TEXT-BOOKS, 1736-1741 161 



*' I. Then he supposes that x by increasing bè- 

 comes;ir + ^, and from hence he deduces the relation 

 of the increment of x and ;r". 



'*2. Again, in order to find the last ratio of the 

 increments vanishing, he supposes to decrease till 

 it vanishes, or becomes equal to nothing. . . . 

 These are evidently no more inconsistent and con- 

 tradictory, than to suppose a man should first go 

 up stairs, and then come down again. To suppose 

 the increment to be something and nothing at the 

 same time, is contradictory ; but to suppose them 

 first to exist, and then to vanish, is perfectly con- 

 sistent ; nor will the consequences drawn from the 

 supposition of their prior existence, if just, be any 

 ways affected by the supposition of their subsequent 

 vanishing, because the truth of the latter supposition 

 no ways would have been an inconsistency ; but to 

 suppose them first unequal, and afterwards to become 

 equal, has not the shadow of difficulty in it. . . . 

 must confess there seems to be some objection against 

 considering quantities as generated from moments. 

 What moments, what \)i\^ principia janijam nascentia 

 finitaruiìi qziantitatum, are in themselves, I own, I 

 don't understand. I can't, I am sure, easily con- 

 ceive what a quantity is before it comes to be of 

 some bigness or other ; and therefore moments 

 considered as parts of the quantities whose moments 

 they are, or as really fixed and determinate quanti- 

 ties of any kind, are beyond my comprehension, nor 

 do I indeed think that Sir Isaac Newton himself did 

 thus consider them " (pp. 35-41). 



Il 



