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DESCARTES, René (1596–1650); Frans van Schooten (1615–1660)

Geometria, à Renato des Cartes anno 1637 Gallicè edita ; postrema autem una cum notis Florimondi de Beaune ... atque Francisci à Schooten ... nunc demum ab eodem diligenter recognita, locupletioribus commentariis instructa, multisque egregiis accessionibus, tam ad ulteriorem explicationem, quam ad ampiandam huius Geometriae excellentiam facientibus, exornata, quorum omnium catalogum pagina versa exhibet

Amsterdam: ex typographia Bavaiana, 1683
4to: *–2*4 A–3T4; χ2 *–2*4A–3F4 3G2 2*4, 268; 224 leaves, pp. [16] 520; [20] 420 8. Engraved portrait on *1v facing the main titlepage, signed ‘Franciscus à Schooten Dn Math ad vivum delineavit et fecit Anno 1644’, title printed in red and black with woodcut printer’s device, woodcut diagrams in the text.
Condition: 197 x 153mm.
Binding: Contemporary English panelled calf, red sprinkled page edges. Joints cracked but cords holding, spine and corners worn, lettering piece lacking.
Provenance: 1. Engraved armorial book plate of Philip Henry, Earl Stanhope, FRS (1781–1855); 2. D. T. Whiteside (1932–2008), Newtonian scholar, with Newton’s annotations copied by him in ink and a page of notes laid in.
Third Latin edition (first 1649, second with additions 1659-61).

The deliberately obscure style of La géometrie as first published in the Discours de la méthode (1637 and 1658 but dropped from subsequent editions, see above) limited the appreciation of Descartes’ innovations before Florimond de Beaune’s Latin translation was published with Franciscus van Schooten’s commentary in 1649. Apparently Descartes was not completely satisfied with van Schooten’s edition but ‘it found a broad and receptive audience by virtue of its more carefully executed figures and its full commentary’ (DSB 12:206a) and it was through van Schooten’s editions that Newton and other contemporaries acquired an understanding of Descartes’ work. In his second edition (2 volumes of 1659–61) van Schooten added a number of additional papers by other hands. The present edition is a reprint of the 1659–61 edition with the same pagination.
This copy was owned by the Newton scholar D. T. Whiteside and used in his analysis of Newton’s objections to Descartes. Newton owned both the 1649 and 1659–61 editions, but it was the latter that he annotated (Harrison 507). Whiteside has transcribed Newton’s annotations into this copy on 14 pages in part 1, his addition to De Witt’s ‘Elementa curvarum’ in part 2, p. 221 (not noticed by Harrison) and his comparisons with the 1649 edition, part 1, p. 253. Newton’s annotations, ‘Error’, ‘non probo’, ‘Non Geom.’ and ‘Impft’, Harrison explains ‘are not an emotional reaction or snap judgement on Newton’s part, but rather a series of catchwords for a more developed criticism on intrinsic mathematical grounds which he elaborated in a contemporary piece on “Errores Cartesij Geometriae”. (John Harrison, The Library of Isaac Newton, pp. 14–15 citing Newton’s Mathematical Papers edited by Whiteside (1971) iv, 336–45).