Page:Cyclopaedia, Chambers - Supplement, Volume 1.djvu/684

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and leaps furprifingly j it feeds on the fruits it finds in the woods. Ray's Syn. Quad. p. 156.

There is alfo another fpecies of this creature in Guinea of the fize of the former, and of a blacktfh brown on the greateft part of the body, but of a bluifh grey on the belly, and the lower half of its tail is of a fort of tawney colour ; its mouth and nofe are blue, and its cheeks adorned with a multitude of yellow hairs cluttered together like thofe of a goat's beard. Its legs and feet are wholly black, it is a fprightly animal, and fkips and plays like the other ; bcfides thefe there is alfo a third of the Exauima kind fmaller than the others, and of a mixt colour of brown, yellow, and grey ; this has a long tail, a fmall head, and no beard.

EXSIBILANTES, in antiquity, a kind of hitters, who, in the theatre, and other public auditories, ulcd to make a noife with their feet, and even fometimes beat the feats with battons. Pitifc. Lex. Ant. in voc.

EXSUCCATIO,awordufed by fomechirurgical writers toexprefs

an enchymofts, or fugillation. See the article Enchymosis.

EXSUFFLATION, aceremonyobfervedinbaptifm, by which the candidate was fuppufed to renounce the devil. See Bap- tism.

EXTEND, in the manege. To extend a borfe is an expreffion ufed by fome, to import the fame with making a horfe go large. See Large.

Extend, inlaw. See Extending, Cych

EXTENDENTIUM-Tnfcrwr, in anatomy, a name given by Spi- gelius and others to a mufcle of the wrift, called by Albinus ulnaris externus, and by Winflow and others cubitalis exter- nus. See Cubitalis externus.

EXTENDI Facias, in law, a writ of extent, whereby the value of lands is commanded to be made and levied, &c. Reg. Orig.

EXTENSION (Cyd.)-~ The infinite divifibilityof Extenfion has been a famous quefiion in all ages. The doctrine of mathema- ticians on this head is not eafy to reconcile with the tenets of fome philofophers. Thofe who hold that all Extenfonznd mag- nitude are compounded of a certain minima fenftbitia, and that a line for inftance cannot increafe or decreafe, but by certain in- divifible increments or decrements only, muft confiftently with themfelvcs affirm, that all lines are commenfurable to each other, contrary to the tenth book of Euclid; whodemonftrates, that the diagonal of a fquare is incommenfurable to its fide. But if all lines were compofed of certain indiv ifible elements, it is plain one of thofe elements muft be the common meafure of the diagonal and the fide. This is a gordian knot which none of the pbilofophers have yet thought fit to untie. An ingenious author of this age, who has (aid feveral plaufible things againft the doctrine of mathematicians, afks, when it is faid or im- plied that fuch a certain line delineated on paper contains more than any aflignable number of parts, whether any more in truth ought to be underftood, than that it is a fign indiffe- rently repreienting all finite lines, be they ever fo great; in which relative capacity it contains /'. e. ftands for more than any affignnble number of parts ? and whether it be not altogether ab- furd to fuppofe a finite line confidered in itfelf, or in its own pofi- tive nature, fhould contain an infinite number of parts,? But we own ourfelvcs at a lofs to fee how, fuppofing a line divifible into any aflignable number of parts in its relative capacity only, will folve the difficulties attending Euclid's doctrine of incom- mcnfurables, which neither this author nor any other has yet been able to refute. Suppofing, for inftanccj a line in its own pofitive nature to contain but 10 parts, and fuppofe a fquare formed on this line, this fquare muft neceffarily contain 100 parts. The diagonal of the fquare muft have fome length ; but what ? Shall we fay 14 or 15 parts, if the firft, the fquare of the diagonal muft contain 196 parts; if the fecond, it muft contain 225 parts, neither of which numbers are double of 300, the parts contained in the fquare of the fide. Now it is moft evident without any intricacy of geometrical demonstra- tion, that the fquare of the diagonal of every fquare muft be precifely double of the fquare itfelf. But farther, fuppofing the fide to contain 100 parts, it is eafily feen as before, that the diagonal can neither be cxpreiled by 141 nor by 142 ; .and there can be no fractions in the expreffion, each part by the fuppofitio'n being indivifible. This leads us to the fame abfurdity as before, with this addition ; that as neither 141 nor 142 are in proportion to 100, as 14 or 15 are to 10, it follows that the Ifofceles triangle which is the half of a great fquare is not fimilar to the Ifofceles triangle, that is the half of a leffer fquare. But can any thing be more inconceivable, more repugnant to the moft obvious notions of fimilar figures than this. ?

But it may be worth while to hear this author himfelf, in ano- ther part of his works, urging his difficulties againft the com- monly received doctrine of mathematicians. He obferves, the infinite divifibility of finite Extenfion, though it is not exprefsly laid down either as an axiom or theorem in the elements, of geometry ; yet is throughout the fame every where fiippofed, and thought to have fo infeparable and ef- fential a connection with the principles and demonftrations in geometry, that mathematicians never admit it into doubt, or make the leaft queftion of it. And as this notion is the fource from whence do fpring all thofe amufing geometrical paradoxes which have fuch a direct repugnancy to the plain

common fenfe of mankind, and are admitted with fo much reluctance into a mind not yet debauched by learning ■ fo in it the principal occafion of all that nice and extreme fubtilty which renders the ftudy of mathematics fo difficult and te- dious. Hence, fays he, if we can make it appear, that no finite Extenjicn contains innumerable parts, or is infinitely divifible it follows that we {hall at once clear the fcience of geometry from a great number of difficulties and contradictions, which have ever been efteemed a reproach to human reafon, and withal make the attainment thereof a bufinefs of much lefs time and pains, than it hitherto hath been. Every particular finite Extenfion, which may poflibly be the object of our thought, is an idea exilting only in the mind, and confequently each part thereof muft be perceived. If therefore I cannot perceive innumerable parts in any finite Ex~ tenfion that I confuler, it is certain they are not contained in it ; but it is evident, that I cannot diftinguifh innumerable parts in any particular line, furface, or folid, which I either perceive by fenfe, or figure to myfelf in my mind : where- fore I conclude they are not contained in it. Nothing can ba plainer to me, than that the ExtenfonsI have in vie ware no other than my own ideas; and it is no lefs plain, that I cannot refolve any one of my ideas into- an infinite number of other ideas, that is, that they are not infinitely divifible. If by infinite Extenfion be meant fomething diftinct from a finite idea, I declare I do not know what that is, and fo cannot affirm or deny any thing of it. But if the terms Extenfion, parts, and the like, are taken in any fenfe conceivable, that is, for ideas ; then to fay a finite quantity or Extenfion confifts of parts infi- nite in number, is fo manifeft a contradiction, that every one at firft fight acknowledges it to be fo.

Hewhofeunderftanding isprepoffeftwith thedoctrineofabftract: general ideas, may be perfuaded, that (whatever be thought of the ideas of fenfe,) extenfion in abftract is infinitely divifible* And one who thinks the objects of fenfe exift without the mind will perhaps in virtue thereof be brought to admit, that a line but an inch long may contain innumerable parts really exifting, tho* too fmall to be difcerned. Thefe errors are grafted as well in the minds of geometricians, as of other men, and have a like influence on their reafonings ; and it were no difficult thing to fhew how the arguments from geometry made ufe of to fupport the infinite divifibility of Extenfion? are bottomed on them. At prefent we fhall only obferve in general, whence it is that the mathematicians are all fo fond and tenacious of this doctrine.

The theorems and demonftrations in geometry are converfant about univerfal ideas, which is to be underftood in this fenfe : To wit, that the particular lines and figures included in the diagram* are fuppofed to ftand for innumerable others of dif- ferent fizes ; or in other words, the geometer confiders them abftracting. from their magnitude ; which doth not imply that he forms an abftract idea* but only that he cares not what the particular magnitude is, whether great or fmall, but looks on that as a thing indifferent to the demonftration. Hence it fol- lows, that a line in the fcheme, but an inch long, muft be fpoken of, as though it contained ten thoufand parts; fince it is regarded not in itfelf, but as it is univerfal only in its fig- nification, whereby it reprefents innumerable lines greater than itfelf, in which may be diftinguiihed ten thoufand partsr or more, though there may not be above an inch in it. Af- ter this manner the properties of the lines fignified are (by a very ufual figure) transferred to the fign, and thence through mrftake thought to appertain to it confidered in its own nature.

Becaufe there is no number of parts fo great, but it is pofii- ble there may be a line containing more ; the inch line is faid to contain parts more than any affignable number ; which is true, not of the inch taken abfolutely, but only for the things fignified by it. But men not retaining that difiinction in their thoughts, flide into a belief that the fmall particular line defcribed on paper contains in itfelf parts innumerable : There is no fuch thing as the ten thoufandth part of an inch ; but there is of a mile or diameter of the earth, which maybe fignified by that inch. When therefore I delineate a triangle on paper, and take one fide not above an inch, for example, in length to be the radius ; this I confider as divided into ten thoufand or an hundred thoufand parts, or more. For tho' the ten thou- fandth part of that line confidered in itfelf, is nothing at all, and confequently may be neglected without any error or incon- veniency ; yet thefe defcribed lines being only marks {land- ing for greater quantities, whereof it may be the ten thoufandth part is very confiderable, it follows, that to prevent notable errors in practice, the radius muft be taken of ten thoufand parts, or more.

From what hath been faid the reafon is plain why, to the end any theorem may become univerfal in its ufe, it is neceffary we fpeak of the lines defcribed on paper, as though they con- tained parts which really they do not. In doing of which, if we examine the matter throughly, we fhall perhaps diicover that we cannot conceive an inch itfelf as confuting of, or being, divifible into a thoufand parts, but only fome other line which' is far greater than an inch, and reprefented by it. And that when we fay a line is infinitely divifible, we muft mean a line which is infinittly great. What we have here obferved

feems