Roberval
NAME: Roberval, Gilles Personne de
ACHIEVEMENT(S): Geometry of curves
NICKNAME/ALIAS: None
DATE AND PLACE OF BIRTH: August 10, 1602, Roberval, near Senlis, France
DATE/PLACE OF DEATH/AGE AT DEATH: October 27, 1675, Paris, France. Aged 73
DISCIPLINE: Mathematician
FIELD: Mathematics
LANGUAGE: French
PARENTS: Unknown
SIBLINGS: Unknown
SPOUSE: None
CHILDREN: None
EDUCATION: Rudimentary
MAJOR WORK: "Treatise on Indivisibles"
LIFE AND TIMES:
Because his formal education was meager, Roberval made a point of attending university classes in all the French regions he visited. In Bordeaux, he met Fermat*. In Paris, in 1628, he was invited to join the select circle surrounding Mersenne*, becoming the group's only professional mathematician. He and Mersenne’s friend Blaise Pascal* got along particularly well. Mersenne was so impressed with Roberval, he used some of Roberval's work in his treatises.
In 1632, Roberval was appointed professor of philosophy at the College de Maitre Gervais in Paris and, two years later, won the triennial competition for the Ramus chair at the College Royal, a post he kept for the rest of his life. (In 1655, he was appointed to Gassendi*'s chair of mathematics, which he also kept until the end of his life.)
By 1636, Roberval was a leading expert on the geometry of infinitesimals, which he claimed he took directly from Archimedes without knowing anything about the method of indivisibles used by Italian mathematician Bonaventura Cavalieri. Roberval studied the methods for calculating surface area (quadrature) and the volume of solids (cubature), and developed methods for the early study of integration, which were published by the Academie des Sciences in 1639 as: "Treatise on Indivisibles."
He computed the definite integral of the rational power and the integration of sine x. He was the first to square the surface of an oblique cone, and succeeded in the quadrature of the cycloidal curve and in the cubature of the solid that it generates in turning around its base. He also computed the arc length of a spiral.
Roberval developed his methods during early research on the cycloid (the curve generated by a point on the circumference of a circle that rolls along a straight line). His discoveries relating to this method of the "composition of movements" along plane curves made him the founder of kinematic geometry. Its most famous application was the construction of the tangent to a curve. This involved treating a curve as the result of the motion of a moving point and by resolving the motion of the point into two simpler components.
During the early 1640s, Roberval also applied this procedure to the comparison of the lengths of curves, a subject almost untouched since antiquity. In 1643, he equated not only the spiral and the parabola in their ordinary forms, but also several curves.
He also discovered a method for obtaining one curve from another, by means of which planar regions of finite dimensions can be calculated, that are equal in area to the regions between certain curves and their asymptotes (lines that the curves approach but never intersect). Italian mathematician Torricelli* gave the name "Roberval lines" to these curves, which were also used to calculate areas.
It was Roberval's claim that before1640 he had rectified (i.e. found the length of the curve of) the simple cycloid by reducing it kinematically to the integration of the sine, but there has been no objective proof of this. If it were so, it would contradict Torricelli's claim that he was the first to rectify a cycloid in 1644-45.
From 1644-48, Roberval investigated atmospheric pressure (Torricelli and Pascal were conducting similar tests at the same time), using a barometric tube, mentioned in two "Narrationes" (1647-48). In the second "Narratione", he described an apparatus he had invented to support the new theory that atmospheric pressure existed, and it served as a prototype for one used by Pascal in his experiments. Roberval did not, however, look into the question of whether a vacuum existed in nature.
In 1647, Roberval had a discussion with Descartes* on the center of oscillation of the compound pendulum. In 1666, he was elected to the Academie Royal des Sciences, a society he had co-founded.
Three years later, he presented details to the Academie of a particular type of balance using a linked mechanism that still bears his name, and which is now almost universally used for commercial weighing machine.
Roberval published only two works. In 1636, his work led to the law of the composition of forces. In 1644, in a work on the solar system, Roberval supported Aristarchus's cosmological theories, but, inspired by the work of Kepler*, accepted the existence of universal attraction.
Roberval also worked with Picard* on cartography and composed a short treatise detailing a method of mapping France. He also suggested the application of telescopic sights to the quadrant and sextant, and wrote treatises on algebra and algebraic geometry, both published after his death.
ASSESSMENT: A leading proponent of the geometry of infinitesimals, which he claimed originated with Archimedes.
EXTRA CONNECTIONS: His work related to that of Leibniz*,
Met Huyghens*
His material was used by Mariotte*
ONELINER: GP de Roberval, 17th-century expert on curves
BIBLIOGRAPHY:
Auger, Leon, Un savant meconnu: Gilles Personne de Roberval (1602- 1675): son activite intellectuelle dans les domaines mathematique, physique, mecanique et philosophique, Paris, 1962