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Of Curves of the fecond Kind, that is, the Conick Sections, only the Hyperbola has Afymptotes, which are two in Number.
All Curves of the third Kind have at leaft one Afymptote, but they may have three; and all Curves of the fourth Kind may have four Afymptotes. See Curve of higher Kind.
The Conchoid, Ciflbid, and Logarithmick Curve, though not reputed Geometrical Curves^ have each alfo one Afymptote. See Mechanical, Transcendental, &c;
Asymptote of the Conchoid. — The Nature of Afymptotes will be eafily conceived in the Inffance of the Afymptote of a Con- choid.— Suppofe MMAM, &c. (Tab. Afialyfs, Fig. 1.) be a Part of a Conchoid, C its Pole, and the right Line Bd, fo drawn that the Parrs QM, EA, OM, &c. of right Lines drawn from the Pole C, are equal to each other; Then will the Line BD be an Afymptote of the Curve : Becaufe the Perpendicular MI, &c. is fhorter than MO, and MR than MQj &c. fo that the two Lines continually approach ; yet the Points M, &c. and R, can never coincide, in regard there is ftill a Portion of a Line to keep them afunder; which Portion of a Line is infinitely divifible, and confequently muft be diminiuYd infinitely e're it become no- thing. See Divisibility, Infinite, &c. See alfo Con- choid.
Asymptotes of the Hyperbola are thus defcribed. — Suppofe a right Line DE (Tab. Conicks, Fig. 20) drawn through the Ver- tex A of the Hyperbola, parallel to the Ordinates Mm, and equal to the Conjugate Axes, viz.. the Part DA, and that AE to the Semi-axis : Then, two right Lines drawn from the Centre C, of the Hyperbola, through the Points D and E j viz. the right Lines CF and CG, are Afymptotes of the Curve.
For the Properties of the Asymptotes of a Hyperbola, fee Hy- perbola.
If the Hyperbola GMR, Fig. iz. be of any kind whofe Na- ture with regard to the Curve and its Afymptote) is exprefs'd, by this general Equation x m y N =a m +-»; and the right Line PM be drawn any where Parallel to the Afymptote CS, and the Paralle- logram PCOM, be compieated : This Parallelogram is to the hyperbolick Space PMGB, contained under the determinate Line PM, the Curve of the Hyperbola GM indefinitely continued towards G, and the Part PB of the Afymptote indefinitely [conti- nued the fame way, as m — » is to n : And fo if m be greater than «, the faid Space is fquareable; but when *»=«, as it will be in the common Hyperbola, the Ratio of the foregoing Parallelo- gram to that Space is as o to 1 ; that is, the Space is in6nitely greater than the Parallelogram, and fo cannot be had : And when m is lefs than n, the Parallelogram will be to the Space, as a nega- tive Number to a pofitive one, and the faid Space is fquareable, and the Solid generated by the revolving of the indeterminate Space GMOL about the Afymptote CE, is double of the Cylinder ge- nerated by the Motion of the Parallelogram PCOM about the Axis CO.
Asymptote of a Logarithmic Curve. — If MS be the Loga- rithmic Curve, PR an Afymptote, PT the Subtangent, and MP an Ordinate; then will the indeterminate Space RPMS— PM-j- PT; and the Solid, generated by the Rotation of this Curve a- bout the Afymptote VP, will be 4- of a Cylinder, whofe Altitude is equal to the Length of the Subtangent, and the Semidiameter of the Bale equal to the Ordinate QV. See Logarithmic ASYMPTOTIC Spaces. See Hyperbola. ASYNDETON, a Figure in Grammar, implying a defect or want of Conjunctions in a Sentence. See Figure and Con- junction.
As, in the Inftance, Veni? Vtdi, Vict, I came, I faw, I conquer'd ; where the Copulative et, and, is omitted.
The Word is derived from the privative *, and <rWV'«, colligo, bind together.
Afyndeton ftands oppofed to Polyfyndeton. See Polysynde- ton.
ATAMADULET, the firft Minifter in the Perfon Empire. See Minister.
The Atamadulet, or, as Tavernier writes it, Athematdoukt ; and Sanfon, Etmadattict, is much the fame with the Grand Vilier in Turky ; excepting that he has not the Command of the Army, which the Vilier has. See Visier.
The Atamadaulet is Great Chancellor of the Kingdom, Prefi- dent of the Council, Superintcndant of the Finances,' and has the Charge of all Foreign Affairs. — The Atmadaulet is in effed Vice-Roy of the Kingdom: He ilTues the King's Mandates, or Orders, in this Style, Bende derga Ali il alia Etmadohet ; that is, I who am the fupport of the Power, the Creature of this Port, the higheft of all Ports, &c.
The Word is Arabick, compounded of Itimade and daulet, that is, the Truft of Majefty, or according to Tavernier, the Support of Riches.
ATARAXY, Ataraxia, a Term much ufed by the Sto- icks, to denote that calmnefs and tranquillity of Mind, and that firmnefs of Judgment which fets us free from any Agitations or Emotions ariiing from Self-Opinion, and the Knowledge we ima- gine our felves poifefs'd of. SeeSToicKS.
In this Ataraxy, they fuppoled the fovereign Good to confift. See Good.
The Word is purely Greek, compounded of #*-«£ and ?«■&, Or- der. See Ataxy.
ATAXY, Ataxia, a want of Order or Regularity.— The Term is chiefly ufed in Medicine, where the Order of the Critical Days, or other Phenomena of a Difeafe, is inverted. See Cri- tical, <&c.
The Phyficians have frequent recourfe to an Ataxy or Irre- gularity of the Spirits, when at a lols to account for any Diforder in the Body. The Spirit^ Dr. Drake oblerves, being always at Hand, are forced to bear the blame of a thoufand things they are innocent of. See Spirit-
The Word is compounded of the privative *, and r«!j<;, Or- der.
ATCHIEVEMENT, in Heraldry, the Coat of Arms of any Perfon or Family, duly marfhaU'd with its external Ornaments, as Supporters, Hel?n?t> Wr?.tth^ Creft, and Motto. See Coat and Arms. See alfo Supporter, Helmet, &c.
Such are ufually hung out on the Fronts of" Houfes after the Death of feme coniiderable Pcrlon ; and are now corruptly call- ed Hatchments.
The Word is form'd of the French, Achevement, finishing, Consummation, Perfection.
ATELLAN-&, or Attellanve, in Antiquity, a kind of comic and fatyric Pieces, prefented on the Roman Theater; fome- what lefs ludicrous than the Farces on the Eng/ifh Stage, and yet lefs grave and feiious than the Greek ox Latin Comedies and Tra- gedies. Sec Comedy, Tragedy, Scene, &t.
The Atellants, or Fabula Aitella??^ of the Romans, anfwer'd to the Satyra among the Greeks. See Satyr, Fable, &c.
They were thus called from Atella, or Attella, a City of Tuf- cany, where they were firft reprefented.
They became fo licentious and impudent, that the Senate was at length obliged to fupprefs them. See Scenic.
ATHANASIAN Creed. See Creed, Trinity, &c.
Athanasians. 'See Arians and Arianism.
ATHANATI, an Order of Soldiers among the antient Perfi- ans. — The Word is originally Greek, and iigmfies immortal '; be- ing compounded of the privative a, and tW«Te$, Death.
The Athanati were a Body of Cavalry, conlifting of ten thou- fand Men, always compleat, becaufe, when any one of 'em di- ed, another was immediately put into his Place. — It was for this Reafon that they were call'd Athanati, or immortales.
ATHANOR, in Chymiftry, a large immoveable Furnace, built of Brick or Earth, andcover'd with a Tower a-top; pro- per to maintain a temperate and equable Degree of Heat for a confiderable time. See Furnace, Heat, &c.
The Heat of the Athanor is intended or remitted by opening or lhutting a Regifter. See Register.
It is made to communicate its Heat by Tubes or Apertures at the Side of the Hearth or Fire-Place, to feveral adjacent Veilels ; by which means different Operations are carry'd on at the fame time. — We meet with divers Forms and Conftru£Uons of this Furnace, in the Writers of Chymiftry.
The Athanor is alfo call'd Piger Henricus, flow Harry ; becaufe chiefly ufed in the flower Operation ; and becaufe when once filled with Coals, it keeps burning a long time ; whence the Greeks call it awhw, q. d. giving vo trouble^ as it does need to be conti- nually attended.' — It is alfo call'd the Pkihfhphkal Furnace, or Fur- ?iace of Arcana, and popularly, the Tower Bar nacs.
The Word Athanor is borrowed from the Arabs, who call an Oven, Tanneron from the Hebrew "VJn, l.annour, an Oven, or Furnace j whence, with the additional Particle al, "P^H 1 ??*, Al- tannour, &c— Others chufe to derive) the Name from the Greek kSxvutcs, Immortal^ becaufe of its durable Fire.
ATHEIST, Atheus, a Perfon who denies the Deity; who does not believe the Exiftence of a God, nor a Providence; and who has no Religion, true nor falfe. See God, Provi- dence, Religion.
In general, a Man is faid to be an Atheifb who owns no Being fuperior to Nature, that is, to Men and the other fenlible Beings in ths World. See Nature.
In this Senle, Spinofa may be faid to bean Atheifb and it is an Impropriety to rank him, as the learned commonly do, among De//rV; fince he allows of no other God befide Nature, of which Mankind makes a Part ,- and there is no AtL : fl but allows of the Exiftence of the World, and of his own in particular. See Spi- nosism. See alfo Existence, Substance, &c.
Plato diftinguiihes three kinds of Atheifts.Some, who deny abfolutely rhat there are any Gods ; others who allow the Exiftence of Gods, but maintain that they don't concern themfelves with human Affairs, and fo deny a Providence , and others, who be- lieve there are Gods, but think they are eafily appeas'd with a little Prayer, or the like.; and that they remit the greateii Crimes for the fmalleft Supplication. See Epicurean, &c.
The Word Atbetfi is derived from the privative «, and ®m> God.
ATHEN^A, a Feaft of the antient Greeks^ held in Honour of Minerva, who was call'd 'AA-'n). See Feast.
Thefe were afterwards call'd Panathentea. See Panathe-
N/EA.
ATHENAEUM, in Antiquity, a publick Place wherein the Profeflbrs of the liberal Arts held their AfTemblies, the Rheto- ricians declaimed, and the Poets rehearfed their Verfes.
The
