Construction and the interpretation of exactness in Descartes’ studies of c. 1619

Abstract

In 1618 Descartes met Isaac Beeckman in Breda. From their association precious documents have survived, in particular five letters¹ that Descartes wrote to Beeckman in early 1619. In the second of these, dated 26 March 1619, Descartes formulated a program for his future investigations. The text is deservedly famous;² it shows how Descartes at an early age charted his scientific quest with remarkable clarity and determination. For my present purpose the text has ad value because Descartes formulated his program entirely in terms of a classification of mathematical problems with respect to their solution by calculation or construction. Thus the letter to Beeckman provides a natural starting point of my inquiry into the development of Descartes’ ideas about construction.

Descartes to Beeckman 24-I-1619 ([Descartes 1964–1974] vol. 10, pp. 151–153), 26-III-1619 (ibid. pp. 154–160), 20-IV-1619 (ibid. pp. 161), 23-IV-1619 (ibid. pp. 162–164), 29-IV-1619 (ibid. pp. 164–166); cf. also Beeckman to Descartes, 6-V-1619 (ibid. pp. 167–169). The text of the letters has survived because Beeckman copied them in the Journal hekept. This journal was discovered in 1905 by C. de Waard (cf. [Descartes 1964–1974] pp. 17–18), who later edited the the complete journal, cf. [Beeckman 1939–1953].

Cf. [Shea 1991] p. 44, see also [Costabel 1969] and [Costabel 1983]on the early mathematical studies of Descartes.