I N F, 



between the method of fluxions, and tliat of infiiiitefimals 

 thus appears more perfeft. 



And however fafe and convenient this method may be, 

 yet fo:ne -.^-ill al.vays fcruple to admit infinitely little quan- 

 tities and infinite orders of infinitefimals, into a fcience that 

 boafts of the raoft evident and accurate principles, as well 

 as of the moft rigid de:nonftrations It is therefore proper, 

 that this cxtenfu-e and iifefal dodrine {hou)d be eilablifhed 

 on unexceptionable principles. See the articles 1"luxio\ 

 and Limit.. See alfo Mr. Maclaurin's Treat, of Fluxions, 

 in the Introdudion, p. 39, 40, &c. and book i. art. 495 to 

 502. 



Infinitely Irfin'.te FraSions, or all the powers of all the 

 fraftions whofe numerator is one, are together equal to an 

 unit. See the demonftration hereof given by Dr. Wood, in 

 Hook, Phil. Coll. N 3 p. 45, feq. 



Hence, it is deduced, i •. That there are not only infinite 

 progreflions, or progreflions in infinitum ; but alfo infinitely 

 farther than one kind of infinity. 2 '. That the infinitely 

 infinite proo-renioas are notwithftanding computable, and to 

 be brought into one fum ; and that not one finite, but fo 

 fmall as to be lefs than any afUgnable number. 3 . That of 

 infinite quantities, fonie are equal, others unequal. 4". That 

 one infinite quantity may be equal to two, three, or more 

 other quantities, -vhether infinite or finite. 



INFINITIVE, in Grammar, the name of one of the 

 moods, which ferve for the conjugating of verbs. 



Tl'.e infinitive does not denote any precife time, nor does 

 it determinate the nuniber, or perfons, but exprefles things 

 in a loofe indefinite manner ; a«, to teach, &c. 



Hence the Latin and modern ,'rammarians have called 

 verbs under this mode, from this their indefinite nature, infi- 

 nitivcs. Sanftius has given them the name of imperfonals ; 

 and the Greeks that of a-jtfEfiJxIx from the fame reafon of 

 their not difcovering either perfon or number. 



Infinitives, fays Mr. Harris, not only lay afide the cha- 

 rafter of attributives, but they alfo alTume that of fubftan- 

 tives, and are diftinguilhed with their feveral attributes : e. g. 

 *' D'jlce & decorum eft pro patria nwri; fcire tuum nihil 

 eft, &c." 



Hence the infinitive has been fometimes called ovo/xi 

 fr,u%-t<n, a verbal noun ; fometimes o-,oux ^Ji-u. ■'«.-, the verb's 

 noun. The reafon of the appellation is evident in Greek, 

 by its taking the prepofitive articles before it in all cafes ; 

 thus TO -/e»?tiv, T- -/;«?;ii, TM -/fKesiv. The fame conftruclion 

 is not unknown in Englifh. Thus Spencer, 



" For not to have been dipped in Lethe's lake 

 Could fave the fon of Thetis/ro;n to die :" i. e. 



The lloics held the infinitive as the genuine ir.u.-x, or verb, 

 a name which they denied to all other modes ; becaufe the 

 true verbal character was conceived to be contained firaple 

 and unmixed in the infinitive only : thus, to walk, means 

 fimply that energy, and nothing more ; the other modes, 

 befides exprcfling' this energy, fuperadd certain affeaions 

 which rcfped perfons and circuniftances. The infinitive, 

 fays Prifcian, " fignificat ipfam rem, quam continet ver- 

 bum." The infinitive, in the application of it, naturally co- 

 alefces with all thole verbs, that denote any tendency, deiire, 

 or volition of the foul, but not readily with others. See 

 Harris's Hermes, p. 163, &c. 



In moft languages, both ancient and modern, the infini- 

 tive is diftinguifiied by a termination peculiar to it ; as ti/tIiiv 

 in the Greek, fcrtbere in the Latin, ccrire in the French, 

 Jcrivere in the Itahan, &c. but the Enghfh is defeftive in 

 this point ; fo that to denote the infinitive, we are obliged to 



Vol.. XIX. 



I N F 



have reconrfe to the article to : excepting fometimes when 

 two or more infinitives follow cacli other. 



The praftice of ufing a number of infinitives fucceffively, 

 is a great but a common fa'tlt in language; as he offered to go 

 to teach to -write Englilli. — Indeed, where the infinitives have 

 no dependence on each other, thiy may be ufcd elegantly 

 enougli ; as to mourn, to figh, tofmt, tofwoon, to die. 



INFINITO, in the 'Italian Mujic, is ufed for fuch canons 

 or fugues, as may be begun again and again : whence they 

 are alio cAliztX perpetual fugues. See FuGUE. 



INFINITY, the quality which denominates a thing in- 

 finite. The idea fignified by the name infinity is beft exa- 

 mined by confidering to what things infinity is by the mind 

 attributed, and how the idea it felf is framed : finite and in- 

 finite are looked upon as the modes of quantity, and are 

 attribited primarily to things that have parts, and are capable 

 of increafe or diminution, by the addition or fubtradiion of 

 any the leaft part. Such are the ideas of fpace, duration, 

 and number. When we apply this idea to the Supreme 

 Being, we do it primarily in refpeft of his duration and ubi- 

 quity : and more figuratively, when to his wifdom, power, 

 goodnefs, and olher atttibutes, which are properly inexhauf- 

 tible and incmnprchenfible : for when we call them infinite, 

 we have no other idea of this infinity but what carries with 

 it fome reflexion on the number, or the extent of tlie 

 acls or objects of God's power and wifdom, which can never 

 be fuppofed fo great, or fo many, that thefe attributes will 

 not always furmount and exceed, though we multiply them 

 in our thoi:ghts with the infinity of endlefs number. We do 

 not pretend to fay, how thefe attributes are in God, who is 

 infinitely beyond the reach of our narrow capacities : but 

 this is our way of conceiving thena, and thefe are our ideas of 

 their infinity. 



We come by the idea of infinity thus : every one that has 

 any idea of any ilated length or fpace, as a foot, yard, &c. 

 finds that he can repeat that idea, and join it to another, to 

 a third, and fo on, without ever coming to an end of his 

 additions. From this power of enlarging his idea of fpace, 

 he takes the idea of infinite fpace, 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 num- 

 ber, we alfo come by the idea of eternity. 



If our idea of infinity be got by repeating without end 

 our own ideas, it may be aflved, why do we not attribute it 

 to other ideas, as well as thofe of fpace and duration ; fince 

 t'lcy may be as eafily, and as often repeated in our minds, 

 as tlie otiier ? yet nobody ever thinks of infinite fweetnefs, 

 or whitenefs, tliough he can repeat the idea of fvvect or 

 white, as frequently as thofe of yard or day i To this it 

 is anl'wered, that thofe ideas wliich have parts, and are ca- 

 pable of increafe by the addition of any parts, alford us by 

 tlieir repetition an idea of infinity ; becaufe with tlie eijdlefs 

 repetition there is connecled an enlargement, of wiiich there 

 is no end : but it is not fo in other ideas ; for if to the moll 

 pcrfecl idea I have of white, I add another of equal white- 

 nefs, it enlarges not my idea at all. Thofe ideas, which 

 confift not of parts, cannot be augmented to what propor- 

 tion men pleafe, or be ftrctclied beyond what they have 

 received by their fenfes ; but fpace, duration, and number, 

 being capable of increafe by repetitiou, leave in the mind 

 an idea of an endlefs room for more ; and fo tliofe idea* 

 alone lead the mind towards the thought of infinity. 



We are carefully to diftinguifh between the idea of the 

 infinity of fpace, and the idea of the fpace infinite. The 

 firll is nothing but a fuppofed endlefs progreffion of the 

 mind over any repeated idea of fpace ; but to have actually 

 ill the miad the idea of fpace infi:iite,— is to fuppofe tlio 

 N mind 



