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Geometry and Girard Desargues

Published online by Cambridge University Press:  03 November 2016

B. A. Swinden
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Extract

It is a far cry from the Conics of Apollonius to the theory of linear spaces and matrix algebra and many men have helped to build the road between. This article is about one of the builders whose work for a time was discarded and whose name was almost forgotten. But his name finds frequent mention now, when the latter aspect of geometry bears so little resemblance to the former, and metrical geometry has given place to projective geometry with its non-metrical homogeneous coordinates, which make it possible to publish a book on coordinate geometry which does not contain a single figure.

Type
Research Article
Information
The Mathematical Gazette , Volume 34 , Issue 310 , December 1950 , pp. 253 - 260
Copyright
Copyright © Mathematical Association 1950

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References

page 253 note * Todd, J. A., Projective and Analytical Geometry, 1947.Google Scholar

page 254 note * Short History of Mathematics, sixth edition, p. 257

page 254 note † For further discussion see G. de B. Robinson, The Foundations of Geometry, Toronto, 1946. Hilbert, Grundlagen der Geometrie, seventh edition, pp. 85 et seq. shows that D.’s theorem cannot be proved in a plane without using a third dimension or some congruence axiom, and gives an example of a two dimensional space in which the theorem is not true.

page 254 note ‡ M. Poudra (Oeuvres de Desargues, Paris, 1864) collected practically every literary reference which would help to build up a picture of the history and character of D., and I acknowledge my debt to him.

page 254 note § The archives of Lyons contain some correspondence which passed in 1646 between the municipal authority and “the celebrated architect Desargues, a son of the borough” relating to plans for a new town hall.

page 254 note ‖ Mersenne was very much concerned with mathematicians and exponents of other branches of learning, and seems to have acted as a “clearing-house” of knowledge; results were frequently communicated to him before publication and letters from one scientist to another were passed through him; e.g. Desargues and Beaugrand, the King’s Secretary, who were not on speaking terms, communicated through the intermediar y of Mersenne. It may be that the Letters of Mersenne, published by Mme. Tannery during the last fifteen years, would throw still more light on Desargues, but I have not seen the relevant volumes.

page 255 note * Cousin, vol. 8, p. 493, 28th February, 1641.

page 255 note † Cousin, , vol. 8. p. 433 Google Scholar, 31st December, 1640.

page 255 note ‡ British Museum, Add. MS., 23,198 vv. 435-538.

page 255 note § Ball, l.c. p. 256.

page 255 note ‖ Archimedes rejected a similar method as not rigorous, v. The “Method” of Archimedes, edition T. L. Heath, 1912, p. 13.

page 256 note * Cousin, vol. 8, p. 88.

page 256 note † Coolidge, J-L., History of Geometrical Methods, 1947, pp. 104-5Google Scholar, expresses the same view with regard to the present situation in synthetic projective geometry.

page 256 note ‡ Father of Philippe de la Hire, the geometer (1640-1719).

page 257 note * D.’s critics, Curabelle and others, spoke of a work on Conics called Leçons de ténèbres of which we have no trace. I suspect that this was merely an alternative title to the Brouillon-projet.

page 257 note † Coolidge, I.e. p. 109, calls Desargues “the bad boy of the whole story” of Perspective.

page 258 note * Cousin, , vol. 8, p. 214.Google Scholar

page 258 note † Probably the pamphlet was the composition of Tavernier himself based on a MS. by the Friar Dubreuil.

page 258 note ‡ Beaugrand wrote a Commentary on the Cycloid, one or perhaps two books on “Geostatica” and a commentary on Vieta’s principal work.

page 259 note * v. Baillet’s Life of Descartes, quoted by M. Poudra.

page 260 note * Ball, l.c. p. 317 says that P de la Hire was Desargues’ favourite pupil. I think this is wrong; anyhow Philippe was no more than ten years old when Desargues left Paris. Laurent, Philippe’s father, was one of the Academicians who gave Bosse a declaration of thanks for his offer to publish his works in the name of the Academy.

page 260 note † Aperçu historique, etc. 1837.

page 260 note ‡ Boutroux in Pascal’s Works (Paris, 1923) vol. 1, pp. 245 et seq.