MACLAURIN'S TREATISE, 1742 183 



antient geometricians. This is our design in the 

 following treatise ; wherein we do not propose to 

 alter Sir Isaac Newton's notion of a fluxion, but to 

 explain and demonstrate his method, by deducing 

 it at length from a few self-evident truths, in that 

 strict manner : and, in treating of it, to abstract 

 from ali principles and postulates that may require 

 the imagining any other quantities but sudi as may 

 be easily conceived to have a real existence. We 

 shall not consider any part of space or time as 

 indivisible, or infinitely little ; but we shall consider 

 a point as a term or limit of a line, and a moment 

 as a term or limit of time ... [p. 41]. If we are 

 able to join infinity to any supposed idea of a deter- 

 minate quantity, and to reason concerning magni- 

 tude actually infinite, it is not surely with that 

 perspicuity that is required in geometry. In the 

 same manner, no magnitude can be conceived so 

 small, but a less than it may be supposed ; but 

 we are not therefore able to conceive a quantity 

 infinitely small ..." 



166. In the posthumous work, An Account of Sir 

 Isaac NewtoìCs Philosophical Discoveries^ by Colin 

 Maclaurin, 2nd ed., London, 1750, there is printed 

 a life of Maclaurin, from which we glean the follow- 

 ing (pp. viii, ix, and xviii) relating to Berkeley 's 

 attack in the Analyst : 



" Mr. Maclaurin found it necessary to vindicate 

 his favourite study, and repel an accusation in which 

 he was most unjustly included. He began an 

 answer to the bishop's hook ; but as he proceeded, 



