VOt. LXIV.] PHILOSOPHICAL TRANSACTIONS. 5\Q 



last two particulars, certainly, and I think the first also, have no foundation in 

 the account Dr. Pemberton has given of this matter. His words are: " I have 

 often heard him (Sir Isaac) censure the handling geometrical subjects by algebraic 

 calculations; and his book, of algebra he called by the name of Universal Arith- 

 metic, in opposition to the injudicious title of geometry, which Descartes had 

 given to the treatise, wherein he shows, how the geometer may assist his inven- 

 tion by such kind of computations." — Dr. Pemberton's expression does not at all 

 imply, that Sir Isaac Newton censured himself for handling geometrical subjects 

 by algebraic calculations ; the only idea it suggests is, that he censured that way 

 in general, and those who practised it, and that he had his eye particularly on 

 Descartes ; and, far from intimating, that he had inconsiderately called his book 

 of algiebra by the name of Universal Arithmetic, and afterwards censured him- 

 self for doing so, and wished that he had rather called it Greometry, as Descartes 

 did his; it directly affirms, on the contrary, that by express design and choice, 

 he called it Arithmetic, in opposition to Descartes's injudicious title of 

 Geometry. 



It is true indeed, that in a following passage. Dr. Pemberton says, " of their 

 (the ancients) taste and form of demonstration. Sir Isaac always professed him- 

 self a great admirer: I have heard him even censure himself for not following 

 them yet more closely than he did; and speak with regret of his mistake, at the 

 beginning of his mathematical studies, in applying himself to the works of Des- 

 cartes, and other algebraic writers, before he had considered the elements of 

 Euclid with that attention, which so excellent a writer deserves." — But the mode 

 of expression here used, is so different from the foregoing, that there can be no 

 doubt, but that it was intended to convey a different meaning. And if in the 

 censure first mentioned, viz. " for handling geometrical subjects by algebraic 

 calculations," Dr. Pemberton had understood that Sir Isaac meant to include 

 himself, this last passage would have been a mere tautology. But this last 

 strongly implies, on the contrary, that Sir Isaac had, in general, endeavoured to 

 follow closely the ancient geometrical form of demonstration, in preference to 

 that by algebraic calculation; which is of modern invention. 



There is a remarkable instance of the attention he paid to the distinction be- 

 tween these methods, and of the preference he gave to the former, in his great 

 work of the Principia. Having in lemma 1 9, and its corollaries, given a concise 

 and elegant solution of a noted geometric problem, he subjoins: " Atque ita 

 problematis veterum de quatuor lineis ab Euclide incoepti, et ab Apollonio conti- 

 nuati, non calculus, sed compositio geometrica, qualem veteres quaerebant, in 

 hoc coroUario exhibetur." That the words, " non calculus sed compositio geo- 

 metrica," refer to Descartes's prolix algebraic solution of this problem, in his 

 Geometry, p. 25-34, will, I believe, be readily granted by every one acquainted 

 with Sir Isaac Newton's writings. 



