P O I
P o s
fefponding to the common verfed fine = x, the diameter of the greater circle =*? R, and the diameter of the JefTcr circle = S, it is certain, that zz = 4R x, — 4 ■*■* and that yy = 4 S x — 4 xx, as Mr. Robartes fays. But what follows from thence ? No more than this, that the ratio of zz to yy is the fame with the ratio of 4 Rx — 4.XX to4b\v— - 4-xw, or dividing both thefe terms by 4*, asR — jfistoS — .vj and that the ulti- mate or limiting ratio of zz to yy, is the fame with the ulti- mate or limiting ratio of R — *• to S — x. But the ultimate ratio of R — .vtoS — a- is the ratio of R to S, and confe- quently, the ratio ot R to S is the ultimate ratio of zz to yy ; or, the ratio of */R to */S is the ultimate ratio of z to_y. But what then? Does it follow that the terms of this ultimate ratio muft be conceived as Points ? Nothing lefs. The ulti- mate ratio of z to y does not imply that the quantities z and y ever exift under this ultimate ratio of */R to y/S, but only that they may approach to this ratio, fo as to differ from it by lefs than any affigned ratio. Mr. Robartes was milled by the too prevailing language of infinitefimals. See the article Fluxio n and Limits, Suppl. — [ a PhiI. Tranf. N°. 334 ]
Singular Point in geometry, is ufed for any Point of a curve, which has fomething peculiar to diftinguifh" it from the other Points of the curve. Cramer, Analyf. des lign. courbes, p. 148.
Of thefe Points there are various kinds, fucli as double, triple, &c. or in general, multiple Points ; Points of Inflexion or contrary flexure, &c. Every Point of a curve is Jimple, or multiple.
kftmple Point, is that which belongs only to one branch of a curve.
A multiple Point is that which is common to feveral branches of a curve, in particular :
Trouble Point is that which is common to two branches of a -curve. The conic fections or lines of the fecond order have no double Points; but we find them in the lines of the third order.
triple Point is that which is common to three feveral branches of a curve.
Hence the terms quadruple, quintuple, &c. Point are eafily underftood,
If a Point be fuppofed to defcribe a curve, it will pafs twice thro' a double Point ; thrice thro' a triple Point, &c.
A Jimple Point is fometimes fmgular, as when it becomes a Point of contrary flexure, of double inflexion, and in many other cafes ; for a detail of which we refer to Cramer, Analyf. delignes courbes, chap, x, p. 400. feq. and chap. xiii. p. 568. feq.
In the cafe mentioned in the Supplement, under the head Point of contrary Flexure, where a double infinitely final! flexure or inflexion is laid to be formed in a Paint, this Point is called by fome a Point of double inflexion, and by Monfieur de Maupertuis*, and Mr. Cramer b , Point de Serpentement, and by others, Point of reftitude. — [ a Mem. Acad. Scien. 172.9. p. 277. Ed. Paris. b Analyf. des lignes courbes.]
Point of Retl'itude, is defined by Sir Ifaac Newton, to be that in which the radius of flexure becomes infinite, or its center at an infinite diihnce : fuch it is at the vertex of the parabola alx=zy$.
The Point of Rectitude is commonly the limit of contrary flexure : but there are alfo Points of Reclitude, which do not come between the parts of contrary flexure. For the methud of investigating thefe Points, fee Newton's Mcth- of Flux, and Inf. Series, pag. 72.
Thefe Points of retlitude are not found in lines of a lower order than the fourth. In lines of this, and of higher orders, ' a tangent at a Point of inflexion may alfo meet the curve in another Point, and if the diftance between this Point and the Point of inflexion be fuppofed to be infinitely diminifhed, the fecant will become a tangent, and the con tail: in this cafe will be equivalent to four interferons, in the fame manner that the contacT: at a Point of contrary flexure is equivalent to three interfeciions. See Cramer, lib. cit. p. 403. and Neiuton, Method of Fluxions p. 72.
Thefe Points of double Inflexion, are alfo called Points of rn- •v'tfible Inflexion ; becaufe in effect they are not fenfible, but only known by their analytical properties. Analyffs have confidered feveral degrees of thefe Points. Cramer, loc. cit.
POINTERS, in (hip-building, are pillars in an oblique pota- tion, from the floor-rider heads on each fide, pointing or meeting each other at the middle of the gun-deck beams. Blancklefs, Naval Expofitor, p. 121.
POISON (Suppl.)— la the Philofophical Transactions vol. 47. pag. 75. feq, we have an account of feveral experiments made by Monfieur HerilTan, on living animals, with the In- dian Poifon brought over by Monfieur de la Condamine ; and mentioned in the Supplement under this bead. This Poifon which feems to be of a very fubtile and danger- ous nature is extracted by fire from divers plants, efpecially from thofe which the French call Lianes. The Indians in va- rious places of South America prepare this Poifon, and make ufe of it for the killing of wild beafts, in this manner : Thofe favages are very dextrous at making long trunks,
whlch are the moft common weapon ufed by them m hunting. To thefe trunks or tubes they fit little arrows made of patrn- tree, on which they put a little roll of cotton exactly fitting the bore of the tube. They moot thefe with their breath and feldom mifs the mark. They dip the points of thefe lit- tle arrows, as well as of thofe of their bows, in this Poifon • which is fo active, that in lefs than a minute, efpecially when frefh, it kills certain animals, from which the arrow has drawn blood.
Tho' a very fmall drop of this Poifon, conveyed into the blood by puncture is fometimes fufficient to kill a man, or at leaff. to caufe great difturbance in the animal ceconomy, it is quite otherwife when taken in at the mouth ; for then it does no fort of mifchief. See Phil. Tranf. loc. cit.
Poison- £*<,#, a name by which fome call the Tithymalus, See the article Tithymalus, Suppl.
POKE or Pork Pbyfic, the name by which the Phytolacca of botanifts is fometimes called. See the article Phytolacca
Suppl: *
POLE-cat, in zoology, the Englifh name of a creature of the
weafcl-kind, called by authors Putorius. See the article Putorius, Suppl.
POLEY '-Mountain, in botany, the Englifh name of a difrincl genus of plants, called by botanifts Pollum. See the article Polium, Suppl.
POLYANTHES, in the Linnsean fyftem of botany, the name of a diftinct genus of plants, called by fome Tubcrofa, and 'Tuberofe Hyacinth.
The characters are thefe : There is no cup ; the flower con- fifts of one leaf, of an infundibuliform fhape ; the tube it oblong and crooked ; the limb is divided into fix fegments - 3 the ftamina are fix fubulated filaments, connivent, and of the length of the limb ; the antherae are linear; the germen is roundifh, and ftands in the bottom of the corolla ; the ftyle is filiform, and fhorter than the corolla ; the ftigma is tri- fid, thick, and covered with a honey-like juice ; the fruit is acapfule, of a roundifh, but obtufuly trigonal form, compofed of three valves, containing three cells, and wrapped up in the bafe of the corolla ; the feeds are numerous, femiorbicu- lar, plane, and placed in a double feries. Linnai Gen. Plant, p. 140.
POLYANTHUS, the name by which the primula veris of botanifts is fometimes called. See the article Primula Suppl.
POLYCNEMUM, in the Linnsan fyftem of botany, the name of a diftmcl genus of plants, called by Tournefort Cam- pborata. See the article Camphorata, Suppl. The characters of it are thefe: The cup is a fubulated, acute and permanent perianthium, confuting of three leaves ; the flower confifts of five petals, extremely like thofe of the cup, only fhorter ; the ftamina are three capillary filaments, fhorter than the flower ; the antherse are obtufe ; the germen of the piftil is roundifh ; the ftyle is bifid, and of the length of the ftamina ; the ftigmata are obtufe ; the feed, which follows every flower, is fingle, and has fcarce any covering, at moft, only a very thin membrane. Linn&i Gen. Plant, p. 21.
POLYTRICHUM, 'majfyxfr See the article Adiantum, Suppl.
PON D-zveed (Suppl.) — Water Potm-weed, a name fometimes given to a fpecies of Perficaria. See the article Per-
SICARIA, Suppl.
POOR-man's Pepper, a name fometimes given to the Lepidi- umoi botanical writers. See the article Lepidium, Suppl.
POPPY (Suppl.)— Prickly Poppy, a name by which fome call the Argemowe, a diftinct genus of plants. See the ar- ticle Argemone, Suppl.
Spatling Poppy, a name by which the Lychnis is fometimes called. See the article Lychnis, Suppl.
POPULUS, thcPoplar in botany, the name of a genus of trees. See the article Poplar^ Suppl.
PORCUPINE-^, in ichthyology, the Englifh name of fe- veral fpecies of OJlracion. See the article Ostracion, Suppl.
POROPHYLLUM, a name given by Vaillant to a genus of plants, called by Linnaeus Kleinia. See the article Klei- nia, Append.
POSSET {Suppl.) — -Hwr-PossET. See the article Zy- thogala, Suppl,
POSTULATE, or Postulatum (Cycl.) — Authors are not agreed as to the fignification of the term pjtulaium. Many, with whom the Cyclopaedia 'agrees, make the differ- ence between axioms and pojlulata, to be the fame as that between theorems and problems ; axioms, according to thofe authors, being indemonftrable theoretical truths, and pojlulata indemon Arable practical truths.
But others will have it, that axioms, or common notions are primitive, and common to all things partaking of the nature of quantity, and which therefore may become the objects of mathematical fcience, fuch as number, time, extenfion, weight, motion, &c. and that pojlulata relate particularly to magnitudes ftrictly fo called, or to things having local exten-
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