while Newton's invention remained a secret, communicated only to a few friends, the calculus of Leibniz was spreading over the Continent. No rivalry or hostility existed, as yet, between the illustrious scientists. Newton expressed a very favourable opinion of Leibniz's inventions, known to him through the above correspondence with Oldenburg, in the following celebrated scholium (Principia,
first edition, 1687, Book II., Prop. 7, scholium):–-
"In letters which went between me and that most excellent geometer, G. G. Leibniz, ten years ago, when I signified that I was in the knowledge of a method of determining maxima and minima, of drawing tangents, and the like, and when I concealed it in transposed letters involving this sentence (Data æquatione, etc., above cited), that most distinguished man wrote back that he had also fallen upon a method of the same kind, and communicated his method, which hardly differed from mine, except in his forms of words and symbols."
As regards this passage, we shall see that Newton was afterwards weak enough, as De Morgan says: "First, to deny the
plain and obvious meaning, and secondly, to omit it entirely from the third edition of the Principia." On the Continent, great progress was made in the calculus by Leibniz and his coadjutors, the brothers James and John Bernoulli, and
Marquis de l'Hospital. In 1695 Wallis informed Newton by
letter that "he had heard that his notions of fluxions passed in Holland with great applause by the name of `Leibniz's Calculus Differentialis.' " Accordingly Wallis stated in the preface to a volume of his works that the calculus differentialis
was Newton's method of fluxions which had been communicated to Leibniz in the Oldenburg letters. A review of Wallis' works, in the Leipzig Acts for 1696, reminded the reader of Newton's own admission in the scholium above cited.
For fifteen years Leibniz had enjoyed unchallenged the honour of being the inventor of his calculus. But in 1699 Fato de Duillier, a Swiss, who had settled in England, stated in a
mathematical paper, presented to the Royal Society, his conviction that Newton was the first inventor; adding that, whether Leibniz, the second inventor, had borrowed anything from the other, he would leave to the judgment of those who had seen the letters and manuscripts of Newton. This was the first distinct insinuation of plagiarism. It would seem that the English mathematicians had for some time been cherishing suspicions unfavourable to Leibniz. A feeling had doubtless long prevailed that Leibniz, during his second visit to London in 1676, had or might have seen among the papers of Collins,
Newton's Analysis per æquationes, etc., which contained applications of the fluxionary method, but no systematic development or explanation of it. Leibniz certainly did see at least part of this tract. During the week spent in London, he took note of whatever interested him among the letters and papers of Collins. His memoranda discovered by Gerhardt in 1849 in
the Hanover library fill two sheets.40 The one bearing on our question is headed "Excerpta ex tractatu Newtoni Msc. de Analysi per æquationes numero terminorum infinitas." The notes are very brief, excepting