NEWTON. 
title of Geometry, which Des Cartes had 
given to the treatise in which he shews how 
the geometrician may assist his invention 
by such kind of computations. He fre- 
quently praised Shisius, Barrow, and Huy- 
gens, for not being influenced by the false 
taste which then began to prevail. He 
used to commend the laudable attempt of 
Hugo d’Oraerique to restore the ancient 
analysis ; and very much esteemed Apolo- 
nius’s book De Sectione Rationis, for giving 
us a clearer notion of that analysis than we 
had before. Dr. Barrow may be esteemed 
as having shewn a compass of invention, 
equal, if not superior, to any of the modems, 
our author only excepted ; but Newton 
particularly recommended Huygens’s style 
and manner ; he thought him the most ele- 
gant of any mathematical writer of modern 
times, and the truest imitator of the an- 
cients. 
Of their taste and mode of demonstration 
our author always professed himself a great 
admirer; and even censured himself for not 
following them yet more closely than he 
did ; and spoke with regret of his mistake 
at tlie beginning of his matiiematical stu- 
dies, 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 excel- 
lent a writer deserves. 
But if this was a fault, it is certain it was 
a fault to which we owe, both his great in- 
ventions in speculative mathematics, and 
the doctrine of fluxions and infinite series. 
And perhaps this might be one reason why 
his particular reverence for the ancients is 
omitted by Fontenelle, who however cer- 
tainly makes some amends by that just elo- 
gium which he makes of our author’s mo- 
desty,which amiable quality he represents as 
standing foremost in the character of this 
great man’s mind and manners. It was 
in reality greater than can be easily imagin- 
ed, or will be readily believed ; yet it al- 
ways continued so without any alteration, 
though the whole world, says Fontenelle, 
conspired against it ; let us add, though he 
was thereby robbed of his invention of 
Fluxions. Nicholas Mercator publishing 
his Logarithmotechnia in 1668, where he 
gave the quadrature of the hyperbola by an 
infinite series, which was the first appear- 
ance in tlie learned world of a series of this 
sort drawn from the particular nature of the 
curve, and that in a manner very new and 
abstracted. Dr. Barrovv, at that time at 
Cambridge, where Mr. Newton, then about 
twenty-six years of age, resided, recollect- 
ed that he had met with the same thing in 
the writings of that young gentleman, and 
there not confined to the hyperbola only, 
but extending, by general forms, to all 
sorts of curves, even such as are mechanical ; 
to their quadratures, their rectifications, 
and centres of gravity ; to the solids formed 
by their rotations, and to the superficies of 
those'solids, so that, when their determina- 
tions were possible, the series stopped at a 
certain point, or at least their sums were 
given by stated rules ; and if the absolute 
determinations were impossible, they could 
yet be infinitely approximated ; which is the 
happiest and most refined method, says 
Fontenelle, of supplying the defects of hu- 
man knowledge, that man’s imagination 
could possibly invent. To be master of so 
fruitful and general a theory was a mine of 
gold to a geometrician ; but it was a greater 
glory to have been the discoverer of so sur- 
prising and ingenious a system. So that 
Newton, finding by Blercator’s book, that 
he was in the way to it, and that others 
might follow in his track, should naturally 
have been forward to open his treasures, 
and secure the property which consisted in 
making tlie discovery ; but he contented 
himself with his treasure, which he had 
found, without regarding the glory. What 
an idea does it give us of his unparalleled 
modesty, when we find him declaring, that 
he thought Mercator had entirely disco- 
vered his secret, or that others would, be- 
fore he should become of a proper age for 
writing! His manuscript upon Infinite Series 
was communicated to none but Mr. John 
Collins, and Lord Brounker, then President 
of the Royal Society, who had also done 
something in this way himself ; and even 
that had not been complied with, but for 
Dr. Barrow, who would not suffer him to 
indulge his modesty so much as he de- 
sired. 
It is further observed, concerning this 
part of his character, that he never talked 
either of himself or others, nor ever behaved 
in such a manner as to give the most mali- 
cious censurers the least occasion even to 
suspect him of vanity. He was candid and 
affable, and always put himself upon a level 
with his company. He never thought either 
his merit or his reputation suflBcient to ex- 
cuse him from any of the common offices of 
social life. No singularities, either natural 
or affected, distinguished him from other 
men. Though he was firmly attached to the 
Church of England, he was averse from the 
