Gregorii perbrevem libellum in 4 in quo videbatur aliqua contineri promotio serierum convergentium, sed aenigmaticos quamquam mihi inspicere tantum in transitu non legere vacarit” (AIII, 7, p. Gregorius insignis geometra olim lapsus erat, quaemadmodum recte a viro celeberrimo Christiano Hugenio fuit observatum.” Other critical references to Gregory can be found in a letter to Wallis, dated May 28 (or June 7) 1697, in which Leibniz remarked: “Ostendit mihi olim Hugenius Parisiis Jac. 174), and in the context of a controversy on Tschirnhaus’ alleged method for the integrability of algebraic curves: “Id ipsum scilicet ego objeci, verum hujus precautionis nullum in ejus edito Schediasmate reperitur vestigium, sed quia probaverat non dari quadraturam circuli portionumque ejus indefinitam, quod dudum constabat, sine haesitatione concluserat impossibilitatem quadraturae totius circuli, in quo argumentandi modo et Jac. For instance, Leibniz was outspoken about this in a letter to Tschirnhaus, from 1684 (AIII, 4, p. Gregory’s achievements were discussed by Leibniz on other occasions too, all of which, however, fell after 1676, and thus outside the historical bounds of this study. Finally, I shall use the abbreviation ‘LSG’ for Gerhardt’s historical edition of Leibniz’s mathematical works published in seven volumes (1849–1863, Leibniz 1849–1863). See also Leibniz ( 2004) for a French translation, and Leibniz ( 2015) for a Spanish translation.). A new, recent edition of Leibniz’s treatise, with a German translation, is Leibniz ( 2016). Knobloch in 1993 (for simplicity, I will use the shorthand ‘LKQ’ in order to refer to Knobloch’s edition. In particular, AVII6, 51 contains a new critical edition of De quadratura arithmetica, with an additional passage with respect to the first edition released by E. Thus, ‘AVII6’ will refer to the sixth volume of the seventh series of the Edition of the Akademie der Wissenschaften, and ‘AVII6, 51’ will refer to the text number 51 contained in that volume. Here and in the following sections, I will use the letter ‘A,’ followed by one Roman and one Arabic numeral, in order to refer to the edition of Leibniz’s collected works published in the Academy Edition of Leibniz’s miscellaneous works (Leibniz 1923).
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