1676, he gives yet clearer hints of his method, and illustrates it by examples, and lays down a rule, by which, from the ordinates of certain curves, their areas may be obtained in finite terms, when it is possible.
By these lights, and assisted by such examples, the acute Leibnitz might have learned the Newtonian method.
It is plain he did so; for in 1684, he first published, in the Leipsic Acts, his Elements of the Differential Calculus, without pretending to have had the method before the year 1677, the year he received the two letters from Newton: and yet, when Sir Isaac published his books of the number of curves of the first kind, and of the quadrature of figures,

the editors of the Acts said Leibnitz was the first inventor of the differential calculus, and Newton had substituted fluxions for differences, just as Honoratus Faber, in his Synopsis Geometrica, had substituted a progression of motion for Cavallerius's method of indivisibles; that is, Leibnitz was the first inventor of the method, Newton had received it from him (from his Elements of the Differential Calculus), and had substituted fluxions for differences; but the way of investigation in each is the same, and both center in the same conclusions.
This excited Mr. Keil to reply; and he made it appear very plain from Sir Isaac's letters, published by Dr. Wallis, that he (Newton) was the first inventor of the algorith, or practical rules of fluxions; and Leibnitz did no more than publish the same, with an alteration of the name, and manner of notation. This however did not silence Leibnitz, nor satisfy the foreigners who admired him. He abused Dr. Keil, and appealed to the Royal Society against him; that they would be pleased to restrain the Doctor's vain babblings and unjust calumniations, and report their judgment as he thought they ought to do, that is, in his favour. But this was not in the power of the Society, if they did justice; for it appeared quite clear to a committee of the members, appointed

to examine the original letters, and other papers, relating to the matter, which were left by Mr. Oldenburgh and Mr. J. Collins, that Sir Isaac Newton was the first inventor of fluxions; and accordingly they published their opinion. This determines the affair. When this is the case, it is senseless for any foreigner to say Leibnitz was the author of fluxions. To the divine Newton belongs this greatest work of genius, and the noblest thought that ever entered the