Gilles de Roberval

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Gilles de Roberval
Portrait of Gilles Personne de Roberval (1602-1675) at the inauguration of the French Academy of Sciences, 1666, where he was a founding member.
Born(1602-08-10)August 10, 1602
Roberval near Beauvais, France
DiedOctober 27, 1675(1675-10-27) (aged 73)
Paris, France
Known forRoberval Balance
Coining the term 'trochoid'
Scientific career
InstitutionsGervais College, Paris
Royal College of France
Academic advisorsÉtienne Pascal
Marin Mersenne
Notable studentsFrançois du Verdus
Isaac Barrow

Gilles Personne de Roberval (August 10, 1602 – October 27, 1675), French mathematician, was born at Roberval near Beauvais, France. His name was originally Gilles Personne or Gilles Personier, with Roberval the place of his birth.[1]


Like René Descartes, he was present at the siege of La Rochelle in 1627. In the same year he went to Paris, and in 1631 he was appointed the philosophy chair at Gervais College, Paris. Two years after that, in 1633, he was also made the chair of mathematics at the Royal College of France. A condition of tenure attached to this particular chair was that the holder (Roberval, in this case) would propose mathematical questions for solution, and should resign in favour of any person who solved them better than himself. Notwithstanding this, Roberval was able to keep the chair until his death.[2]

Roberval was one of those mathematicians who, just before the invention of the infinitesimal calculus, occupied their attention with problems which are only soluble, or can be most easily solved, by some method involving limits or infinitesimals, which would today be solved by calculus. He worked on the quadrature of surfaces and the cubature of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use, while Bonaventura Cavalieri published a similar method which he independently invented.[2]

Another of Roberval’s discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions.[3] He also discovered a method of deriving one curve from another, by means of which finite areas can be obtained equal to the areas between certain curves and their asymptotes. To these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name "Robervallian lines."[2][4]

Between Roberval and René Descartes there existed a feeling of ill-will,[5][6] owing to the jealousy aroused in the mind of the former by the criticism that Descartes offered to some of the methods employed by him and by Pierre de Fermat; and this led him to criticize and oppose the analytical methods that Descartes introduced into geometry about this time.[2]

As results of Roberval’s labours outside of pure mathematics may be noted a work on the system of the universe, in which he supports the Copernican heliocentric system and attributes a mutual attraction to all particles of matter and also the invention of a special kind of balance, the Roberval Balance.[7]


  • Traité de Mécanique des Poids Soutenus par des Puissances sur des Plans Inclinés à l’Horizontale (1636).
  • Le Système du Monde d’après Aristarque de Samos (1644).
  • Divers Ouvrages de M. de Roberval (1693).


  1. ^ Walker, Helen M (1936). "An Unpublished Hydraulic Experiment of Roberval, 1668". Osiris. 1: 726. doi:10.1086/368451. S2CID 145477013.
  2. ^ a b c d Chisholm 1911, p. 407.
  3. ^ Wolfson, Paul R (2001). "The Crooked Made Straight: Roberval and Newton on Tangents". The American Mathematical Monthly. 108 (3): 206–216. doi:10.2307/2695381. JSTOR 2695381.
  4. ^ "ROBERVALLIAN Lines, a name given to certain lines used for the transformation of figures; thus called from their inventor Roberval, an eminent French mathematician, who died in 1675, aged seventy-six. The abbe Gallois, in the Memoirs of the Royal Academy, 1693, observes that the method of transforming figures, explained at the latter end of Roberval's Treatise of Indivisibles, was the same with that afterwards published by James Gregory, in his Geometria Universalis, and also by Barrow in his Lectiones Geometricæ; and that, by a letter of Torricelli, it appears that Roberval was the inventor of this manner of transforming figures, by means of certain lines, which Torricelli therefore called Robervallian lines." — The London Encyclopaedia, Thomas Curtis (ed.), Vol. XVIII. London: Thomas Tegg, 1839, p. 627.
  5. ^ Jullien, Vincent (1998). "Descartes-Roberval, une Relation Tumultueuse". Revue d'Histoire des Sciences. 51 (2/3): 363–371. doi:10.3406/rhs.1998.1330.
  6. ^ Grayling, A.C. (2006). Descartes: The Life of Rene Decartes and Its Place in His Times. New York: Simon and Schuster, p. 203.
  7. ^ Chisholm 1911, pp. 407–408.


Further reading[edit]

  • Carroll, Maureen T.; Dougherty, Steven T.; Perkins, David (2013). "Indivisibles, Infinitesimals and a Tale of Seventeenth-Century Mathematics". Mathematics Magazine. 86 (4): 239–254. doi:10.4169/math.mag.86.4.239. S2CID 117979730.
  • Itard, Jean (1975). "La Lettre de Torricelli à Roberval d'Octobre 1643". Revue d'Histoire des Sciences. 28 (2): 113–124. doi:10.3406/rhs.1975.1131.
  • Jullien, Vincent (1993). "Les Étendues Géométriques et la Ligne Droite de Roberval". Revue d'Histoire des Sciences. 46 (4): 493–526. doi:10.3406/rhs.1993.4645.
  • Jullien, Vincent (1996). Eléments de Géométrie de G. P. de Roberval. Paris: Vrin.
  • Hara, K. (1981). "Roberval, Gilles Personne". In: Gillispie, C. C. (Ed). Dictionary of Scientific Biography. New York: Charles Scribner’s Sons, Vol. 11, p. 486–491.

External links[edit]

  1. ^ Whiteside, D. T. (June 1963). "Review: Un Savant méconnu, Gilles Personne de Roberval. by Léon Auger". Isis. 54 (2): 303–305. doi:10.1086/349729. JSTOR 228566.