92 LIMITS AND FLUXTONS 



deserve to be called sophistical \ although I should 

 not like to say so publicly. He subtracts, you 

 know, (A-|^)(B-P) from (A + J ^)(B + J /^) ; 

 whereby, of course, ab disappears in the result. 

 But by what righi, or what reason other than to 

 give an unreal air of simplicity to the calculation, 

 does h.Q pT-epare the products thus ? Might it not be 

 argued similarly that the difference, 



was the moment of A^ ; and is it not a sufifìcient 

 indication that the mode of procedure adopted is not 

 the fit one for the subject, that it quite masks the 

 notion of a limit ; or rather has the appearance of 

 treating that notion as foreign and irrelevant, not- 

 withstanding ali that had been said so well before, 

 in the First Section of the First Book ? Newton 

 does not seem to have cared for being very consis- 

 tent in bis philosophy, if he could anyway get hold 

 of ti-uth, or what he considered to be such. ..." 



We give also Hermann Weissenborn's objec- 

 tion 1 to Newton's procedure of taking half of 

 the increments a and b ; with equal justice 

 one might take, says he, (A + f ^)(B + 1 b) — 

 (A — \ a){^ — \ /;), and the result would then be 

 \b-\-^a-\-\ab. 



112. Walton's two (or three) articles do not 

 iieem to have been read much. They are seldom 

 mentioned. The pamphlets are now rare. Pro- 



^ H. Weissenborn, Principien der h'òheren Analysis iti ihrer Ent- 

 wickelung von Leibniz bis auf Lagrange, Halle, 1856, p. 42. 



