TEXT-BOOKS, 1736-1741 151 



several orders and properties, which, to ali sober 

 Inquirers into mathematica! Truths, must certainly 

 appear very notional and visionary " (p. xii), for 

 "Absolute Infinity, as such, can hardly be the 

 object either of our Conceptions or Calculations, 

 but relative Infinity may, under a proper regula- 

 tion " (p. xii). Newton " observes this distinction 

 very strictly, and introduces none but infinitely 

 little Quantities that are relatively so." Colson 

 answers Berkeley's criticism in the Analyst of 

 Lemma 2, Book li, in the Principia in the follow- 

 ing manner : — 



"Let X and Y be two variable Lines. . . . Let 

 there be three periods of time, at which X becomes 

 K — \a, AjA-f-J^; and Y becomes V> — \b, B, and 

 B + i^ . . . Then ... the Rectangle XY will 

 become . . . KV>-\a?>-\bK^\ab, AB, and 

 AB + i^B + i<^A + i^^. Now in the interval from 

 the first period of time to the second . . . its whole 

 Increment during that interval is \aY>-\-\bK — \ab. 

 And in the interval from the second period of time 

 to the third, ... its whole Increment during that 

 interval is \à^-\-\bh.-\-\ab. Add these two Incre- 

 ments together, and we shall bave a^ + b\ for the 

 compleat Increment of the Product XY " (p. xiii), 

 called the " Moment of the Rectangle" when a and 

 b are infinitely little. 



Another mode of procedure is this: ''the Fluxions 

 or Velocities of increase, are always proportional 

 to the contemporary Moments." " When the Incre- 

 ments become Moments, that is, when a and b are 



