Gérard Desargues

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Gérard Desargues

Gérard Desargues , also Girard Desargues , (born February 21, 1591 in Lyon ; † October 1661 ibid) was a French architect and mathematician who is considered one of the founders of projective geometry .

life and work

Desargues came from a distinguished family of lawyers in Paris and Lyon, where the family owned several houses and an estate. His father was a royal notary and held high offices in Lyon. Desargues was the third of six children. His two older brothers were lawyers at the parliament in Paris. Little is known about his life. In 1621 he is recorded as a silk merchant in Lyon. In 1626 he went on a trip to Flanders and applied for a patent for the construction of fountains from the city of Paris. In 1628, after the death of his two older brothers, he applied for the family inheritance. Possibly he took part in the siege of La Rochelle (1627-1628) , but this is not documented. Richelieu is said to have valued his talent as an engineer, and René Taton suspected that he earned most of his living (his legacy was not very great) as an engineer on behalf of the Cardinal.

Pratique du trait a preuves (1643)

His circle of acquaintances during his time in Paris from around 1630 included, among others, René Descartes , Pierre Gassendi , Marin Mersenne , Étienne Pascal (the father of Blaise Pascal) and Blaise Pascal (with whom he had contacts in 1639 and whom he worked on his own projective work Geometry suggested). Mersenne headed a kind of academy in Paris , which Desargues attended regularly from 1635. In his letters, Mersenne mentions a treatise on Desargues' perspective in 1634 (which appeared only two years later). In the 1640s Desargues was assassinated and in 1648 he returned to Lyon to avoid the confusion ( Fronde ) of the time . He only worked as an architect in Paris and Lyon from around 1645. One of his works is the facade of Lyon's town hall. He is also believed to have designed a novel spiral staircase and pump that was built near Paris and was based on epicycloids . From around 1657 he was back in Paris (e.g. his stay in 1660 is documented in a letter from Christian Huygens ), where he worked as an architect. He was also active in the Academy of Montmor in 1660.

He wrote about perspective (Paris 1636), stone carving (1640) and sundials (1640), but his writings are often difficult to understand (in some cases he uses the language of craftsmen), which Descartes criticized. This applies in particular to the font known as Brouillon Projet , which appeared in Paris in 1639 and in which he developed the foundations of a new form of geometry that went beyond the classical Euclidean geometry of the Greeks, the projective geometry, which was based on considerations of perspective originated. He treated points in infinity (which, however, Kepler already considered) on the same level, introduced duality of points and straight lines for the first time and gave a theory of conic sections from a projective point of view.

The set of Desargues projective geometry states that the intersections of corresponding sides are two triangles on a straight line when the straight line connecting corresponding vertices intersect at a point (and vice versa). It is not found in the Brouillon Projet, but was first published in 1648 by the engraver Abraham Bosse in his work on perspective. The sentence plays an important role in the fundamentals of projective geometry, as David Hilbert in particular worked out at the end of the 19th century. Bosse also published another important theorem by Desargues, the projective invariance of the double ratio . Bosse was a friend and pupil (from around 1641) of Desargues and presented his ideas in a more understandable form with the permission of Desargues. Desargues privately taught various craftsmen and artists in his teaching of perspective from around 1639.

Projective geometry faded into the background again after Desargues and Pascal and was only revived by Gaspard Monge and his students in France at the end of the 18th century and the beginning of the 19th century.

About his doctrine of perspective and other of his writings, Desargues got into a dispute with the mathematician and royal secretary Jean de Beaugrand (1584 / 88–1640), who criticized him in several treatises from 1636, and with Jacques Curebelle, who in 1644 the treatise Examen des Oeuvres du Sieur Desargues published. The argument with Curebelle, which also included a bet and went to court, was one reason why Desargues went back to Lyon. Bosse, who represented the teaching of Desargues, was therefore exposed to attacks and was neither allowed to present nor defend his teaching in the Royal Academy.

Only one copy of the original print of the Brouillon Projet has survived. It was discovered in 1951 and published by René Taton . Before that, the book was only known (since 1845, through Michel Chasles ) from a manuscript copy by Philippe de la Hire .

Facade of the Hotel de Ville in Lyon

In 1964 the IAU named the lunar crater Desargues after him, as did the asteroid (227151) Desargues in 2010 .

literature

  • René Taton : Desargues, Girard . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 4 : Richard Dedekind - Firmicus Maternus . Charles Scribner's Sons, New York 1971, p. 46-51 .
  • the same: L'Oeuvre Mathématique de Desargues , Paris, Presse Universitaire de France 1951
  • the same La géométrie projective en France de Desargues à Poncelet , Paris 1951
  • JV Field The Invention of Infinity: Mathematics and Art in the Renaissance , Oxford 1997
  • JV Field, Jeremy Gray The geometrical work of Girard Desargues , Springer Verlag, 1987
  • Kirsti Andersen The Geometry of an Art - The History of the mathematical theory of perspective from Alberti to Monge , Springer 2007
  • the same: Desargues 'method of perspective: its mathematical content, its connection to other perspective methods and its relation to Desargues' ideas on projective geometry , Centaurus, Volume 34, 1991, pp. 44-91
  • Jan Hogendijk Desargues' Brouillon project and the Conics of Apollonius , Centaurus, Volume 34, 1991, pp. 1-43
  • Jean Dhombres, Joel Sakarovitch (editor) Desargues et son temps , Paris 1994 (therein Jean-Pierre Le Goff Desargues et la naissance de la geometrie projective , pp. 157-206)
  • M. Poudra (editor) Oeuvre de Desargues , 2 volumes, Paris 1864 (the Brouillet Projet is in volume 1 with a biography of Desargues by Poudra, in volume 2 is an analysis of the works of Bosse), volume 1 online , volume 2 online
  • The Brouillon project at Gallica

Web links

Individual evidence

  1. ^ Richard Westfall on Desargues in the Galilei Project
  2. ^ Brouillon project d'une atteinte aux événemens des rencontres du cone avec un plan . Published in German translation by Max Zacharias in 1922 at Ostwald's Klassikern: First draft of an experiment on the results of the meeting of a cone with a plane , Akademische Verlagsgesellschaft, Leipzig, 1922
  3. ↑ Poncelet quotes from it in his book on projective geometry
  4. ↑ Chasle's history of geometry , Halle 1839, p. 344ff
  5. ↑ Chasle's History of Geometry , p. 347
  6. ^ In addition: Taton Documents nouveaux concernant Desargues , Arch. Internat. Hist. Sci. (NS), Vol. 4, 1951, pp. 620-630
personal data
SURNAME Desargues, Gérard
ALTERNATIVE NAMES Desargues, Girard
BRIEF DESCRIPTION French architect and mathematician
DATE OF BIRTH February 21, 1591
PLACE OF BIRTH Lyon
DATE OF DEATH October 1661
Place of death Lyon