and finite.

Salv.If you refuse to grant me, that the principles of the motions of grave bodies downwards and upwards,Contrary principles cannot naturally reside in the same subject. are equally internal and natural; what would you do, if I should say, that they may also be the same in number?

Simpl.I leave it to you to judge.

Salv.But I desire you your self to be the Judge: Therefore tell me, Do you believe that in the same natural body, there may reside interne principles, that are contrary to one another?

Simpl.I do verily believe there cannot.

Salv.What do you think to be the natural inclination of Earth, of Lead, of Gold, and in sum, of the most ponderous matters; that is, to what motion do you believe that their interne principle draweth them?

Simpl.To that towards the centre of things grave, that is, to the centre of the Universe, and of the Earth, whither, if they be not hindered, it will carry them.

Salv.So that, if the Terrestrial Globe were bored thorow, and a Well made that should passe through the centre of it, a Cannon bullet being let fall into the same, as being moved by a natural and intrinsick principle, would passe to the centre; and it would make all this motion spontaneously, and by intrinsick principle, is it not so?

Simpl.So I verily believe.

Salv.But when it is arrived at the centre, do you think that it will passe any further, or else that there it would immediately stand still, and move no further?

Simpl.I believe that it would continue to move a great way further.

Salv.But this motion beyond the centre, would it not be upwards, and according to your assertion preternatural, and violent? And yet on what other principle do you make it to depend, but only upon the self same, which did carry the ball to the centre, and which you called intrinsecal, and natural? Finde, if you can, another external projicient, that overtaketh it again to drive it upwards. And this that hath been said of the motion thorow the centre,The natural motion changeth it selfe into that which is called preternatural and violent. is also seen by us here above; for the interne impetus of a grave body falling along a declining superficies, if the said superficies be reflected the other way, it shall carry it, without a jot interrupting the motion, also upwards. A ball of lead that hangeth by a thread, being removed from its perpendicularity, descendeth spontaneously, as being drawn by its internal inclination, and without any interposure of rest, passeth beyond the lowest point of perpendicularity: and without any additional mover, moveth upwards. I know that you will not deny, but that the principle of grave bodies that moveth them downwards, is no less natural, and intrinsecal, than that principle of light bodies, which moveth them upwards: so that I propose to your consideration a ball of lead, which descending through the Air from a great altitude, and so moving by an intern principle, and comming to a depth of water, continueth its descent, and without any other externe mover, submergeth a great way; and yet the motion of descent in the water is preternatural unto it; but yet nevertheless dependeth on a principle that is internal, and not external to the ball. You see it demonstrated then, that a moveable may be moved by one and the same internal principle, with contrary motions.

Simpl.I believe there are solutions to all these objections, though for the present I do not remember them; but however it be, the Author continueth to demand, on what principle this circular motion of grave and light bodies dependeth; that is, whether on a principle internal, or external; and proceeding forwards, sheweth, that it can be neither on the one, nor on the other, saying; Si ab externo; Deusne illum excitat per continuum miraculum? an verò Angelus, an aër? Et hunc quidem multi assignant. Sed contra———[In English thus] If from an externe principle; Whether God doth not excite it by a continued Miracle? or an Angel, or the Air? And indeed many do assign this. But on the contrary———.

Salv.Trouble not your self to read his argument; for I am none of those who ascribe that principle to the ambient air. As to the Miracle, or an Angel, I should rather incline to this side; for that which taketh beginning from a Divine Miracle, or from an Angelical operation; as for instance, the transportation of a Cannon ball or bullet into the concave of the Moon, doth in all probability depend on the vertue of the same principle for performing the rest. But, as to the Air, it serveth my turn, that it doth not hinder the circular motion of the moveables, which we did suppose to move thorow it. And to prove that, it sufficeth (nor is more required) that it moveth with the same motion, and finisheth its circulations with the same velocity, that the Terrestrial Globe doth.

Simpl.And he likewise makes his opposition to this also; demanding who carrieth the air about, Nature, or Violence? And proveth, that it cannot be Nature, alledging that that is contrary to truth, experience, and to Copernicus himself.

Salv.It is not contrary to Copernicus in the least, who writeth no such thing; and this Author ascribes these things to him with two excessive courtesie. It's true, he saith, and for my part I think he saith well, that the part of the air neer to the Earth, being rather a terrestrial evaporation, may have the same nature, and naturally follow its motion; or, as being contiguous to it, may follow it in the same manner, as the Peripateticks say, that the superiour part of it, and the Element of fire, follow the motion of the Lunar Concave, so that it lyeth upon them to declare, whether that motion be natural, or violent.

Simpl.The Author will reply, that if Copernicus maketh only the inferiour part of the Air to move, and supposeth the upper part thereof to want the said motion, he cannot give a reason, how that quiet air can be able to carry those grave bodies along with it, and make them keep pace with the motion of the Earth.

Salv.Copernicus will say,The propension of elementary bodies to follow the Earth, hath a limited Sphere of activity. that this natural propension of the elementary bodies to follow the motion of the Earth, hath a limited Sphere, out of which such a natural inclination would cease; besides that, as I have said, the Air is not that which carrieth the moveables along with it; which being separated from the Earth, do follow its motion; so that all the objections come to nothing, which this Author produceth to prove, that the Air cannot cause such effects.

Simpl.To shew therefore, that that cannot be, it will be necessary to say, that such like effects depend on an interne principle, against which position, oboriuntur difficillimæ, immò inextricabiles quæstiones secundæ, of which sort are these that follow. Principium illud internum vel est accidens, vel substantia. Si primum; quale nam illud? nam qualitas locomotiva circum, hactenus nulla videtur agnita. (In English thus:) Contrary to which position there do arise most difficult, yea inextricable second questions, such as these; That intern principle is either an accident, or a substance. If the first; what manner of accident is it? For a locomotive quality about the centre, seemeth to be hitherto acknowledged by none.

Salv.How, is there no such thing acknowledged? Is it not known to us, that all these elementary matters move round, together with the Earth? You see how this Author supposeth for true, that which is in question.

Simpl.He saith, that we do not see the same; and me thinks, he hath therein reason on his side.

Salv.We see it not, because we turn round together with them.

Simpl.Hear his other Argument. Quæ etiam si esset, quomodò tamen inveniretur in rebus tam contrariis? in igne, ut in aquâ; in aëre, ut in terra; in viventibus, ut in animà carentibus? [in English thus:] Which although it were, yet how could it be found in things so contrary? in the fire, as in the water? in the air, as in the earth? in living creatures, as in things wanting life?

Salv.Supposing for this time, that water and fire are contraries; as also the air and earth; (of which yet much may be said) the most that could follow from thence would be, that those motions cannot be common to them, that are contrary to one another: so that v. g. the motion upwards, which naturally agreeth to fire, cannot agree to water; but that, like as it is by nature contrary to fire: so to it that motion suiteth, which is contrary to the motion of fire, which shall be the motion deorsum; but the circular motion, which is not contrary either to the motion sursum, or to the motion deorsum, but may mix with both, as Aristotle himself affirmeth, why may it not equally suit with grave bodies and with light? The motions in the next place, which cannot be common to things alive, and dead, are those which depend on the soul: but those which belong to the body, in as much as it is elementary, and consequently participateth of the qualities of the elements, why may not they be common as well to the dead corps, as to the living body? And therefore, if the circular motion be proper to the elements, it ought to be common to the mixt bodies also.

Sagr.It must needs be, that this Author holdeth, that a dead cat, falling from a window, it is not possible that a live cat also could fall; it not being a thing convenient, that a carcase should partake of the qualities which suit with things alive.

Salv.Therefore the discourse of this Author concludeth nothing against one that should affirm, that the principle of the circular motions of grave and light bodies is an intern accident: I know not how he may prove, that it cannot be a substance.

Simpl.He brings many Arguments against this. The first of which is in these words: Si secundum (nempè, si dicas tale principium esse substantiam) illud est aut materia, aut forma, aut compositum. Sed repugnant iterum tot diversæ rerum naturæ, quales sunt aves, limaces, saxa, sagittæ, nives, fumi, grandines, pisces, &c. quæ tamen omnia specie & genere differentia, moverentur à naturà suâ circulariter, ipsa naturis diversissima, &c. [In English thus] If the second, (that is, if you shall say that this principle is a substance) it is either matter, or form, or a compound of both. But such diverse natures of things are again repugnant, such as are birds, snails, stones, darts, snows, smoaks, hails, fishes, &c. all which notwithstanding their differences in species and kind, are moved of their own nature circularly, they being of their natures most different, &c.

Salv.If these things before named are of diverse natures, and things of diverse natures cannot have a motion in common, it must follow, if you would give satisfaction to all, that you are to think of, more than two motions onely of upwards and downwards: and if there must be one for the arrows, another for the snails, another for the stones, and another for fishes; then are you to bethink your self of worms, topazes and mushrums, which are not less different in nature from one another, than snow and hail.

Simpl.It seems that you make a jest of these Arguments.

Salv.No indeed, Simplicius, but it hath been already answered above, to wit, that if one motion, whether downwards or upwards, can agree with all those things afore named, a circular motion may no less agree with them: and as you are a Peripatetick, do not you put a greater difference between an elementary comet and a celestial star, than between a fish and a bird? and yet both those move circularly. Now propose your second Argument.

Simpl.Si terra staret per voluntatem Dei, rotaréntne cætera, an non? si hoc, falsum est à naturâ gyrare; si illud, redeunt priores quæstiones. Et sanè mirum esset, quòd Gavia pisciculo, Alauda nidulo suo, & corvus limaci, petraque, etiam volans, imminere non posset. [Which I thus render:] If the Earth be supposed to stand still by the will of God, should the rest of bodies turn round or no? If not, then it's false that they are revolved by nature; if the other, the former questions will return upon us. And truly it would be strange that the Sea-pie should not be able to hover over the small fish, the Lark over her nest, and the Crow over the snail and rock, though flying.

Salv.I would answer for my self in general terms, that if it were appointed by the will of God, that the Earth should cease from its diurnal revolution, those birds would do what ever should please the same Divine will. But if this Author desire a more particular answer, I should tell him, that they would do quite contrary to what they do now, if whilst they, being separated from the Earth, do bear themselves up in the air, the Terrestrial Globe by the will of God, should all on a sudden be put upon a precipitate motion; it concerneth this Author now to ascertain us what would in this case succeed.

Sagr.I pray you, Salviatus, at my request to grant to this Author, that the Earth standing still by the will of God, the other things, separated from it, would continue to turn round of their own natural motion, and let us hear what impossibilities or inconveniences would follow: for I, as to my own particular, do not see how there can be greater disorders, than these produced by the Author himself, that is, that Larks, though they should flie, could not be able to hover over their nests, nor Crows over snails, or rocks: from whence would follow, that Crows must suffer for want of snails, and young Larks must die of hunger, and cold, not being able to be fed or sheltered by the wings of the old ones. This is all the ruine that I can conceive would follow, supposing the Authors speech to be true. Do you see, Simplicius, if greater inconveniences would happen?

Simpl.I know not how to discover greater; but it is very credible, that the Author besides these, discovered other disorders in Nature, which perhaps in reverend respect of her, he was not willing to instance in. Therefore let us proceed to the third Objection. Insuper quî fit, ut istæ res tam variæ tantùm moveantur ab Occasu in Ortum, parallelæ ad Æquatorem? ut semper moveantur, nunquam quiescant? [which speaks to this sense:] Moreover, how comes it to pass that these things, so diverse, are onely moved from the West towards the East, parallel to the Æquinoctial? that they always move, and never rest?

Salv.They move from West to East parallel to the Aequinoctial without ceasing, in the same manner as you believe the fixed stars to move from East to West, parallel to the Æquinoctial, without ever resting.

Simpl.Quarè, quò sunt altiores, celeriùs; quò humiliores, tardiùs? (i. e.) Why are the higher the swifter, and the lower the slower?

Salv.Because that in a Sphere or circle, that turns about upon its own centre, the remoter parts describe greater circuits, and the parts nearer at hand describe lesser in the same time.

Simpl.Quare, quæ Æquinoctiali propriores, in majori; quæ remotiores, in minori circulo feruntur? [scilicet:] Why are those near the Æquinoctial carried about in a greater circle, and those which are remote in a lesser?

Salv.To imitate the starry Sphere, in which those nearest to the Æquinoctial, move in greater circles, than the more remote.

Simpl.Quarè Pila eadem sub Æquinoctiali tota circa centrum terræ, ambitu maximo, celeritate incredibili; sub Polo verò circa centrum proprium, gyro nullo, tarditate supremà volveretur? [That is:] Why is the same ball under the Æquinoctial wholly turned round the centre of the Earth in the greatest circumference, with an incredible celerity; but under the Pole about its own centre, in no circuite, but with the ultimate degree of tardity?

Salv.To imitate the stars of the Firmament, that would do the like if they had the diurnal motion.

Simpl.Quare eadem res, pila v. g. plumbea, si semel terram circuivit, descripto circulo maximo, eandem ubique non circummigret secundùm circulum maximum, sed translata extra Æquinoctialem in circulis minoribus agetur? [Which speaketh thus:] Why doth not the same thing, as for example, a ball of lead turn round every where according to the same great circle, if once describing a great circle, it hath incompassed the Earth, but being removed from the Æquinoctial, doth move in lesser circles?

Salv.Because so would, nay, according to the doctrine of Ptolomey, so have some fixed stars done, which once were very near the Æquinoctial, and described very vast circles, and now that they are farther off, describe lesser.

Sagr.If I could now but keep in mind all these fine notions, I should think that I had made a great purchase; I must needs intreat you, Simplicius, to lend me this Book, for there cannot chuse but be a sea of rare and ingenious matters contained in it.

Simpl.I will present you with it.

Sagr.Not so, Sir; I would not deprive you of it: but are the Queries yet at an end?

Simpl.No Sir; hearken therefore. Si latio circularis gravibus & levibus est naturalis, qualis est ea quæ fit secundùm lineam rectam? Nam si naturalis, quomodo & is motus qui circum est, naturalis est, cùm specie differat à recto? Si violentus, quî fit, ut missile ignitum sursum evolans scintillosum caput sursùm à terrâ, non autem circum volvatur, &c. [Which take in our idiom:] If a circular lation is natural to heavy and light things, what is that which is made according to a right line? For if it be natural, how then is that motion which is about the centre natural, seeing it differs in species from a right motion? If it be violent, how is it that a fiery dart flying upwards, sparkling over our heads at a distance from the Earth, but not turning about, &c.

Salv.It hath been said already very often,Of the mixt motion we see not the part that is circular, because we partake thereof. that the circular motion is natural to the whole, and to its parts, whilst they are in perfect disposure, and the right is to reduce to order the parts disordered; though indeed it is better to say, that neither the parts ordered or disordered ever move with a right motion, but with one mixed, which might as well be averred meerly circular: but to us but one part onely of this motion is visible and observable, that is, the part of the right, the other part of the circular being imperceptible to us, because we partake thereof. And this answers to the rays which move upwards, and round about, but we cannot distinguish their circular motion, for that, with that we our selves move also. But I believe that this Author never thought of this mixture; for you may see that he resolutely saith, that the rays go directly upwards, and not at all in gyration.

Simpl.Quare centrum sphære delapsæ sub AEquatore spiram describit in ejus plano: sub aliis parallelis spiram describit in cono? sub Polo descendit in axe lineam gyralem, decurrens in superficie cylindricâ consignatam? (In English to this purpose:) Why doth the centre of a falling Globe under the Æquinoctial describe a spiral line in the plane of the Æquator; and in other parallels a spiral about a Cone; and under the Pole descend in the axis describing a gyral line, running in a Cylindrical Superficie?

Salv.Because of the lines drawn from the Centre to the circumference of the sphere, which are those by which graves descend, that which terminates in the Æquinoctial designeth a circle, and those that terminate in other parallels describe conical superficies; now the axis describeth nothing at all, but continueth in its own being. And if I may give you my judgment freely, I will say, that I cannot draw from all these Queries, any sense that interfereth with the motion of the Earth; for if I demand of this Author, (granting him that the Earth doth not move) what would follow in all these particulars, supposing that it do move, as Copernicus will have it; I am very confident, that he would say that all these effects would happen, that he hath objected, as inconveniences to disprove its mobility: so that in this mans opinion necessary consequences are accounted absurdities: but I beseech you, if there be any more, dispatch them, and free us speedily from this wearisom task.

Simpl.In this which follows he opposes Copernicus & his Sectators, who affirm, that the motion of the parts separated from their whole, is onely to unite themselves to their whole; but that the moving circularly along with the vertigenous diurnal revolution is absolutely natural: against which he objecteth, saying, that according to these mens opinion; Si tota terra, unà cum aquà in nihilum redigeretur, nulla grando aut pluvia è nube decideret, sed naturalater tantùm circumferetur, neque ignis ullus, aut igneum ascenderet, cùm illorum non improbabili sententià ignis nullus sit suprà. [Which I translate to this sense:] If the whole Earth, together with the Water were reduced into nothing, no hail or rain would fall from the clouds, but would be onely naturally carried round; neither any fire or fiery thing would ascend, seeing to these that men it is no improbable opinion that there is no fire above.

Salv.The providence of this Philosopher is admirable, and worthy of great applause; for he is not content to provide for things that might happen, the course of Nature continuing, but will shew hic care in what may follow from those things that he very well knows shall never come to pass. I will grant him therefore, (that I may get som pretty passages out of him) that if the Earth and Water should be reduced to nothing, there would be no more hails or rains, nor would igneal matters ascend any longer upwards, but would continually turn round: what will follow? what will the Philosopher say then?

Simpl.The objection is in the words which immediately follow; here they are: Quibus tamen experientia & ratio adversatur. Which nevertheless (saith he) is contrary to experience and reason.

Salv.Now I must yield, seeing he hath so great an advantage of me as experience, of which I am unprovided. For as yet I never had the fortune to see the Terrestrial Globe and the element of Water turn'd to nothing, so as to have been able to observe what the hail and water did in that little Chaos. But he perhaps tells us for our instruction what they did.

Simpl.No, he doth not.

Salv.I would give any thing to change a word or two with this person, to ask him, whether when this Globe vanished, it carried away with it the common centre of gravity, as I believe it did; in which case, I think that the hail and water would remain insensate and stupid amongst the clouds, without knowing what to do with themselves. It might be also, that attracted by that great void Vacuum, left by the Earths absenting, all the ambients would be rarified, and particularly, the air, which is extreme easily drawn, and would run thither with very great haste to fill it up. And perhaps the more solid and material bodies, as birds, (for there would in all probability be many of them scattered up and down in the air) would retire more towards the centre of the great vacant sphere; (for it seemeth very reasonable, that substances that under small bulk contain much matter, should have narrower places assigned them, leaving the more spacious to the more ra•ified) and there being dead of hunger, and resolved into Earth, would form a new little Globe, with that little water, which at that time was among the clouds. It might be also, that those matters as not beholding the light, would not perceive the Earths departure, but like blind things, would descend according to their usual custom to the centre, whither they would now go, if that globe did not hinder them. And lastly, that I may give this Philosopher a less irresolute answer, I do tell him, that I know as much of what would follow upon the annihilation of the Terrestrial Globe, as he would have done that was to have followed in and about the same, before it was created. And because I am certain he will say, that he would never have been able to have known any of all those things which experience alone hath made him knowing in, he ought not to deny me pardon, and to excuse me if I know not that which he knows, touching what would ensue upon the annihilation of the said Globe: for that I want that experience which he hath. Let us hear if he have any thing else to say.

Simpl.There remains this figure, which represents the Terrestrial Globe with a great cavity about its centre, full of air; and to shew that Graves move not downwards to unite with the Terrestrial Globe, as Copernicus saith, he constituteth this stone in the centre; and demandeth, it being left at liberty, what it would do; and he placeth another in the space of this great vacuum, and asketh the same question. Saying, as to the first: Lapis in centro constitutus, aut ascendet ad terram in punctum aliquod, aut non. Si secundum; falsum est, partes ob solam sejunctionem à toto, ad illud moveri. Si primum; omnis ratio & experientia renititur, neque gravia in suæ gravitatis centro conquiescent. Item si suspensus lapis, liberatus decidat in centrum, separabit se à toto, contra Copernicum: si pendeat, refragatur omnis experientia, cùm videamus integros fornices corruere. (Wherein he saith:) The stone placed in the centre, either ascendeth to the Earth in some point, or no. If the second, it is false that the parts separated from the whole, move unto it. If the first; it contradicteth all reason and experience, nor doth the grave body rest in the centre of its gravity. And if the stone being suspended in the air, be let go, do descend to the centre, it will separate from its whole, contrary to Copernicus: if it do hang in the air, it contradicteth all experience: since we see whole Vaults to fall down.

Salv.I will answer, though with great disadvantage to my self, seeing I have to do with one who hath seen by experience, what these stones do in this great Cave: a thing, which for my part I have not seen; and will say, that things grave have an existence before the common centre of gravity:Things grave are before the centre of gravity. so that it is not one centre alone, which is no other than indivisible point, and therefore of no efficacie, that can attract unto it grave matters; but that those matters conspiring naturally to unite, form to themselves a common centre, which is that about which parts of equal moment consist:The great maß of grave bodies being transferred out of their place, the separated parts would follow that maß. so that I hold, that if the great aggregate of grave bodies were gathered all into any one place, the small parts that were separated from their whole, would follow the same, and if they were not hindered, would penetrate wherever they should find parts less grave than themselves: but coming where they should meet with matters more grave, they would descend no farther. And therefore I hold, that in the Cave full of air, the whole Vault would press, and violently rest it self onely upon that air, in case its hardness could not be overcome and broken by its gravity; but loose stones, I believe, would descend to the centre, and not swim above in the air: nor may it be said, that they move not to their whole, though they move whither all the parts of the whole would transfer themselves, if all impediments were removed.

Simpl.That which remaineth, is a certain Errour which he observeth in a Disciple of Copernicus, who making the Earth to move with an annual motion, and a diurnal, in the same manner as the Cart-wheel moveth upon the circle of the Earth, and in it self, did constitute the Terrestrial Globe too great, or the great Orb too little; for that 365 revolutions of the Æquinoctial, are less by far than the circumference of the great Orb.

Salv.Take notice that you mistake, and tell us the direct contrary to what must needs be written in that Book; for you should say, that that same Copernican Author did constitute the Terrestrial Globe too little, and the great Orb too big; and not the Terrestrial Globe too big, and the annual too little.

Simpl.The mistake is not mine; see here the words of the Book. Non videt, quòd vel circulum annuum æquo minorem, vel orbem terreum justo multò fabricet majorem. (In English thus:) He seeth not, that he either maketh the annual circle equal to the less, or the Terrestrial Orb much too big.

Salv.I cannot tell whether the first Author erred or no, since the Author of this Tractate doth not name him; but the error of this Book is certain and unpardonable, whether that follower of Copernicus erred or not erred; for that your Author passeth by so material an error, without either detecting or correcting it. But let him be forgiven this fault, as an error rather of inadvertencie, than of any thing else: Farthermore, were it not, that I am already wearied and tired with talking and spending so much time with very little profit, in these frivolous janglings and altercations, I could shew, that it is not impossible for a circle, though no bigger than a Cart-wheel,It is not impossible with the circumference of a small circle few times revolved to measure and describe a line bigger than any great circle whatsoever. with making not 365, but lesse than 20 revolutions, to describe and measure the circumference, not onely of the grand Orb, but of one a thousand times greater; and this I s y to shew, that there do not want far greater subtilties, than this wherewith your Author goeth about to detect the errour of Copernicus: but I pray you, let us breath a little, that so we may proceed to the other Philosopher, that opposeth of the same Copernicus.

Sagr.To confesse the truth, I stand as much in need of respite as either of you; though I have onely wearied my eares: and were it not that I hope to hear more ingenious things from this other Author, I question whether I should not go my ways, to take the air in my * Gondola.* Pleasure-boat.

Simpl.I believe that you will hear things of greater moment; for this is a most accomplished Philosopher, and a great Mathematician, and hath confuted Tycho in the businesse of the Comets, and new Stars.

* The name of the Author is Scipio Claramontius.Salv.Perhaps he is the same with the Author of the Book, called Anti-Tycho?

Simpl.He is the very same: but the confutation of the new Stars is not in his Anti-Tycho, onely so far as he proveth, that they were not prejudicial to the inalterability and ingenerability of the Heavens, as I told you before; but after he had published his Anti-Tycho, having found out, by help of the Parallaxes, a way to demonstrate, that they also are things elementary, and contained within the concave of the Moon, he hath writ this other Book, de tribus novis Stellis, &c. and therein also inserted the Arguments against Copernicus: I have already shewn you what he hath written touching these new Stars in his Anti-Tycho, where he denied not, but that they were in the Heavens; but he proved, that their production altered not the inalterability of the Heavens, and that he did, with a Discourse purely philosophical, in the same man¦ner as you have already heard. And I then forgot to tell you, how that he afterwards did finde out a way to remove them out of the Heavens; for he proceeding in this confutation, by way of computations and parallaxes, matters little or nothing at all understood by me, I did not mention them to you, but have bent all my studies upon these arguments against the motion of the Earth, which are purely natural.

Salv.I understand you very well: and it will be convenient after we have heard what he hath to say against Copernicus, that we hear, or see at least the manner wherewith he, by way of Parallaxes, proveth those new stars to be elementary, which so many famous Astronomers constitute to be all very high, and amongst the stars of the Firmament; and as this Author accomplisheth such an enterprize of pulling the new stars out of heaven, and placing them in the elementary Sphere, he shall be worthy to be highly exalted, and transferred himself amongst the stars, or at least, that his name be by fame eternized amongst them. Yet before we enter upon this, let us hear what he alledgeth against the opinion of Copernicus, and do you begin to recite his Arguments.

Simpl.It will not be necessary that we read them ad verbum, because they are very prolix; but I, as you may see, in reading them several times attentively, have marked in the margine those words, wherein the strength of his arguments lie, and it will suffice to read them.The opinion of Copernicus overthrows the Criterium of Philosophy The first Argument beginneth here. Et primo, si opinio Copernici recipiatur, Criterium naturalis Philosophiae, ni prorsus tollatur, vehementer saltem labefactari videtur. [In our Idiom thus] And first, if Copernicus his opinion be imbraced, the Criterium of natural Philosophy will be, if not wholly subverted, yet at least extreamly shaken.

Which, according to the opinion of all the sects of Philosophers requireth, that Sense and Experience be our guides in philosophating: But in the Copernican position the Senses are greatly deluded, whil'st that they visibly discover neer at hand in a pure Medium, the gravest bodies to descend perpendicularly downwards, never deviating a single hairs breadth from rectitude; and yet according to the opinion of Copernicus, the sight in so manifest a thing is deceived, and that motion is not reall straight, but mixt of right and circular.

Salv.This is the first argument, that Aristotle, Ptolomy, and all their followers do produce; to which we have abundantly answered, and shewn the Paralogisme, and with sufficient plainnesse proved, that the motion in common to us and other moveables, is, as if there were no such thing; but because true conclusions meet with a thousand accidents,Common motion is, as if it never were. that confirme them, I will, with the favour of this Philosopher, adde something more; and you Simplicius personating him, answer me to what I shall ask you:The argument taken from things falling perpendicularly, another way confuted. And first tell me, what effect hath that stone upon you, which falling from the top of the Tower, is the cause that you perceive that motion; for if its fall doth operate upon you neither more nor lesse, than its standing still on the Towers top, you doubtlesse could not discern its descent, or distinguish its moving from its lying still.

Simpl.I comprehend its moving, in relation to the Tower, for that I see it one while just against such a mark in the said Tower, and another while against another lower, and so successively, till that at last I perceive it arrived at the ground.

Salv.Then if that stone were let fall from the tallons of an Eagle flying, and should descend thorow the simple invisible Air, and you had no other object visible and stable, wherewith to make comparisons to that, you could not perceive its motion?

Simpl.No, nor the stone it self; for if I would see it, when it is at the highest,Whence the motion of a cadent body is collected. I must raise up my head, and as it descendeth, I must hold it lower and lower, and in a word, must continually move either that, or my eyes, following the motion of the said stone.

Salv.You have now rightly answered: you know then that the stone lyeth still,The motion of the eye argueth the motion of the object looked on. when without moving your eye, you alwayes see it before you; and you know that it moveth, when for the keeping it in sight, you must move the organ of sight, the eye. So then when ever without moving your eye, you continually behold an object in the self same aspect, you do always judge it immoveable.

Simpl.I think it must needs be so.

Salv.Now fancy your self to be in a ship, and to have fixed your eye on the point of the Sail-yard: Do you think, that because the ship moveth very fast, you must move your eye, to keep your sight alwayes upon the point of the Sail-yard, and to follow its motion?

Simpl.I am certain, that I should need to make no change at all; and that not only in the sight; but if I had aimed a Musket at it, I should never have need, let the ship move how it will, to stir it an hairs breadth to keep it full upon the same.

Salv.And this happens because the motion, which the Ship conferreth on the Sail-yard, it conferreth also upon you, and upon your eye; so that you need not stir it a jot to behold the top of the Sail-yard: and consequently, it will seem to you immoveaable. Now this Discourse being applied to the revolution of the Earth, and to the stone placed in the top of the Tower, in which you cannot discern any motion, because that you have that motion which is necessary for the following of it, in common with it from the Earth; so that you need not move your eye. When again there is conferred upon it the motion of descent, which is its particular motion, and not yours, and that it is intermixed with the circular, that part of the circular which is common to the stone, and to the eye, continueth to be imperceptible, and the right onely is perceived, for that to the perception of it, you must follow it with your eye, looking lower and lower. I wish for the undeceiving of this Philosopher, that I could advise him, that some time or other going by water,An experiment that sheweth how the common motion is imperceptible. he would carry along with him a Vessel of reasonable depth full of water, and prepare a ball of wax, or other matter that would descend very slowly to the bottome, so that in a minute of an hour, it would scarce sink a yard; and that rowing the boat as fast as could be, so that in a minute of an hour it should run above an hundred yards, he would let the ball submerge into the water, & freely descend, & diligently observe its motion. If he would but do thus, he should see, first, that it would go in a direct line towards that point of the bottom of the vessel, whither it would tend, if the boat should stand still; & to his eye, and in relation to the vessel, that motion would appear most straight and perpendicular, and yet he could not say, but that it would be composed of the right motion downwards, and of the circular about the element of water. And if these things befall in matters not natural, and in things that we may experiment in their state of rest; & then again in the contrary state of motion, and yet as to appearance no diversity at all is discovered, & that they seem to deceive our sense what can we distinguish touching the Earth, which hath been perpetually in the same constitution, as to motion and rest? And in what time can we experiment whether any difference is discernable amongst these accidents of local motion, in its diverse states of motion and rest, if it eternally indureth in but one onely of them?

Sagr.These Discourses have somewhat whetted my stomack, which those fishes, and snails had in part nauseated; and the former made me call to minde the correction of an errour, that hath so much appearance of truth, that I know not whether one of a thousand would refuse to admit it as unquestionable. And it was this, that sailing into Syria, and carrying with me a very good Telescope, that had been bestowed on me by our Common Friend, who not many dayes before had invented, I proposed to the Mariners, that it would be of great benefit in Navigation to make use of it upon the round top of a ship, to discover and kenne Vessels afar off. The benefit was approved, but there was objected the difficulty of using it,An ingenuous consideration about the possibility of using the Telescope with as much facility on the round top of the Mast of a ship, as on the Deck. by reason of the Ships continual fluctuation; and especially on the round top, where the agitation is so much greater, and that it would be better for any one that would make use thereof to stand at the Partners upon the upper Deck, where the tossing is lesse than in any other place of the Ship. I (for I will not conceal my errour) concurred in the same opinion, and for that time said no more: nor can I tell you by what hints I was moved to return to ruminate with my self upon this businesse, and in the end came to discover my simplicity (although excusable) in admitting that for true, which is most false; false I say, that the great agitation of the basket or round top, in comparison of the small one below, at the partners of the Mast, should render the use of the Telescope more difficult in finding out the object.

Salv.I should have accompanied the Mariners, and your self at the beginning.

Simpl.And so should I have done, and still do: nor can I believe, if I should think of it an hundred years, that I could understand it otherwise.

Sagr.I may then, it seems, for once prove a Master to you both. And because the proceeding by interrogatories doth in my opinion much dilucidate things, besides the pleasure which it affords of confounding our companion, forcing from him that which he thought he knew not, I will make use of that artifice. And first, I suppose that the Ship, Gally, or other Vessel, which we would discover, is a great way off, that is, four, six, ten, or twenty * I deviate here from the strict Sea Diallect, which denominates all distances by Leagues.* miles, for that to kenne those neer at hand there is no need of these Glasses: & consequently, the Telescope may at such a distance of four or six miles conveniently discover the whole Vessel, & a much greater bulk. Now I demand what for species, & how many for number are the motions that are made upon the round top, depending on the fluctuation of the Ship.

Salv.We will suppose that the Ship goeth towards the East. First,Different motions depending on the fluctuation of the Ship. in a calme Sea, it would have no other motion than this of progression, but adding the undulation of the Waves, there shall result thence one, which alternately hoysting and lowering the poop and prow, maketh the round top, to lean forwards and backwards; other waves driving the vessel sidewayes, bow the Mast to the Starboard and Larboard; others, may bring the ship somewhat abovt, and bear her away by the Misne from East, one while towards the * Greco, which the Latine Translator according to his usual carelessenesse (to call it no worse) translates Corum Ventum, the Northwest Wind, for Ventum Libanotum.* Northeast, another while toward the Southeast; others bearing her up by the Carine may make her onely to rise, and fall; and in sum, these motions are for species two, one that changeth the direction of the Telescope angularly, the other lineally, without changing angle, that is, alwayes keeping the tube of the Instrument parallel to its self.

Sagr.Tell me,Two mutations made in the Telescope, depending on the agitation of the Ship. in the next place, if we, having first directed the Telescope yonder away towards the Tower of ** This is a Castle six Italian miles from Venice Northwards. Burano, six miles from hence, do turn it angularly to the right hand, or to the left, or else upwards or downwards, but a †† Vn nero d' ugna, the black or paring of a nail. straws breadth, what effect shall it have upon us touching the finding out of the said tower?

Salv.It would make us immediately lose sight of it, for such a declination, though small here, may import there hundreds and thousands of yards.

Sagr.But if without changing the angle, keeping the tube alwayes parallel to it self, we should transfer it ten or twelve yards farther off to the right or left hand, upwards or downwards, what alteration would it make as to the Tower?

Salv.The change would be absolutely undiscernable; for that the spaces here and there being contained between parallel rayes, the mutations made here and there, ought to be equal, and because the space which the Instrument discovers yonder, is capable of many of those Towers; therefore we shall not lose sight of it.

Sagr.Returning now to the Ship, we may undoubtedly affirm, that the Telescope moving to the right or left, upwards, or downwards, and also forwards or backwards ten or fifteen fathom; keeping it all the while parallel to its self, the visive ray cannot stray from the point observed in the object, more than those fifteen fathom; and because in a distance of eight or ten miles, the Instrument takes in a much greater space than the Gally or other Vessel kenn'd; therefore that small mutation shall not make me lose sight of her. The impediment therefore, and the cause of losing the object cannot befall us, unlesse upon the mutation made angularly; since that Telescopes transportation higher or lower, to the right, or to the left, by the agitation of the ship, cannot import any great number of fathomes. Now suppose that you had two Telescopes fixed, one at the Partners close by the Deck, and the other at the round top, nay at the main top, or main top-gallant top, where you hang forth the Pennon or streamer, and that they be both directed to the Vessel that is ten miles off, tell me, whether you believe that any agitation of the ship, & inclination of the Mast, can make greater changes, as to the angle, in the higher tube, than in the lower? One wave arising, the prow will make the main top give back fifteen or twenty fathom more than the foot of the Mast, and it shall carry the upper tube along with it so greata space, & the lower it may be not a palm; but the angle shall change in one Instrument aswell as in the other; and likewise a side-billow shall bear the higher tube an hundred times as far to the Larboard or Starboard, as it will the other below; but the angles change not at all, or else alter both alike. But the mutation to the right hand or left, forwards or backwards, upwards or downwards, bringeth no sensible impediment in the kenning of objects remote, though the alteration of the angle maketh great change therein; Therefore it must of necessity be confessed, that the use of the Telescope on the round top is no more difficult than upon the Deck at the Partners; seeing that the angular mutations are alike in both places.

Salv.How much circumspection is there to be used in affirming or denying a proposition? I say again, thar hearing it resolutely affirmed, that there is a greater motion made on the Masts top, than at its partners, every one will perswade himself, that the use of the Telescope is much more difficult above than below. And thus also I will excuse those Philosophers, who grow impatient and fly out into passion against such as will not grant them, that that Cannon bullet which they cleerly see to fall in a right line perpendicularly, doth absolutely move in that manner; but will have its motion to be by an arch, and also very much inclined and transversal: but let us leave them in these labyrinths, and let us hear the other objections, that our Author in hand brings against Copernicus.

Simpl.The Author goeth on to demonstrate that in the Doctrine of Copernicus, it is requisite to deny the Senses, and the greatest Sensations,The annual motion of the Earth must cause a perpetual and strong winde. as for instance it would be, if we that feel the respirations of a gentle gale, should not feel the impulse of a perpetual winde that beateth upon us with a velocity that runs more than 2529 miles an hour, for so much is the space that the centre of the Earth in its annual motion passeth in an hour upon the circumference of the grand Orb, as he diligently calculates; and because, as he saith, by the judgment of Copernicus, Cum terra movetur circumpositus aër, motus tamen ejus, velocior licet ac rapidior celerrimo quocunque vento, à nobis non sentiretur, sed summa tum tranquilitas reputaretur, nisi alius motus accederet. Quid est verò decipi sensum, nisi hæc esset deceptio? [Which I make to speak to this sense.] The circumposed air is moved with the Earth, yet its motion, although more speedy and rapid than the swiftest wind whatsoever, would not be perceived by us, but then would be thought a great tranquillity, unlesse some other motion should happen; what then is the deception of the sense, if this be not?

Salv.It must needs be that this Philosopher thinketh, that that Earth which Copernicus maketh to turn round, together with the ambient air along the circumference of the great Orb, is not that whereon we inhabit, but some other separated from this; for that this of ours carrieth us also along with it with the same velocity,The air alwayes touching us with the same part of it cannot make us feel it. as also the circumjacent air: And what beating of the air can we feel, when we fly with equal speed from that which should accost us? This Gentleman forgot, that we no less than the Earth and air are carried about, and that consequently we are always touch'd by one and the same part of the air, which yet doth not make us feel it.

Simpl.But I rather think that he did not so think; hear the words which immediatey follow. Præterea nos quoque rotamur ex circumductione terræ &c.

Salv.Now I can no longer help nor excuse him; do you plead for him and bring him off, Simplicius.

Simpl.I cannot thus upon the sudden think of an excuse that pleaseth me.

Salv.Go to; take this whole night to think on it, and defend him to morrow; in the mean time let us hear some other of his objections.

Simpl.He prosecuteth the same Objection, shewing, that in the way of Copernicus,He that will follow Copernicus, must deny his senses. a man must deny his own senses. For that this principle whereby we turn round with the Earth, either is intrinsick to us, or external; that is, a rapture of that Earth; and if it be this second, we not feeling any such rapture, it must be confessed that the sense of feeling, doth not feel its own object touching it, nor its impression on the sensible part: but if the principle be intrinsecal, we shall not perceive a local motion that is derived from our selves, and we shall never discover a propension perpetually annexed to our selves.

Salv.So that the instance of this Philosopher lays its stress upon this, that whether the principle by which we move round with the Earth be either extern, or intern, yet however we must perceive it, and not perceiving it, it is neither the one nor the other, and therefore we move not, nor consequently the Earth. Now I say,Our motion may be either interne or externe, and yet we never perceive or feel it. that it may be both ways, and yet we not perceive the same. And that it may be external, the experiment of the boat superabundantly satisfieth me; I say, superabundantly, because it being in our power at all times to make it move, and also to make it stand still, and with great exactness to make observation, whether by some diversity that may be comprehended by the sense of feeling, we can come to know whether it moveth or no, seeing that as yet no such science is obtained: Will it then be any matter of wonder, if the same accident is unknown to us on the Earth, the which may have carried us about perpetually, and we, without our being ever able to experiment its rest?The motion of a Boat insensible to those that are with in it, as to the sense of feeling. You, Simplicius, as I believe, have gone by boat many times to Padoua, and if you will confess the truth, you never felt in your self the participation of that motion, unless when the boat running a-ground, or encountring some obstacle, did stop, and that you with the other Passengers being taken on a sudden, were with danger over-set. It would be necessary that the Terrestrial Globe should meet with some rub that might arrest it, for I assure you, that then you would discern the impulse residing in you, when it should toss you up towards the Stars. It's true, that by the other senses, but yet assisted by Reason,The boats motion is perceptible to the sight joyn'd with reason. you may perceive the motion of the boat, that is, with the sight, in that you see the trees and buildings placed on the shoar, which being separated from the boat, seem to move the contrary way.The terrestrial motion collected from the stars. But if you would by such an experiment receive intire satisfaction in this business of the Terrestrial motion, look on the stars, which upon this reason seem to move the contrary way. As to the wondering that we should not feel such a principle, supposing it to be internal, is a less reasonable conceit; for if we do not feel such a one, that cometh to us from without, and that frequently goeth away, with what reason can we expect to feel it, if it immutably and continually resides in us? Now let us see what you have farther to allege on this argument.

Simpl.Take this short exclamation. Ex hac itaque opinione necesse est diffidere nostris sensibus, ut penitùs fallacibus vel stupidis in sensilibus, etiam conjunctissimis, dijudicandis. Quam ergò veritatem sperare possumus à facultate adeò fallaci ortum trahentem? [Which I render thus:] From this opinion likewise, we must of necessity suspect our own senses, as wholly fallible, or stupid in judging of sensible things even very near at hand. What truth therefore can we hope for, to be derived from so deceiveable a faculty?

Salv.But I desire not to deduce precepts more profitable, or more certain, learning to be more circumspect and less confident about that which at first blush is represented to us by the senses, which may easily deceive us. And I would not have this Author trouble himself in attempting to make us comprehend by sense, that this motion of descending Graves is simply right, and of no other kind; nor let him exclaim that a thing so clear, manifest, and obvious should be brought in question; for in so doing, he maketh others believe, that he thinketh those that deny that motion to be absolutely streight, but rather circular, the stone did sensibly see it to move in an arch, seeing that he inviteth their senses more than their Reason, to judg of that effect: which is not true, Simplicius, for like as I, that am indifferent in all these opinions, and onely in the manner of a Comedian, personate Copernicus in these our representations, have never seen, nor thought that I have seen that stone fall otherwise than perpendicularly, so I believe, that to the eyes of all others it seemed to do the same. Better it is therefore, that deposing that appearance in which all agree, we make use of our Reason, either to confirm the reality of that, or to discover its fallacy.

Sagr.If I could any time meet with this Philosopher, who yet me thinks is more sublime than the rest of the followers of the same doctrines, I would in token of my affection put him in mind of an accident which he hath doubtless very often beheld; from which, with great conformity to that which we now discourse of, it may be collected how easily one may be deceived by the bare appearance, or, if you will, representation of the sense. And the accident is, the Moons seeming to follow those that walk the streets in the night, with a pace equal to theirs, whilst they see it go gliding along the Roofs of houses, upon which it sheweth just like a cat, that really running along the ridges of houses, leaveth them behind. An appearance that, did not reason interpose, would but too manifestly delude the sight.

Simpl.Indeed there want not experiments that render us certain of the fallacy of the meer senses;Arguments against the Earths motion taken, ex rerum natura. therefore suspending such sensations for the present, let us hear the Arguments that follow which are taken, as he saith, ex rerum naturâ. The first of which is, that the Earth cannot of its own nature move with three motions very different; or otherwise we must deny many manifest Axioms.Three Axioms that are supposed manifest. The first whereof is, that Omnis effectus dependeat ab aliquâ causà; [i. e.] that every effect dependeth on some cause. The second, that Nulla res seipsam producat; [i. e.] that nothing produceth it self: from whence it follows, that it is not possible that the move and moved should be totally the same thing: And this is manifest, not onely in things that are moved by an extrinsick mover; but it is gathered also from the principles propounded, that the same holdeth true in the natural motion dependent on an intrinsick principle; otherwise, being that the mover, as a mover, is the cause, and the thing moved, as moved, is the effect, the same thing would totally be both the cause and effect. Therefore a body doth not move its whole self, that is, so as that all moveth, and all is moved; but its necessary in the thing moved to distinguish in some manner the efficient principle of the motion, and that which with that motion is moved. The third Axiom is, that in rebus quæ sensui subjiciuntur, unum, quatenus unum, unam solam rem producat; i. e. That in things subject to the senses, one, as it is one, produceth but onely one thing: That is, the soul in animals produceth its true divers operations, as the sight, the hearing, the smell, generation, &c. but all these with several instruments. And in short, in things sensible, the diversity of operations, is observed to derive it self from the diversity that is in the cause.A simple body as the Earth, cannot move with three several motions. Now if we put all these Axioms together, it will be a thing very manifest, that one simple body, as is the Earth, cannot of its own nature move at the same time with three motions, very divers: For by the foregoing suppositions, all moveth not its self all; it is necessary therefore to distinguish in it three principles of its three motions; otherwise one and the same principle would produce many motions; but if it contein in it three principles of natural motions, besides the part moved, it shall not be a simple body, but compounded of three principle movers,The Earth cannot move with any of the motions assigned it by Copernicus. and of the part moved. If therefore the Earth be a simple body, it shall not move with three motions; nay more, it will not move with any of those which Copernicus ascribeth to it, it being to move but with one alone, for that it is manifest, by the reasons of Aristotle, that it moveth to its centre, as its parts do shew, which descend at right angles to the Earths Spherical Surface.

Salv.Many things might be said, and considered touching the connection of this argument;Answers to the arguments contrary to the Earths motion, taken ex rerum natura. but in regard that we can resolve it in few words, I will not at this time without need inlarge upon it; and so much the rather, because the same Author hath furnished me with an answer, when he saith that from one sole prinple in animals, there are produced divers operations; so that for the present my answer shall be, that in the same manner the Earth from one onely principle deriveth several operations.

Simpl.But this answer will not at all satisfie the Author who makes the objection, yea, it is totally overthrown by that which immediately after he addeth for a greater confirmation of his argument, as you shall hear. He re-inforceth his argument, I say, with another Axiome,A fourth Axiome against the motion of the Earth which is this; That natura in rebus necessariis nec deficiat, nec abundat: i. e. That nature in things necessary is neither defective, nor superfluous.Flexures necessary in animals for the diversity of their motions. This is obvious to the observers of natural things, and chiefly of animals, in which, because they are to move with many motions, Nature hath made many flexures, and hath thereunto commodiously knitted the parts for motion, as to the knees, to the hips, for the inabling of living creatures to go, and run at their pleasure. Moreover in man he hath framed many flexions, and joynts, in the elbow, and hand, to enable them to perform many motions.Another argument against the three fold motion of the Earth. From these things the argument is taken against the threefold motion of the Earth. [Either the Body, that is one, and continuate, without any manner of knittings or flexions, can exercise divers motions, or cannot: If it can without them, then in vain hath nature framed the flexures in animals; which is contrary to the Axiome: but if it cannot without them, then the Earth, one body, and continuate, and deprived of flexures, and joynts, cannot of its own nature move with plurality of motions.] You see now how craftily he falls upon your answer, as if he had foreseen it.

Salv.Are you serious, or do you jest?

Simpl.I speak it with the best judgment I have.

Salv.You must therefore see that you have as fortunate an hand in defending the reply of this Philosopher, against some other rejoynders made to him; therefore answer for him, I pray you, seeing we cannot have him here. You first admit it for true, that Nature hath made the joynts, flexures, and knuckles of living creatures, to the intent that they might move with sundry and divers motions; and I deny this proposition; and say, that these flexions are made, that the animal may move one, or more of its parts,The Flexures in animals are not made for the diversity of motions. the rest remaining immoved: and I say, that as to the species and differences of motions those are of one kind alone, to wit, all circular, and for this cause you see all the ends of the moveable bones to be convex or concave,The motions of animals are of one sort. and of these some are spherical, as are those that are to move every way, as in the shoulder-joynt, The ends of the bones are all rotund. the arme of the Ensigne doth, in displaying the Colours, and that of the Falconer in bringing his Hawk to the lure; and such is the flexure of the elbow, upon which the hand turns round, in boring with an augure: others are circular onely one way, and as it were cylindrical, which serve for the members that bend onely in one fashion,It is demonstrated, that the ends of the bones are of necessity to be rotund. as the joynts of the fingers one above another, &c. But without more particular inductions, one only general discourse may make this truth understood; and this is, that of a solid body that moveth, one of its extreams standing still without chanching place,The motions of animals are all circular. the motion must needs be circular, and no other: and because in the living creatures moving, one of its members doth not separate from the other its conterminal, therefore that motion is of necessity circular.

Simpl.How can this be? For I see the animal move with an hundred motions that are not circular, and very different from one another, as to run, to skip, to climbe, to descend, to swim, and many others.

Salv.Tis well:Secondary motions of animals dependent on the first but these are secondary motions, depending on the preceding motions of the joynts and flexures. Upon the plying of the legs to the knees, and the thighs to the hips, which are circular motions of the parts, is produced, as consequents, the skip, or running, which are motions of the whole body, and these may possibly not be circular. Now because one part of the terrestrial Globe is not required to move upon another part immoveable, The Terrestriall Globe hath noe need of flexures. but that the motion is to be of the whole body, there is no need in it of flexures.

Simpl.This (will the aduersary rejoyn) might be, if the motion were but one alone, but they being three, and those very different from each other, it is not possible that they should concur in an ** Without joynts articulate body.

Salv.I verily believe that this would be the answer of the Philosopher. Against which I make opposition another way; and ask you, whether you think that by way of joynts and flexures one may adapt the terrestrial Globe to the participation of three different circular motions? Do you not answer me? Seeing you are speechlesse, I will undertake to answer for the Philosopher, who would absolutely reply that they might; for that otherwise it would have been superfluous, and besides the purpose to have proposed to consideration, that nature maketh the flexions, to the end, the moveable may move with different motions; and that therefore the terrestrial Globe having no flexures, it cannot have those three motions which are ascribed to it. For if he had thought, that neither by help of flexures, it could be rendered apt for such motions, he would have freely affirmed, that the Globe could not move with three motions. Now granting this, I intreat you,It is desired to know, by means of what flexures and joynts the Terrestrial Globe might move with three diverse motions. and by you, if it were possible, that Philosopher, Author of the Argument, to be so courteous as to teach me in what manner those flexures should be accommodated, so that those three motions might commodiously be excercised; and I grant you four or six moneths time to think of an answer. As to me, it seemeth that one principle onely may cause a plurality of motions in the Terrestrial Globe,One only principle may cause a plurality of motions in the Earth. just in the same manner that, as I told you before, one onely principle with the help of various instruments produceth sundry and divers motions in living creatures. And as to the flexures there is no need of them, the motions being of the whole, and not of some particular parts; and because they are to be circular, the meer spherical figure is the most perfect articulation or flection that can be desired.

Simpl.The most that ought to be granted upon this, would be, that it may hold true in one single motion, but in three different motions, in my opinion, and that of the Author, it is impossible; as he going on, prosecuting the objection, writes in the following words. Let us suppose, with Copernicus, that the Earth moveth of its own faculty, and upon an intrinsick principle from West to East in the plane of the Ecliptick; and again, that it also by an intrinsick principle revolveth about its centre, from East to West; and for a third motion, that it of its own inclination deflecteth from North to South, and so back again. It being a continuate body, and not knit together with joints and flections, our fancy and our judgment will never be able to comprehend, that one and the same natural and indistinct principle, that is, that one and the same propension, should actuate it at the same instant with different, and as it were of contrary motions. I cannot believe that any one would say such a thing, unlesse he had undertook to maintain this position right or wrong.

Salv.Stay a little; and find me out this place in the Book. Fingamus modo cum Copernico, terram aliqua suâ vi, & ab indito principio impelli ab Occasu ad Ortum in Eclipticæ plano; tum rursus revolvi ab indito etiam principio, circa suimet centrum, ab Ortu in Occasum;tertio deflecti rursus suopte nutu à septentrione in Austrum, & vicissim. A grosse error of the opposer of Copernicus.I had thought, Simplicius, that you might have erred in reciting the words of the Author, but now I see that he, and that very grossely, deceiveth himself; and to my grief, I find that he hath set himself to oppose a position, which he hath not well understood; for these are not the motions which Copernicus assignes to the Earth. Where doth he find that Copernicus maketh the annual motion by the Ecliptick contrary to the motion about its own centre? It must needs be that he never read his Book, which in an hundred places, and in the very first Chapters affirmeth those motions to be both towards the same parts, that is from West to East. But without others telling him, ought he not of himself to comprehend, that attributing to the Earth the motions that are taken, one of them from the Sun, and the other from the primum mobile, they must of necessity both move one and the same way.

Simpl.Take heed that you do not erre your self,A subtil and withal simple argument against Copernicus. and Copernicus also. The Diurnal motion of the primum mobile, is it not from East to West? And the annual motion of the Sun through the Ecliptick, is it not on the contrary from West to East? How then can you make these motions being conferred on the Earth, of contraries to become consistents?

Sagr.Certainly, Simplicius hath discovered to us the original cause of error of this Philosopher; and in all probability he would have said the very same.

Salv.Now if it be in our power, let us at least recover Simplicius from this errour, who seeing the Stars in their rising to appear above the Oriental Horizon, will make it no difficult thing to understand,The error of the Antagonist is manifest, by declaring that the annual and diurnal motions belonging to the Earth are both one way, and not contrary. that in case that motion should not belong to the Stars, it would be necessary to confesse, that the Horizon, with a contrary motion would go down; and that consequently the Earth would reoolve in it self a contrary way to that wherewith the Stars seem to move, that is from West to East, which is according to the order of the Signes of the Zodiack. As, in the next place, to the other motion, the Sun being fixed in the centre of the Zodiack, and the Earth moveable about its circumference, to make the Sun seem unto us to move about the said Zodiack, according to the order of the Signes, it is necessary, that the Earth move according to the same order, to the end that the Sun may seem to us to possesse alwayes that degree in the Zodiack, that is opposite to the degree in which we find the Earth; and thus the Earth running, verbi gratia, through Aries, the Sun will appear to run thorow Libra; and the Earth passing thorow the signe Taurus, the Sun will passe thorow Scorpio, and so the Earth going thorow Gemini, the Sun seemeth to go thorow Sagittarius; but this is moving both the same way, that is according to the order of the signes; as also was the revolution of the Earth about its own centre.

Simpl.I understand you very well, and know not what to alledge in excuse of so grosse an error.

Salv.And yet, Simplicius, there is one yet worse then this; and it is, that he makes the Earth move by the diurnal motion about its own centre from East to West; and perceives not that if this were so, the motion of twenty four hours appropriated by him to the Universe, would, in our seeming, proceed from West to East; the quite contrary to that which we behold.

Simpl.Oh strange! Why I, that have scarce seen the first elements of the Sphere, would not, I am confident, have erred so horribly.

Salv.Judg now what pains this Antagonist may be thought to have taken in the Books of Copernicus,By another groß error it is seen that the Antagonist had but little studied Copernicus. if he absolutely invert the sense of this grand and principal Hypothesis, upon which is founded the whole summe of those things wherein Copernicus dissenteth from the doctrine of Aristotle and Ptolomy. As again, It is questioned, whether the opponent understood the third motion assigned to the Earth by Copernicus. to this third motion, which the Author assignes to the Terrestrial Globe, as the judgment of Copernicus, I know not which he would mean thereby: it is not that questionlesse, which Copernicus ascribes unto it conjunctly with the other two, annual and diurnal, which hath nothing to do with declining towards the South and North; but onely serveth to keep the axis of the diurnal revolution continually parallel to it self; so that it must be confest, that either the Authour did not understand this, or that else he dissembled it. But although this great mistake sufficeth to free us from any obligation of a farther enquiry into his objections; yet neverthelesse I shall have them in esteem; as indeed they deserve to be valued much before the many others of impertinent Antagonists. Returning therefore to his objection, I say, that the two motions, annual and diurnal, are not in the least contrary, nay are towards the same way, and therefore may depend on one and the same principle. The third is of it self, and voluntarily so consequential to the annual, that we need not trouble our selves (as I shall shew in its place) to study for principles either internal or external, from which, as from its cause, to make it produced.

Sagr.I shall also, as being induced thereto by natural reason, say something to this Antagonist. He will condemn Copernicus,unlesse I be able to answer him to all objections, and to satisfie him in all questions he shall ask; as if my ignorance were a necessary argument of the falshood of his Doctrine. But if this way of condemning Writers be in his judgment legal, he ought not to think it unreasonable, if I should not approve of Aristotle and Ptolomy, when he cannot resolve, better than my self, those doubts which I propound to him, touching their Doctrine. He asketh me, what are the principles by which the Terrestrial Globe is moved The same argument answered by examples of the like motions in other cœlestial bodies.with the Annual motion through the Zodiack, and with the Diurnal through the Equinoctial about its own axis. I answer, that they are like to those by which Saturn is moved about the Zodiack in thirty years, and about its own centre in a much shorter time along the Equinoctial, as the collateral apparition and occultation of its Globes doth evince. They are principles like to those, whereby he scrupleth not to grant, that the Sun runneth thorow the Ecliptick in a year, and revolveth about its own centre parallel to the Equinoctial in lesse than a moneth, as its spots doth sensibly demonstrate. They are things like to those whereby the Medicean Stars run through the Zodiack in twelve years, and all the while revolve in small circles, and short periods of time about Jupiter.

Simp.This Author will deny all these things, as delusions of the fight, caused by the crystals of the Telescope.

Sagr.But this would be to draw a further inconvenience upon himself, in that he holdeth, that the bare eye cannot be deceived in judging of the right motion of descending graves, and yet holds that it is deceived in beholding these other motions at such time as its visive vertue is perfected, and augmented to thirty times as much as it was before. We tell him therefore, that the Earth in like manner partaketh of the plurality of motions: and it is perhaps the same, whereby the Loadstone hath its motion downwards, as grave, and two circular motions, one Horizontal, and the other Vertical under the Meridian. But what more; tell me, Simplicius, between which do you think this Author would put a greater difference, 'twixt right and circular motion, or 'twixt motion and rest?

Motion and rest are more different than right motion and circular.Simp.'Twixt motion and rest, certainly. And this is manifest, for that circular motion is not contrary to the right, according to Aristotle; nay, he granteth that they may mix with each other; which it is impossible for motion and rest to do.

Sagr.Therefore its a proposition lesse improbable to place in one natural body two internal principles, one to right motion, and the other to circular, than two such interne principles one to motion, and the other to rest. Now both these positions agree to One may more rationally ascribe to the Earth two internal principles to the right, and circular motion, than two to motion and rest. the natural inclination that resideth in the parts of the Earth to return to their whole, when by violence they are divided from it; and they onely dissent in the operation of the whole: for the latter of them will have it by an interne principle to stand still, and the former ascribeth to it the circular motion. But by your concession, and the confession of this Philosopher, two principles, one to motion, and the other to rest, are incompatible together, like as their effects are incompatible: but now this evenes not in the two motions, right, and circular, which have no repugnance to each other.

Salv.Adde this more, that in all probability it may be that The motion of the parts of the Earth returning to their whole may be circular.the motion, that the part of the Earth separated doth make whilst it returneth towards its whole, is also circular, as hath been already declared; so that in all respects, as far as concernes the present case, Mobility seemeth more likely than Rest. Now proceed, Simplicius, to what remains.

Simp.The Authour backs his Argument with producing another absurdity, that is, that the same motions agree to Natures extreamly different; but experience sheweth, that the operations The diversity of motions helpeth us in knowing the diversity of natures.and motions of different natures, are different; and Reason confirmeth the same: for otherwise we should have no way left to know and distinguish of natures, if they should not have their particular motions and operations, that might guide us to the knowledge of their substances.

Sagr.I have twice or thrice observed in the discourses of this Authour, that to prove that a thing is so, or so, he still alledgeth, that in that manner it is conformable with our understanding; or that otherwise we should never be able to conceive of it; or that the Criterium of Philosophy would be overthrown.Nature first made things as she pleased, and afterwards capacitated mens understandings for conceiving of them. As if that nature had first made mens brains, and then disposed all things in conformity to the capacity of their intellects. But I incline rather to think that Nature first made the things themselves, as she best liked, and afterwards framed the reason of men capable of conceiving (though not without great pains) some part of her secrets.

Salv.I am of the same opinion. But tell me, Simplicius, which are these different natures, to which, contrary to experience and reason, Copernicus assignes the same motions and operations.

Simpl.They are these. The Water, the Air, (which doubtlesse are Natures different from the Earth) and all things that are in those elements comprised, shall each of them have those three motions, which Copernicus pretends to be in the Terrestriall Globe;Copernicus erroneously assigneth the same operations to different natures and my Authour proceedeth to demonstrate Geometrically, that, according to the Copernican Doctrine, a cloud that is suspended in the Air, and that hangeth a long time over our heads without changing place, must of necessity have all those three motions that belong to the Terrestrial Globe. The demonstration is this, which you may read your self, for I cannot repeat it without book.

Salv.I shall not stand reading of it, nay I think it an impertinency in him to have inserted it, for I am certain, that no Copernican will deny the same. Therefore admitting him what he would demonstrate, let us speak to the objection, which in my judgment hath no great strength to conclude any thing contrary to the Copernican Hypothesis, seeing that it derogates nothing from those motions, and those operations, whereby we come to the knowledge of the natures, &c. Answer me, I pray you, Simplicius: Those accidents wherein some things exactly concur, can they serve to inform us of the different natures of those things?

Simpl.No Sir:From commune accidents one cannot know different natures. nay rather the contrary, for from the idendity of operations and of accidents nothing can be inferred, but an idendity of natures.

Salv.So that the different natures of the Water, Earth, Air, and other things conteined in these Elements, is not by you argued from those operations, wherein all these Elements and their affixes agree, but from other operations; is it so?

Simpl.The very same.

Salv.So that he who should leave in the Elements all those motions, operations, and other accidents, by which their natures are distinguished, would not deprive us of the power of coming to the knowledge of them; although he should remove those operations, in which they unitedly concur, and which for that reason are of no use for the distinguishing of those natures.

Simpl.I think your dissertation to be very good.

Salv.But that the Earth, Water, Air, are of a nature equally constituted immoveable about the centre, is it not the opinion of your self, Aristotle, Ptolomy, and all their sectators?

Simpl.Its on all hands granted as an undeniable truth.

Salv.Then from this common natural condition of quiescence about the centre, there is no argument drawn of the different natures of these Elements, and things elementary, but that knowledge must be collected from other qualities not common; and therefore whoso should deprive the Elements of this common rest only, and should leave unto them all their other operations, would not in the least block up the way that leadeth to the knowledge of their essences. But Copernicus depriveth them onely of this common rest, and changeth the same into a common motion, leaving them gravity, levity, the motions upwards, downwards, slower,The concurrence of the Elements in a common motion importeth no more or lesse, than their concurrence in a common rest. faster, rarity, density, the qualities of hot, cold, dry, moist, and in a word, all things besides. Therefore such an absurdity, as this Authour imagineth to himself, is no Copernican position; nor doth the concurrence in an identity of motion import any more or less, than the concurrence in an identity of rest about the diversifying, or not diversifying of natures. Now tell us, if there be any argument to the contrary.

Simpl.There followeth a fourth objection, taken from a natural observation, which is, A fourth argument against Copernicus. That bodies of the same kind, have motions that agree in kinde, or else they agree in rest. But by the Copernican Hypothesis,Bodies of the same kinde have motions that agree in kinde. bodies that agree in kinde, and are most semblable to one another, would be very discrepant, yea diametrically repugnant as to motion; for that Stars so like to one another, would be neverthelesse so unlike in motion, as that six Planets would perpetually turn round; but the Sun and all the fixeed Stars would stand perpetually immoveable.

Salv.The forme of the argument appeareth good; but yet I believe that the application or matter is defective: and if the Authour will but persist in his assumption, the consequence shall make directly against him. The Argument runs thus; Amongst mundane bodies,From the Earths obscurity, and the splendour of the Sun, and fixed Stars, is argued, that it is moveable, and they immoveable. six there are that do perpetually move, and they are the six Planets; of the rest, that is, of the Earth, Sun, and fixed Stars, it is disputable which of them moveth, and which stands still, it being necessary, that if the Earth stand still, the Sun and fixed Stars do move; and it being also possible, that the Sun and fixed Stars may stand immoveable, in case the Earth should move: the matter of fact in dispute is, to which of them we may with most convenience ascribe motion, and to which rest. Natural reason dictates, that motion ought to be assigned to the bodies, which in kind and essence most agree with those bodies which do undoubtedly move, and rest to those which most dissent from them; and in regard that an eternal rest and perpetual motion are most different, it is manifest, that the nature of the body always moveable ought to be most different from the body alwayes stable. Therefore, in regard that we are dubious of motion and rest, let us enquire, whether by the help of some other eminent affection, we may discover, which most agreeth with the bodies certainly moveable, either the Earth, or the Sun and fixed Stars. But see how Nature, in favour of our necessity and desire, presents us with two eminent qualities, and no less different than motion and rest, and they are light and darkness, to wit, the being by nature most bright, and the being obscure, and wholly deprived of light: the bodies therefore adorned with an internal and eternal splendour, are most different in essence from those deprived of light: The Earth is deprived of light, the Sun is most splendid in it self, and so are the fixed Stars. The six Planets do absolutely want light, as the Earth; therefore their essence agreeth with the Earth, and differeth from the Sun and fixed Stars. Therefore is the Earth moveable, immoveable the Sunne and Starry Sphere.

Simpl.But the Authour will not grant, that the six Planets are tenebrose, and by that negative will he abide. Or he will argue the great conformity of nature between the six Planets, and the Sun, and Fixed Stars; and the disparity between them and the Earth from other conditions than from tenebrosity and light; yea, now I remember in the fifth objection, which followeth, he layeth down the vast difference between the Earth and the Cœlestial Bodies,A fifth argument against Copernicus. in which he writeth, That the Copernican Hypothesis would make great confusion and perturbation in the Systeme of the Vniverse, and amongst its parts: As for instance, amongst Cœbodies that are immutable and incorruptible,Another difference between the Earth and the Cœlestial bodies, taken from purity & impurity. according to Aristotle, Tycho, and others; amongst bodies, I say, of such nobility, by the confession of every one, and Copernicus himself, who affirmeth them to be ordinate, and disposed in a perfect constitution, and removeth from them all inconstancy of vertue amongst, these bodies, I say once more, so pure, that is to say, amongst Venus, Mars, &c. to place the very sink of all corruptible matters, to wit, the Earth, Water, Air, and all mixt bodies.

But how much properer a distribution, and more with nature, yea with God himself, the Architect, is it, to sequester the pure from the impute, the mortal from the immortal, as other Schools teach; which tell us that these impure and frail matters are contained within the angust concave of the Lunar Orb, above which with uninterrupted Series the things Celestial distend themselves.

Salv.It's true that the Copernican Systeme introduceth distraction in the universe of Aristotle;Copernicus introduceth confusion in the Universe of Aristotle. but we speak of our own Universe, that is true and real. Again if this Author will infer the disparity of essence between the Earth and Celestial bodies from the incorruptibility of them, and the corruptibility of it in the method of Aristotle, from which disparity he concludeth motion to belong to the Sun and fixed Stars, and the immobility of the Earth,The Paralogisme of the Author of Anti-Tycho. he will flatter himself with a Paralogisme, supposing that which is in question; for Aristotle inferreth the incorruptibility of Celestial bodies from motion, which is in dispute, whether it belongeth to them or to the Earth. Of the vanity of these Rhetorical Illations enough hath been spoken.It seemeth a folly to affirm the Earth to be without the Heavens. And what can be more fond, than to say, that the Earth and Elements are banished and sequestred from the Celestial Spheres, and confined within the Lunar Orb? Is, not then the Moons Orb one of the Celestial Spheres, and according to consent comprised in the middle of all the rest? Its a new way to separate the pure from the impure, and the sick from the sound, to assigne the infected quarters in the heart of the City: I had thought that the ** Lazeretto Pest-house ought to have been removed as far off as was possible. Copernicus admireth the disposition of the parts of the Universe, for that God hath constituted the grand Lamp, which is to give light all over his Temple in the centre of it, and not on one side. And as to the Earths being betwixt Venus and Mars, we will but hint the same; and do you, in favour of this Author, trie to remove it thence. But let us not ** Intrecciare, to twine flowers in a garland. mix these Rhetorical Flowers with solid Demonstrations, rather let us leave them to the Orators, or if you will to the Poets, who know how in their drolling way to exalt by their prayses things most sordid, yea and sometimes most pernicious. And if any thing else remain, let us dispatch it, as we have done the rest.

Simpl.There is the sixth and last argument;A sixth argument against Copernicus, taken from animals, who have need of rest; though their motion be natural. wherein he maketh it a very improbale thing. [That a corruptible and dissipable body should move with a perpetual and regular motion; and this be confirmeth with the example of living creatures, which moving with a motion natural to them, yet grow weary, and have need of repose to restore their strength.] But what hath this motion to do with that of the Earth, that in comparision to theirs is immense? Besides, to make it move with three motions that run and draw several wayes: Who would ever assert such Paradoxes, unlesse he had sworn to be their defender? Nor doth that avail in this case, which Copernicus alledgeth, that by reason this motion is natural to the Earth and not violent, it worketh contrary effects to violent motions; and that those things dissolve and cannot long subsist, to which impulse is conferred, but those so made by nature do continue in their perfect disposure; this answer sufficeth not, I say, for it is overthrown by that of ours. For the animal is a natural body, and not made by art, and its motion is natural, deriving it self from the soul, that is, from an intrinsick principle; and that motion is violent, whose beginning is without, and on which the thing moved conferreth nothing; however, if the animal continueth its motion any long time, it grows weary, and also dyeth, if it obstinately strive to persist therein. You see then that in nature we meet on all sides with notions contrary to the Copernican Hypothesis, and none in favour of it. And for that I have nothing more wherein to take the part of this Opponent, hear what he produceth against Keplerus (with whom he disputeth) upon that argument, which the said Kepler bringeth against those who think it an inconvenient, nay impossible thing, to augment the Starry Sphere immensely, as the Copernican Hypothesis requireth. Kepler An argument from Kepler in favour of Copernicus.therefore instanceth, saying: Difficilius est, accidens præter modulum subjecti intendere, quàm subjectum sine accidente augere. Copernicus ergo verisimilius facit, qui auget Orbem Stellarum fixarum absque motu, quam Ptolomæus, qui auget motum fixarum immensâ velocitate. [Which makes this English.] Its harder to stretch the accident beyond the model of the subject than to augment the subject without the accident. Copernicus hath more probability on his side, who encreaseth the Orb of the fixed Stars without motion, than Ptolomy who augmenteth the motion of the fixed Stars to an immense degree of velocity. Which objection the Author answereth,The Author of the Anti-Tycho opposeth Kepler. wondering how much Kepler deceived himself, in saying, that in the Ptolomaick Hypothesis the motion encreaseth beyond the model of the subject, for in his judgment it doth not encrease, save onely in conformity to the model, and that according to its encreasement, the velocity of the motion is augmented.The velocity of the circular motion increaseth, according to the encrease of the diameter of the circle. Which he proveth by supposing a machine to be framed, that maketh one revolution in twenty four hours, which motion shall be called most slow; afterwards supposing its semidiameter to be prolonged, as far as to the distance of the Sun, its extreme will equal the velocity of the Sun; and it being continued out unto the Starry Sphere, it will equal the velocity of the fixed Stars, though in the circumference of the machine it be very slow. Now applying this consideration of the machine to the Starry Sphere, let us imagine any point in its semidiameter, as neer to the centre as is the semidiameter of the machine; the same motion that in the Starry Sphere is exceeding swift, shall in that point be exceeding slow; But the great magnitude of the body is that which maketh it of exceeding slow, to become exceeding swift, although it continueth still the same, and thus the velocity encreaseth, not beyond the model of the subject, but rather according to it, and to its magnitude; very differently from the imagination of Kepler.

Salv.I do not believe that this Author hath entertained so mean and poor a conceit of Kepler, as to perswade himself that he did not understand, that the highest term of a line drawn from the centre unto the Starry Sphere, moveth more swiftly than a point of the same line taken within a yard or two of the centre. And therefore of necessity he must have conceived and comprehended that the mind and intention of Kepler was to have said,An explanation of the true sense of Kepler and his defence. that it is lesse inconvenient to encrease an immoveable body to an extraordinary magnitude, than to ascribe an extraordinary velocity to a body, though very bigge, having regard to the model, that is to the gauge, and to the example of other natural bodies; in which we see, that the distance from the centre encreasing, the velocity diminisheth; that is, that the periods of their circulations take up longer times.The greatnesse and smalnesse of the body make a difference in motion and not in rest. But in rest which is not capable of augmentation or diminution, the grandure or smalnesse of the body maketh no difference. So that if the answer of the Author would be directed against the argument of Kepler, it is necessary, that that Author doth hold, that to the movent principle its one and the same to move in the same time a body very small, or very immense, in regard that the augmentation of velocity inseparably attends the augmentation of the masse.The order of nature is to make the lesser Orbs to circulate in shorter times, and the bigger in longer times. But this again is contrary to the Architectonical rule of nature, which doth in the lesser Spheres, as we see in the Planets, and most sensibly in the Medicean Stars, observe to make the lesser Orbs to circulate in shorter times: Whence the time of Saturns revolution is longer than all the times of the other lesser Spheres, it being thirty years; now the passing from this to a Sphere very much bigger, and to make it move in 24. hours, may very well be said to exceed the rules of the model. So that if we would but attentively consider it, the Authors answer opposeth not the intent and sense of the argument, but the expressing and manner of delivering of it; where again the Author is injurious, and cannot deny but that he artificially dissembled his understanding of the words, that he might charge Kepler with grosse ignorance; but the imposture was so very dull and obvions, that he could not with all his craft alter the opinion which Kepler hath begot of his Doctrine in the minds of all the Learned. As in the next place, to the instance against the perpetual motion of the Earth, taken from the impossibility of its moving long without wearinesse, in regard that living creatures themselves, which yet move naturally, and from an intern principle, do grow weary, and have need of rest to relax and refresh their members ———

Sagr.Methinks I hear Kepler answer him to that, that there are some kinde of animals which refresh themselves after wearinesse, by rowling on the Earth; and that therefore there is no need to fear that the Terrestrial Globe should tire,The feigned answer of Kepler covered with an artificial Irony. nay it may be reasonably affirmed, that it enjoyeth a perpetual & most tranquil repose, keeping it self in an eternal rowling.

Salv.You are too tart and Satyrical, Sagredus: but let us lay aside jests, whilst we are treating of serious things.

Sagr.Excuse me, Salviatus, this that I say is not so absolutely besides the business, as you perhaps make it; for a motion that serveth instead of rest, and removeth weariness from a body tired with travail, may much more easily serve to prevent the coming of that weariness,Animals would not grow weary of their motion, proceeding as that which is assigned to the terrestrial Globe. like as preventive remedies are more easie than curative. And I hold for certain, that if the motion of animals should proceed in the same manner as this that is ascribed to the Earth, they would never grow weary; Seeing that the weariness of the living creature, deriveth it self, in my opinion, from the imployment of but one part alone in the moving of its self,The cause of the wearinesse of animals. and all the rest of the body; as v. g. in walking, the thighs and the legs onely are imployed for carrying themselves and all the rest: on the contrary, you see the motion of the heart to be as it were indefatigable, because it moveth it self alone. Besides, I know not how true it may be,The motion of an animal is rather to be called violent than natural. that the motion of the animal is natural, and not rather violent: nay, I believe that one may truly say, that the soul naturally moveth the members of an animal with a motion preternatural, for if the motion upwards is preternatural to grave bodies, the lifting up of the legs, and the thighs, which are grave bodies, in walking, cannot be done without violence, and therefore not without labour to the mover. The climbing upwards by a ladder carrieth the grave body contrary to its natural inclination upwards, from whence followeth weariness, by reason of the bodies natural aversness to that motion: but in moving a moveable with a motion, to which it hath no aversion, what lassitude,The strength diminisheth not, where it is not imployed. what diminution of vertue and strength need we fear in the mover? and how should the forces waste, where they are not at all imployed?

Simpl.They are the contrary motions wherewith the Earth is pretended to move, against which the Authour produceth his argument.

Sagr.It hath been said already, that they are no wise contraries, and that herein the Authour is extteamly deceived, so that the whole strength of the argument recoileth upon the Opponent himself,The argument of Claramontius, recoileth upon himself. whilst he will make the First Mover to hurry along with it all the inferiour Spheres, contrary to the motion which they themselves at the same time exercise. It belongs therefore to the Primum Mobile to grow weary, which besides the moving of its self is made to carry so many other Spheres, and which also strive against it with a contrary motion. So that the ultimate conclusion that the Authour inferred, saying, that discoursing of the effects of Nature, a man alwayes meets with things that favour the opinion of Aristotle and Ptolomy, and never any one that doth not interfer with Copernicus, stands in need of great consideration; and it is better to say, that one of these two Hypotheses being true, and the other necessarily false, it is impossible that a man should ever be able to finde any argument, experience, or right reason, in favour of that which is false,True Propositions meet with many conclusive arguments, so do not the false. like as to the truth none of these things can be repugnant. Vast difference, therefore, must needs be found between the reasons and arguments produced by the one and other party, for and against these two opinions, the force of which I leave you your self to judge of, Simplicius.

Salv.But you, Sagredus, being transported by the velocity of your wit, have taken my words out of my mouth, whilst I was about to say something, touching this last argument of the Author; and although you have more then sufficiently refuted him, yet neverthelesse I will adde somewhat, which then ran in my minde. He proposeth it as a thing very unlikely, that a body dissipable and corruptible, as the Earth, should perpetually move with a regular motion, especially for that we see living creatures in the end to grow weary, and to stand in need of rest: and the improbability is increased, in that the said motion is required to be of velocity incomparable and immense, in respect to that of animals. Now, I cannot see why the velocity of the Earth should, at present, trouble it; so long as that of the starry Sphere so very much bigger doth not occasion in it any disturbance more considerable, than that which the velocity of a machine, that in 24 hours maketh but one sole revolution, produceth in the same. If the being of the velocity of the Earths conversion, according to the model of that machine, inferreth things of no greater moment than that, let the Author cease to fear the Earths growing weary; for that not one of the most feeble and slow-pac't animals, no not a Chamæleon would tire in moving no more than ** Cinque ò sei braccia Fiorentini. four or five yards in 24 hours; but if he please to consider the velocity to be no longer,Wearineß more to be feared in the starry Sphere than in the terrestriall Globe. in relation to the model of the machine, but absolutely, and inasmuch as the moveable in 24 hours is to pass a very great space, he ought to shew himself so much more reserved in granting it to the starry Sphere, which with a velocity incomparably greater than that of the Earth is to carry along with it a thousand bodies, each much bigger than the Terrestrial Globe.

Here it remains for us to see the proofs, whereby the Authour concludes the new stars Anno 1572. and Anno 1604. to be sublunary, and not cœlestial, as the Astronomers of those times were generally perswaded; an enterprize very great certainly; but I have considered, that it will be better, in regard the Book is new and long, by reason of its many calculations, that between this evening and to morrow morning I make them as plain as I can, and so meeting you again to morrow to continue our wonted conferences, give you a brief of what I shall observe therein; and if we have time left, we will say something of the Annual motion ascribed to the Earth. In the mean time, if either of you, and Simplicius in particular, hath any thing to say more, touching what relates to the Diurnal motion, at large examined by me, we have a little time still left to treat thereof.

Simpl.I have no more to say, unlesse it be this, that the discourses that this day have falne under our debate, have appeared to me fraught with very acute and ingenious notions, alledged on Copernicus his side, in confirmation of the motion of the Earth, but yet I find not my self perswaded to believe it; for in short, the things that have been said conclude no more but this, that the reasons for the stability of the Earth are not necessary; but all the while no demonstration hath been produced on the other side, that doth necessarily convince and prove its mobility.

Salv.I never undertook, Simplicius, to remove you from that your opinion; much less dare I presume to determine definitively in this controversie: it onely was, and still shall be in the ensuing disputations my intent, to make it appear to you, that those who have thought that most swift motion of 24 hours doth belong to the Earth alone, and not to the Universe, the Earth onely excluded, were not induced to believe, that so it might and ought to do out of any blind perswasion; but that they did very well see, try, and examine the reasons on the contrary side, and also not slightly answer them. With the same intention, if it stand with your liking, and that of Sagredus, we may passe to the consideration of that other motion; first, by Aristarchus Samius, and afterwards by Nicholaus Copernicus ascribed to the said Terrestrial Globe, which is, as, I believe, you have heretofore heard, made under the Zodiack within the space of a year about the Sun, immoveably placed in the centre of the said Zodiack.

Simpl.The disquisition is so great, and so noble, that I shall gladly hearken to the discussion thereof, perswading my self that I shall hear what ever can be said of that matter. And I will afterwards by my self, according to my usual custome, make more deliberate reflexions upon what hath been, and is to be spoken; and if I should gain no more but this, it will be no small benefit that I shall be able to discourse more Logically.

Sagr.Therefore, that we may no further weary Salviatus, we will put a period to the disputations of this day, and resume our conference to morrow in the usual manner, with hope to hear very pleasing novelties.

Simp. I will leave with you the Book De stellis novis, and carry back this of the Conclusions, to see what is written therein against the Annual motion, which are to be the arguments of our discourse to morrow.