E *55 ] 
It is true, indeed, that in a following p adage. 
Dr. Pemberton fays, “ of their [the antients] tafle 
“ and form of demonflration, Sir isaac. always 
“ profeffed himfelf a great admirer: / have heard 
“ him even cenfure himfelf for not following them 
yet more clofely than he did\ and fpeak with 
“ regret of his miftake, at the beginning of 
“ his mathematical fludies, in applying himfelf 
** to the works of des cartes, and other alge- 
“ braie writers, before he had confidered the ele- 
“ ments of euclid with that attention, which 
“ fo excellent a writer deferves.” — But the mode 
of expreflion here ufed, is fo different from the 
foregoing, that there can be no doubt, but that 
it was intended to convey a different meaning. 
And if, in the cenfure firft mentioned, viz. “for 
“ handling geometrical fubjedls by algebraic cal- 
“ culations f Dr. pemberton had underflood 
that Sir isaac meant to include himfelf this 
laff paffage would have been a mere tauto- 
logy. But this laft flrongly implies, on the con- 
trary, that SirJSAAC had, in general, endeavoured 
to follow clofely the antient geometrical form of de- 
monflration, in preference to that by algebraic cal- 
culation ; which is of modern invention. 
There is a remarkable inftance of the attention 
he paid to the diftindtjon between thefe methods, 
and of the preference he gave to the former, in his 
great work of the Principia. Having in Lemma 
XIX. and its Corollaries, given a concife and ele- 
gant folution of a noted geometric Problem, he 
fubjoins: “ Atque ita problematis veterum de qua- 
X 2 “ tuor 
