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DESCARTES, RENÉ DU PERRON (b. La Haye,
Touraine, France, 31 March 1596; d. Stockholm,
Sweden, 11 February 1650), natural philosophy, scientific
method, mathematics, optics, mechanics, physiology.

qualification that “in the interim we are to desire
that men have patience not to lay aside induction
before they have reason.”18

NOTES

1. Fontenelle, Oeuvres diverses, new ed., III (The Hague, 1729),
405-406.
2. Part of the Olympica incorporated in the Cogitationes
privatae
(1619-1621); see Oeuvres, X, 217.
3. Oeuvres, X, 156.
4. Baillet, II, 165.
5. Ibid., preface, p. xviii.
6. Oeuvres, VI, 63.
7. Rule V; see Oeuvres, X, 380.
8. Letter to Mersenne, 11 Mar. 1640; see Oeuvres, III, 39. The
“Essays” were the volume of 1637.
9. Letter to Mersenne, 27 May 1638; see Oeuvres, II, 141-142.
10. Oeuvres, IX, pt. 2, 2-3.
11. Principia philosophiae, IV, 188; Oeuvres, VIII, pt.
1,
315 (Latin);
IX, pt. 2, 310 (French, alone with passage in square brackets).
12. Letter to Mersenne, 11 Oct. 1638; see Oeuvres, II, 380. For
his comments on Harvey, see Discours V.
13. Principia philosophiae, IV, 203; Oeuvres, VIII, pt.
1,
326 (Latin);
IX, pt. 2, 321-322 (French, alone with passage in square
brackets).
14. Letter to J.-B. Morin, 13 July 1638; see Oeuvres, II, 197-202;
cf. his letters to Vatier, 22 Feb. 1638, ibid., I, 558-565, and to
Mersenne, 1 Mar. 1638, ibid., II, 31-32.
15. Oeuvres, VI, 76.
16. Ibid., pp. 64-65; cf. Principia philosophiae, III, 46;
VIII, pt. 2,
100-101; and IX, pt. 2, 124-125.
17. Oeuvres, XI, 241-242; cf. the comments on this controversy
by J. B. Duhamel, “Quae sit cordis motus effectrix causa,” in
Philosophia vetus et nova. II, Physica generalis, III.ii.2
(Paris,
1684), 628-631.
18. Vindiciae academiarum (Oxford, 1654), p. 25.

BIBLIOGRAPHY

Descartes's complete works can be found in Oeuvres de
Descartes, C. Adam and P. Tannery, eds., 12 vols. (Paris,
1897-1913), together with the revised Correspondance,
C. Adam and G. Milhaud, eds. (Paris, 1936- ). Besides
these, primary sources for Descartes's life are Adrien
Baillet, La vie de Monsieur Descartes, 2 vols. (Paris, 1691),
which should be read with C. Adam, Vie et oeuvres de
Descartes (in Oeuvres, XII); Isaac Beeckman, Journal tenu
... de 1604 à 1634, C. de Waard, ed., 3 vols. (The Hague,
1939-1953): Marin Mersenne, Correspondance, C. de Waard,
R. Pintard, B. Rochot, eds. (Paris, 1932- ).

For Descartes's philosophy and method and their background,
see E. Gilson, Index scolastico-cartésien (Paris,
1912); Études sur le rôle de la pensée
médiévale dans la
formation du système cartésien (Paris, 1930); Discours
de la
méthode: texte et commentaire (Paris, 1947); Alexandre
Koyré, Entretiens sur Descartes (Paris-New York, 1944);
G. Milhaud, Descartes savant (Paris, 1921); L. Roth,
Descartes' Discourse on Method (Oxford, 1937); H. Scholz,
A. Kratzer, and J. E. Hofmann, Descartes (Münster, 1951);
and Norman Kemp Smith, New Studies in the Philosophy
of Descartes (London, 1952).

Specific aspects of Descartes's scientific method are discussed
in A. Gewirtz, “Experience and the Non-mathematical
in the Cartesian Method,” in Journal of the
History of Ideas,2 (1941), 183-210; and A. C. Crombie,
“Some Aspects of Descartes' Attitude to Hypothesis and
Experiment,” in Académie Internationale d'Histoire des
Sciences, Actes du Symposium International des Sciences
Physiques et Mathématiques dans la Première Moitié du
XVIIe Siècle: Pise-Vinci, 16-18 Juin 1958 (Paris,
1960), pp.
192-201. An indispensable bibliography is G. Sebba,
Descartes and His Philosophy: A Bibliographical Guide to
the Literature, 1800-1958 (Athens, Ga., 1959).

A. C. CROMBIE

DESCARTES: Mathematics and Physics.

In this section, Descartes's mathematics is discussed
separately. The physics is discussed in two subsections:
Optics and Mechanics.

Mathematics.

The mathematics that served as
model and touchstone for Descartes's philosophy
was in large part Descartes's own creation and reflected
in turn many of his philosophical tenets.1 Its historical
foundations lie in the classical analytical texts of
Pappus (Mathematical Collection) and Diophantus
(Arithmetica) and in the cossist algebra exemplified
by the works of Peter Rothe and Christoph Clavius.
Descartes apparently received the stimulus to study
these works from Isaac Beeckman; his earliest recorded
thoughts on mathematics are found in the
correspondence with Beeckman that followed their
meeting in 1618. Descartes's command of cossist algebra
(evident throughout his papers of the early
1620's) was perhaps strengthened by his acquaintance
during the winter of 1619-1620 with Johann Faulhaber,
a leading German cossist in Ulm.2 Descartes's
treatise De solidorum elementis, which contains a
statement of “Euler's Theorem” for polyhedra
(V + F = E + 2), was quite likely also a result of
their discussions. Whatever the early influences on
Descartes's mathematics, it nonetheless followed a
relatively independent line of development during the
decade preceding the publication of his magnum opus,
the Géométrie of 1637.3

During this decade Descartes sought to realize two
programmatic goals. The first stemmed from a belief,
first expressed by Petrus Ramus,4 that cossist algebra
represented a “vulgar” form of the analytical method
employed by the great Greek mathematicians. As
Descartes wrote in his Rules for the Direction of the
Mind (ca. 1628):

... some traces of this true mathematics [of the ancient
Greeks] seem to me to appear still in Pappus and
Diophantus.... Finally, there have been some most
ingenious men who have tried in this century to revive
the same [true mathematics]; for it seems to be nothing