IN
Termination peculiar to it, as «nr7«c in the Greek, fcriUre in the Latin, ecrire in the French, fcrivsre in the Italian, &c. but the Englijh is defective in this point ; fo that to denote the Infinitive, we are always obliged to have re- courfe to the Article to, excepting fometimes when two or more Infinitives follow each other. The Practice of ufing a Number of Infinitives fucceffively, is a great, but a com- mon Fault in Language, as he offers to go to teach to write Englifh. Indeed, where thefe infinitives have no depen- dence on each other, they may be ufed elegantly enough ; as to mourn, to figh, to fink, to fvjoon, to die.
INFINITY. The Idea fignified by the name Infinity is bell examined, by confidering to what Infinity is by the Mind attributed, and then how it frames it. Finite and Infinite are looked upon as the Modes of Quantity, and attributed primarily to things that have Parts, and are capable of Increafe or Diminution, by the Addition or Subtract ion of any the leaft Part. Such are the Ideas of Space, Duration, and Number. When we apply this Idea to the Supreme Being, we do it primarily in refpefl of his Duration and Ubiquity ; more figuratively, when to his Wifdom, Power, Goodnefs, and other Attributes, which are properly inexhauftible and incomprehenfible : For when we call them infinite, we have no other Idea of this Infinity, but what carries with it fome Reflect ion on the Number or the Extent of the Afls or Objeas of God's Power and Wifdom, which can never be fuppofed fo great, or fo many, that thefe Attributes will not al- ways furmount and exceed, tho we multiply them in our Thoughts with the Infinity of endlefs Number. We do not pretend to fay, how thefe Attributes arc in Godj who is infinitely beyond the reach of our narrow Capacities ; but this is our way of conceiving them, and thefe our Ideas of their Infinity. We come by the Idea of Infinity thus. Every one that has any Idea of any flaied Lengths of Space, as a Foot, Yard, tic -finds that he can repeat that Idea, and join it to another, to a third, and fo on, without ever coming ro an end of his Additions. From this Power of enlarging his Idea of_ Space, he takes the Idea of infinite Space, or Immenfity. By the fame Power of repeating the Idea of any Length or Duration we have in our Minds, with all the endlefs Addition of Number, we come by the Idea of Eternity. If our Idea of Infinity be got, by repeating without end our own Ideas, why do we not attribute it to other Ideas, as well as thofe of Space and Duration ; fince they may .be as eafily and as often repeated in our Minds as the other ? yet no body ever thinks of infinite Sweet- nefs, or Whitenefs, tho he can repeat the Idea of Sweet or White, as frequently as thofe of Yard or Day ? To this it is anfwer'd, that thofe Ideas which have Parts, and are capable of Increafe by the Addition of any Parts, af- ford us by their Repetition an Idea of Infinity ; becaufe with the endlefs Repetition thete is continued an Enlarge- ment, of which there is no end : but it is not fo in other Ideas ; for if to the perfefteft Idea I have of White, I add another of equal Whitenefs, it enlarges not my Idea at all. Thofe Ideas, that confilt not of Parts, cannot be augmented to what proportion Men pleafe, or be ftretch'd beyond what they have received by their Senfes ; but Space, Duration, and Number being capable of Increafe by Repetiiion, leave in the Mind an Idea of an endlefs room for more ; and fo thofe Ideas alone lead the Mind towards the Thought of Infinity. We are carefully to di- itinguifh between the Idea of the Infinity of Space, and the Idea of a Space infinite. The firlt is nothing but a fuppofed endlefs Progreflion of the Mind over any repeat- ed Idea of Space : But to have actually in the Mind the Idea of a Space infinite, is to fuppofe the Mind already paffed over all thofe repeated Ideas of Space, which an endlefs Repetition can never totally reprefent to it ; which carries in it a plain Contradiction. This will be plainer, if we confider Infinity in Numbers. The Infinity of Numbers, to the End of whofe Addition every ona perceives there is no Approach, eafily appears to any one that reflefts on it : But how clear foever this Idea of the Infinity of Numbers be, there is nothing yet more evi- dent, than the Abfurdity of the aflual Idea of an infinite Number.
INFIRMARY, a Place where the Sick belonging to any Society or Comm un j t y are difpofed.
INFLAMMATION, i„ phyfic, is underflood of a Tu- mour, occafioned from an Obflruclion ; by means whereof the Blood flowing into fome Part falter than it can run off again, fwells up, and caufes a Tenfion, with an unu- fual Sorencfs, Rednefs, and Heat. The immediate Caufe, therefore of all hift 'animations, is an overflowing of Blood. Other Caufes, more remote, may be the Denfity and Coao u l at i on of the Blood, or the Relaxation and Con- tufion of the Fibres. Phyficians have given particular Names to the Inflammations of feveral Parts. That of the Eyes is call'd Ophthalmia, that of the Lungs Peripneumonia, and that of the Liver Hepatites. The word Inflammation
C 387. )
IN
comes from the latin in, and FUmma, Flame. , • ■
'^LATION, a blowing up 5 is the fetching or filling any flaccid or dii.cndable Body, with a flatulent or wind?
ixtSr^rvfe^ the La " n '"' and Z- 2 "". ° f A I blow.
l]N*LtClIOI\, in Optics, is a multiplicate Refrac- tion of the Rays of Light, caufed by the unequal Denfity ot any Medium whereby the Motion or Progrefs of the Kay is hindred from going on m a right Line, and is in- flected or deflected by a Curve, faith Dr. Hook, who firft took uot.ee ot this Property : And this, he faith, differs both from Reflea.on and Refraction, which are both made at the Superficies of the Body, but this in the mid- dle ot it within. Sir IJaac Newton, as you will find under Light, diicover'd alfo by plain Experiment this Infieftioa ot the Kays of Light; and M. de la Hire faith, he found, 1 hat the Beams of the Stars being obferved in a deep Valley, to pafs near rhe Brow of a Hill, are always more rerracled, than if there were no fuch Hill, or the Ob- lervations were made on the top thereof; as if the Rays of Light were bent down into a Curve by pafling near tha Surface of the Mountain. Sir Ifaac Neaton in 'his Optics makes feveral Experiments and Obfervations on the In- flexion of the Rays of Light; which fee under Litht and Rays.
INFLECTION, in Grammar, is the Variation of Nouns and Verbs, in their feveral Cafes, Tenfes, and De- clenhons. Infieelien is a general Name, under which are comprehended both the Conjugation and Declenfion.
INFLECTION POINT of any Curve, in Geometry, fign.fies the Point or Place where the Curve begins to bend back again a contrary way : As for inftance, when a curve Line, as A F K, is partly concave, and partly con- vex toward any right Line, as A B, or towards a fixed fomt, then the Point F, which divides the .concave from the convex Part.and confequently is at the Beginning of the one and End of the other, is called the To'mt of InfeBion, as long as the Curve, being continued in F, keeps its Courfe the fame ; but it is called the Point of Retrogref- fion, when it infl e a s back again towards that Part or Side, from whence it took its Original. See Fig. 2.
Before the Theory of this Inflexion, and Retrogreflion of Curves, can be underflood, it may be neceffary to ex- plain this general Principle. Whatsoever finite Quantity (or if it be a Fluxion, it is all one) goes on continually in- creafing or decreafing, it cannot change from a pofitive to a negative Expreffion, orfrom a negative to a pofitive one, without firfl becoming equal to an infinite or nothing. It is equal to nothing, if it doth continually decreafel and equal to an infinite, if it doth continually increafe. To il- luftrate this, let there be two Circles touching one ano- ther in the Point E {Fig. 1.) their Diameters A E and E I lyin£m one and the fame right Line. Let A E or EI be — d. Let the Diflance between the Extremity A and any Ordinate in either of the Circles be = to x perpe-
tually. I confider now, what will be the Expreffions of the Lines intercepted between E the Point of Coutaa of the Circles ; fuch as are the Lines EB and E F intercep- ted between E and the Ordinates C B and G F. It is cer- tain therefore, that taking a Point, as B, any where be- tween A and E, that then the Expreffion of the inter- cepted B E is d— x ; but taking a Point, as F between E and I, the Expreffion of the intercepted E F, /hall be x — d. ForAB, orAF, being taken for x indifferently, the Values of the intercepted Lines will appear with this Change of Signs. In one cafe therefore the Expreffion is pofitive, in the other negative. But as the Points B or P approach to E, the Quantities BE and E F decreafe con- tinually, and at the Point E are equal to nothing. So that it is plain there is no pafling from a pofitive to a ne- gative Expreffion, in this cafe, of a Quantity continually decreafing, without pafling thro nothing. For the other parr, let us confider the Tangents ("as D A or H I) cut 06? by Lines continually drawn from E, the Point of the Cir- cle's Contaa. If CB, or GF, be put equal to y, tha
Expreffion
