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 of his own algorithm he had made greater progress than by what came to his knowledge in London. Nothing mathematical that he had received engaged his thoughts in the immediate future, for on his way back to Holland he composed a lengthy dialogue on mechanical subjects.

Duillier's insinuations lighted up a flame of discord which a whole century was hardly sufficient to extinguish. Leibniz, who had never contested the priority of Newton's discovery, and who appeared to be quite satisfied with Newton's admission in his scholium, now appears for the first time in the controversy. He made an animated reply in the Leipzig Acts, and complained to the Royal Society of the injustice done him.

Here the affair rested for some time. In the Quadrature of Curves, published 1704, for the first time, a formal exposition of the method and notation of fluxions was made public. In 1705 appeared an unfavourable review of this in the Leipzig Acts, stating that Newton uses and always has used fluxions for the differences of Leibniz. This was considered by Newton's friends an imputation of plagiarism on the part of their chief, but this interpretation was always strenuously resisted by Leibniz. Keill, professor of astronomy at Oxford, undertook with more zeal than judgment the defence of Newton. In a paper inserted in the Philosophical Transactions of 1708, he claimed that Newton was the first inventor of fluxions and "that the same calculus was afterward published by Leibniz, the name and the mode of notation being changed." Leibniz complained to the secretary of the Royal Society of bad treatment and requested the interference of that body to induce Keill to disavow the intention of imputing fraud. Keill was not made to retract his accusation; on the contrary, was authorised by Newton and the Royal Society to explain and defend his statement. This he did in a long letter. Leibniz thereupon complained that the charge was now more open than