Dictionary of Scientific Biography

Dictionary of Scientific Biography

Electronic edition published by Cultural Heritage Langauge Technologies (with permission from Charles Scribners and Sons) and funded by the National Science Foundation International Digital Libraries Program. This text has been proofread to a low degree of accuracy. It was converted to electronic form using data entry.

# 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.

7. Both the term and the concept it denotes are certainly anachronistic. Descartes speaks of the indeterminate equation that links x and y as the “relation [rapport] that all the points of a curve have to all those of a straight line” (Géométrie, p. 341). Strangely, Descartes makes no special mention of one of the most novel aspects of his method, to wit, the establishment of a correspondence between geometrical loci and indeterminate algebraic equations in two unknowns. He does discuss the correspondence further in bk. II, 334-335, but again in a way that belies its novelty. The correspondence between determinate equations and point constructions (i.e., section problems) had been standard for some time.
8. For problems of lower degree, Descartes maintains the classification of Pappus. Plane problems are those that can be constructed with circle and straightedge, and solid problems those that require the aid of the three conic sections. Where, however, Pappus grouped all remaining curves into a class he termed linear, Descartes divides these into distinct classes of order. To do so, he employs in bk. I a construction device that generates the conic sections from a referent triangle and then a new family of higher order from the conic sections, and so on.
9. Two aspects of the symbolism employed here require comment. First, Descartes deals for the most part with specific examples of polynomials, which he always writes in the form xn + a1xn - 1 + ... + an = 0; the symbolism P(x) was unknown to him. Second, instead of the equal sign, = , he used the symbol ?, most probably the inverted ligature of the first two letters of the verb aequare (“to equal”).
10. One important by-product of this structural analysis of equations is a new and more refined concept of number. See Jakob Klein, Greek Mathematical Thought and the Origins of Algebra (Cambridge, Mass., 1968).
11. Here again a totally anachronistic term is employed in the interest of brevity.
12. Ironically, Descartes's method of determining the normal to a curve (bk. II, 342 ff.) made implicit use of precisely the same reasoning as Fermat's. This may have become clear to Descartes toward the end of a bitter controversy between the two men over their methods in the spring of 1638.
13. Cf. Vuillemin, pp. 35-55.
14. Ibid., pp. 11-25; Joseph E. Hofmann, Geschichte der Mathematik, II (Berlin, 1957), 13.
15. The anaclastic is a refracting surface that directs parallel rays to a single focus; Descartes had generalized the problem to include surfaces that refract rays emanating from a single point and direct them to another point. Cf. Milhaud, pp. 117-118.
16. The full title of the work Descartes suppressed in 1636 as a result of the condemnation of Galileo was Le monde, ou Traité de la lumière. It contained the basic elements of Descartes's cosmology, later published in the Principia philosophiae (1644). For a detailed analysis of Descartes's work in optics, see A. I. Sabra, Theories of Light From Descartes to Newton (London, 1967), chs. 1-4.
17. “One must note only that the power, whatever it may be, that causes the motion of this ball to continue is different from that which determines it to move more toward one direction than toward another,” Dioptrique (Leiden, 1637), p. 94.
18. Cf. Descartes to Mydorge (1 Mar. 1638), “determination cannot be without some speed, although the same speed can have different determinations, and the same determination can be combined with various speeds” (quoted by Sabra, p. 120). A result of this qualification is that Descartes in his proofs treats speed operationally as a vector.
19. See the summary of this issue in Sabra, pp. 100 ff.
20. Cf. Carl B. Boyer, The Rainbow: From Myth to Mathematics (New York, 1959).
21. For a survey of Descartes's work on mechanics, which includes the passages pertinent to the subjects discussed below, see René Dugas, La mécanique au XVIIe siècle (Neuchâtel, 1954), ch. 7.
22. Presented in full in the Principia philosophiae, pt. II, pars. 24-54.
23. Cf. Milhaud, pp. 34-36.

## BIBLIOGRAPHY

### I. ORIGINAL WORKS.

All of Descartes's scientific writings can be found in their original French or Latin in the critical edition of the Oeuvres de Descartes, Charles Adam and Paul Tannery, eds., 12 vols. (Paris, 1897-1913). The Géométrie, originally written in French, was trans. into Latin and published with appendices by Franz van Schooten (Leiden, 1649); this Latin version underwent a total of four eds. The work also exists in an English trans. by Marcia Latham and David Eugene Smith (Chicago, 1925; repr., New York, 1954), and in other languages. For references to eds. of the philosophical treatises containing scientific material, see the bibliography for sec. I.

### II. SECONDARY LITERATURE.

In addition to the works cited in the notes, see also J. F. Scott, The Scientific Work of René Descartes (London, 1952); Carl B. Boyer, A History of Analytic Geometry (New York, 1956); Alexandre Koyré, Études galiléennes (Paris, 1939); E. J. Dijksterhuis, The Mechanization of the World Picture (Oxford, 1961). See also the various histories of seventeenth-century science or mathematics for additional discussions of Descartes's work.

MICHAEL S. MAHONEY

## DESCARTES: Physiology.

Descartes's physiology grew and developed as an integral part of his philosophy. Although grounded at fundamental points in transmitted anatomical knowledge and actually performed dissection procedures, it sprang up largely independently of prior physiological developments and depended instead on the articulation of the Cartesian dualist ontology, was entangled with the vagaries of metaphysical theory, and deliberately put into practice Descartes's precepts on scientific method. Chronologically, too, his physiology grew with his philosophy. Important ideas on animal function occur briefly in the Regulae (1628), form a significant part of the argument in the Discours de le méthode (1637), and lie behind certain parts of the Principia philosophiae (1644) and all of the Passions de l'âme (1649). Throughout his active philosophical life, physiology formed one of Descartes's most central and, sometimes, most plaguing concerns.

Descartes hinted at the most fundamental conceptions of his physiology relatively early in his philosophical development. Already in the twelfth regula, he suggested (without, however, elaborating either more rigorously or more fully) that all animal and subrational human movements are controlled solely by unconscious mechanisms. Just as the quill of a pen moves in a physically necessary pattern determined by the motion of the tip, so too do “all the motions

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