"They have changed the whole point of the issue, for... they have set forth their opinion... as to give a dubious credit to Leibniz, they have said very little about the calculus; instead every other page is made up of what they call infinite series. Such things were first given as discoveries by of Holstein who obtained them by the process of division, and Newton gave the more general form by extraction of roots binomial expansion by the interpolation method of Wallis]. This is certainly a useful discovery, for by it arithmetical approximations are reduced to an analytical reckoning; but it has nothing at all to do with the differential calculus. Moreover, even in this they make use of fallacious reasoning; for whenever this rival works out a quadrature by the addition of the parts by which a figure is gradually increased, at once they hail it as the use of the differential calculus... By the selfsame argument, Kepler (in his Stereometria Doliorum), Cavalieri, Fermat, Huygens, and Wallis used the differential calculus; and indeed, of those who dealt with "indivisibles" or the "infinitely small," who did not use it? But Huygens, who as a matter of fact had some knowledge of the method of fluxions as far as they are known and used, had the fairness to acknowledge that a new light was shed upon geometry by this calculus, and that knowledge of things beyond the province of that science was wonderfully advanced by its use."
January 1, 1970