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.
a mystery; in the absence of further evidence, one
must rest content with the derivations in the Dioptrique.
Following those derivations, Descartes devotes the
remainder of the Dioptrique to an optical analysis of
the human eye, moving from the explanation of various
distortions of vision to the lenses designed to
correct them, or, in the case of the telescope, to increase
the power of the normal eye. The laws of
reflection and refraction reappear, however, in the
third of the Essais of 1637, the Météores. There
Descartes presents a mathematical explanation of
both the primary and secondary rainbow in terms of
the refraction and internal reflection of the sun's rays
in a spherical raindrop.20 Quantitatively, he succeeded
in deriving the angle at which each rainbow is seen
with respect to the angle of the sun's elevation. His
attempted explanation of the rainbow's colors, however,
rested on a general theory of colors that could
at the time only be qualitative. Returning to the
model of the tennis ball, Descartes explained color
in terms of a rotatory motion of the ball, the speed
of rotation varying with the color. Upon refraction,
as through a prism, those speeds would be altered,
leading to a change in colors.
Mechanics.
Descartes's contribution to mechanics
lay less in solutions to particular problems
than in the stimulus that the detailed articulation of
his mechanistic cosmology provided for men like
Huygens.21 Concerned with the universe on a grand
scale, he had little but criticism for Galileo's efforts
at resolving more mundane questions. In particular,
Descartes rejected much of Galileo's work, e.g., the
laws of free fall and the law of the pendulum, because
Galileo considered the phenomena in a vacuum, a
vacuum that Descartes's cosmology excluded from the
world. For Descartes, the ideal world corresponded
to the real one. Mechanical phenomena took place
in a plenum and had to be explained in terms of the
direct interaction of the bodies that constituted it,
whence the central role of his theory of impact.22
Two of the basic principles underlying that theory
have been mentioned above. The first, the law of
inertia, followed from Descartes's concept of motion
as a state coequal with rest; change of state required
a cause (i.e., the action of another moving body)
and in the absence of that cause the state remained
constant. That motion continued in a
straight line followed from the privileged status of the
straight line in Descartes's geometrical universe. The
second law, the conservation of the “quantity of motion”
in any closed interaction, followed from the
immutability of God and his creation. Since bodies
acted on each other by transmission of their motion,
the “quantity of motion” (the product of magnitude
and speed) served also as Descartes's measure of force
or action and led to a third principle that vitiated
Descartes's theory of impact. Since as much action
was required for motion as for rest, a smaller body
moving however fast could never possess sufficient
action to move a larger body at rest. As a result of
this principle, to which Descartes adhered in the face
of both criticism and experience, only the first of the
seven laws of impact (of perfectly elastic bodies
meeting in the same straight line) is correct. It concerns
the impact of two equal bodies approaching
each other at equal speeds and is intuitively obvious.
Descartes's concept of force as motive action
blocked successful quantitative treatment of the mechanical
problems he attacked. His definition of the
center of oscillation as the point at which the forces
of the particles of the swinging body are balanced out
led to quite meager results, and his attempt to explain
centrifugal force as the tendency of a body to
maintain its determination remained purely qualitative.
In all three areas—impact, oscillation, and
centrifugal force—it was left to Huygens to push
through to a solution, often by discarding Descartes's
staunchly defended principles.
Descartes met with more success in the realm of
statics. His Explication des engins par l'aide desquels
on peut avec une petite force lever un fardeau fort
pesant, written as a letter to Constantin Huygens in
1637, presents an analysis of the five simple machines
on the principle that the force required to lift a pounds
vertically through b feet will also lift na pounds b/n
feet. And a memoir dating from 1618 contains a clear
statement of the hydrostatic paradox, later made
public by Blaise Pascal.23
NOTES
1. Cf. Gaston Milhaud, Descartes savant (Paris, 1921), and Jules
Vuillemin, Mathématiques et métaphysique chez Descartes
(Paris, 1960).
2. Cf. Milhaud, pp. 84-87.
3. Defending his originality against critics, Descartes repeatedly
denied having read the algebraic works of François Viète or
Thomas Harriot prior to the publication of his own
Géométrie.
The pattern of development of his ideas, especially during the
late 1620's, lends credence to this denial.
4. In his Scholarum mathematicarum libri unus et triginta (Paris,
1569; 3rd. ed., Frankfurt am Main, 1627), bk. I (p. 35 of the
3rd ed.). Descartes quite likely knew of Ramus through
Beeckman, who had studied mathematics with Rudolph Snell,
a leading Dutch Ramist.
5. Regulae ad directionem ingenii, in Oeuvres de
Descartes,
Adam
and Tannery, eds., X (Paris, 1908), rule IV, 376-377.
6. Descartes to Beeckman (26 Mar. 1619), Oeuvres, X, 156-158.
By “imaginary” curve, Descartes seems to mean a curve that
can be described verbally but not accurately constructed by
geometrical means.