Q II A 



other thing of the fame kind, may be faid to be greater or 

 lefs than it ; equal, or unequal, to it. 



Mathematics is the fcience or dodrine of quantity. 

 Quantrty is a general attribute, applied in a very different 

 manner to things of very different nature ; whence it is im- 

 poflible to give any univerfal definition of it. 



Quantity is applied both to things and to modes ; and 

 this either fingularly to one ; or plurally, to feveral. In the 

 firlt cafe it is called i:uigmtude, in the latter multtluik. 



Quantity may be reduced to four claffes ; viz. 



Quantity, Moral, which depends on the manners of 

 men, and the free deterrnmation of their wills. As the 

 prices and value of things ; degrees nf dignity and power, 

 good and evil, merit and demerit, rewards and punifli- 

 ments, &c. 



Ql^ANTiTV, Notional, arifing from the operation of the 



underllanding only. Such as the largenels or narrownefs of 



the capacity of the mind, and its conceptions. In Logic, 



■ univerfals, predicaments, &c. In Grammar, the quantity 



or meafure of fyllables, accents, tones, &c. 



Quantity, Ph^fical, or Natural, which is of two kinds : 

 I. That which nature furnifhes us with in matter, and its 

 extenfion. And, 2. In the powers and properties of natu- 

 ral bodies : as gravity, motion, light, heat, cold, rarity, 

 denilty, &c. 



Quantity, TranfcenJental, as duration, the continuation 

 of ajiy being, exiftence, time, &c. 



Quantity is alfo popularly diftinguillied into continued 

 and difcrctc. 



Quantity, Continued, or Continuous, is when the parts 

 are connefted together, and is commonly called magnitude. 

 This, again, is of two kinds ; either fucceffive, or improper, 

 as time. 



Quantity, Difercte, is when the parts of which it con- 

 fifts exilt diftin&ly, and unconnefted together ; which makes 

 V>'hat we call number or multitude. 



The notion of continued quantity, and its difference from 

 difcrete, appears to fome without foundation. Mr. Macliin 

 confiders all mathematical quantity, or that for which any 

 fymbol is put, as nothing elfe but numbfr, with regard to 

 i'ome meafure, which is confidered as one ; for that we can- 

 not know precifely how much any thing is, but by means 

 of number. The notion of continued quantity, without 

 regard to any meafure, is iiidiftinft and confufed ; and 

 though fome fpecics of fuch quantity, confidered piivficallv, 

 may be defcribed by motion, as lines by the miction of 

 points, and furfaces by the motion of lines ; yet the ma;;-ni- 

 tudcs, or mathematical quantities, are not made by tiie mo- 

 tion, but by numbering according to a meafure. Vide I'liil. 

 Tranf. N^447. p. 228. 



Permanent quantity is farther diftinguifhable into length, 

 breadth, and depth. 



Wolfius feems to give us a more precife notion of mathe- 

 matical quantity, and its two fpecies of difcrete and con- 

 tinued, hatever is referred to unity in the fame manner 

 as one right line to another, is what we call quantity ; or 

 number in general. 



If, now, the thing be relerred to a given unit, aa 3, it 

 is called a determinate number ; it to unity in the general, 

 or at large, it is called a quantity ; which, on this principle, 

 is the fame with indeterminate numl)er. 



Thus, e. gr. the breadth of a river is accounted a quan- 

 tity ; if, then, it be enquired how great it is ; to conceive 

 its quantity, we take fome unit at pleafure, and fee the re- 

 lation of the breadth to it ; and according to the different 

 unit affumed, we exprefs the breadth of tiie river in a dif- 

 ferent determinate number. 



Vol. XXIX. , 



Q U A 



The breadth of the river, therefore, is quantity confi- 

 dered as referred to a vague unit, or to unity at large ; but 

 tlie unit being determined, the thing is underftood by a de- 

 terminate number. 



In this fenfe, algebra is the arithmetic of quantitie,. See 

 on the fubjed of quantity, Harris's Philofophical Arrange- 

 ments, chap. ix. 



Quantity of yl a ion. See Action. 

 Quantity, Impojfdde, and Imaginary. See Root. 

 Quantity of Curvature at any point of a curve is deter- 

 mined by the circle of curvature at that point, and is reci- 

 procally proportional to its radius. Newton's Meth. of 

 Flux, and Inf. Series, p. 60. Maclaurin's Fluxions, b. i. 

 c. xi. See CuRVATURii and Evolujk. 



Quantity of Motion, in Mechanics, is of two kinds ; viz. 

 of momentary motion, and of entire motion. 



Quantity of entire motion. The Cartefians define the 

 entire motion as the momentary one, by the faftum of the 

 mafs, or quantity of matter, into the velocity ; but fince 

 motion is a fucceffivc being, and has no parts co-exilling toge- 

 ther, its quantity ought to be eflimated by the aggregate of 

 the feveral parts exilling fucceflively ; and is therefore equal 

 to the faftum of the momenta into the time. 



Quantity of momentary motion is the faftum of the ve- 

 locity into the mafs ; or it is a meafure arifing from the 

 joint confideration of the quantity of matter, and the velo- 

 city of the motion of tlic body ; the motion of any whole 

 being the fum or aggregate of the motiorr m all its feveral 

 parts. 



Hence, in a body twice as great as another, moved with 

 an equal velocity, the quantity of motion is double ; if the 

 velocity be double alfo, the quantity of the motion will be 

 quadruple. Hence, the quantity of momentary motion coin- 

 cides with what we call the momentum, or impetus of a 

 moving body. See Force. 



In the collifion of bodies, the quantity of momentary mo- 

 tion, which is found by taking the fum of motions tending 

 the fame way, or their difference, if they tend towards con- 

 trary parts, is not at all changed by any actions of the bo- 

 dies on one another. See Percussion. 



Quantity of Matter \n anybody, is the produdl of the 

 denlity into the bulk ; or a quantity arifing from the joint 

 confideration of its magnitude and denfity. 



As, if a body be twice as denfe, and take up twice as 

 much lp:ice as another, it will be four times as great. 



Tliis quantity of matter is the bell difcoverable by the 

 abfolute weiglit of bodies. See Matter. 



Quantity, Infnite. See Infinite Quantity. 



Quantities, in Algebra, are indeterminate numbers, or 

 things referred to unity in general. See Number. 



Qi antities are properly the fubjcft of algebra ; which 

 is wliolly converfant in the computation of fuch quantities. 



Given quantities are ufed to be noted by the firil letters 

 of the alphabet a, b, c, d, &c. the quantities fought by the 

 lall, =,j', .V, &c. See Characters. 



Algebraical quantities are chiefly of two kinds ; pofttive, 

 and negative. 



Quantities, Pofitive, or Affirmative, are thofe which are 

 greater than nothin;^, and wliich are affefted with the fign -|- 

 prefixed ; or fuppofed to be fo. 



Qi:antities, Negative, or Privative, are thofe lefs than 

 nothing : which are affefted with the fign — prefixed. 



Hence, i. Since -f is tiie fign of addition, and — the 



fign of lubtraftion ; a pofitive quantity is produced by 



adding any real quantity to nothing ; e. gr. o -)- 3 — 4- 3 ; 



and o -[■ a = -^ a. And a privative quantity is produced 



A a by 



