In a critique that was made in London on Mr. de Fontenelle’s discourse, the writer presumed to assert that Descartes was not a great geometrician.  Those who make such a declaration may justly be reproached with flying in their master’s face.  Descartes extended the limits of geometry as far beyond the place where he found them, as Sir Isaac did after him.  The former first taught the method of expressing curves by equations.  This geometry which, thanks to him for it, is now grown common, was so abstruse in his time, that not so much as one professor would undertake to explain it; and Schotten in Holland, and Format in France, were the only men who understood it.

He applied this geometrical and inventive genius to dioptrics, which, when treated of by him, became a new art.  And if he was mistaken in some things, the reason of that is, a man who discovers a new tract of land cannot at once know all the properties of the soil.  Those who come after him, and make these lands fruitful, are at least obliged to him for the discovery.  I will not deny but that there are innumerable errors in the rest of Descartes’ works.

Geometry was a guide he himself had in some measure fashioned, which would have conducted him safely through the several paths of natural philosophy.  Nevertheless, he at last abandoned this guide, and gave entirely into the humour of forming hypotheses; and then philosophy was no more than an ingenious romance, fit only to amuse the ignorant.  He was mistaken in the nature of the soul, in the proofs of the existence of a God, in matter, in the laws of motion, and in the nature of light.  He admitted innate ideas, he invented new elements, he created a world; he made man according to his own fancy; and it is justly said, that the man of Descartes is, in fact, that of Descartes only, very different from the real one.

He pushed his metaphysical errors so far, as to declare that two and two make four for no other reason but because God would have it so.  However, it will not be making him too great a compliment if we affirm that he was valuable even in his mistakes.  He deceived himself; but then it was at least in a methodical way.  He destroyed all the absurd chimeras with which youth had been infatuated for two thousand years.  He taught his contemporaries how to reason, and enabled them to employ his own weapons against himself.  If Descartes did not pay in good money, he however did great service in crying down that of a base alloy.

I indeed believe that very few will presume to compare his philosophy in any respect with that of Sir Isaac Newton.  The former is an essay, the latter a masterpiece.  But then the man who first brought us to the path of truth, was perhaps as great a genius as he who afterwards conducted us through it.

Descartes gave sight to the blind.  These saw the errors of antiquity and of the sciences.  The path he struck out is since become boundless.  Rohault’s little work was, during some years, a complete system of physics; but now all the Transactions of the several academies in Europe put together do not form so much as the beginning of a system.  In fathoming this abyss no bottom has been found.  We are now to examine what discoveries Sir Isaac Newton has made in it.