Desargues' Brouillon Project and the Conics of ... - J.P. Hogendijk

40 Jan P Hogendijk
involution, but also the discussion of the existence of the fixed points
of cp.
One may well ask whether Desargues was really bothered by
these gaps. I think he was. The fact that he introduced the foci in
the manner of the Conics, as discussed in Section 4, shows that he
did not yet consider his new theory to be an adequate replacement
for that of Apollonius. His last proposition is therefore an interesting
example of a great mathematician at work.
BIBLIOGRAPHY
Andersen, K.
1991: “Desargues’ Method of Perspective. Its mathematical Content, Its Connection to
Other Perspective Methods and Its Relation to Desargues’ Ideas on Projective
Geometry”, Centaurus 34, pp 4491.
Apollonius, see Czwalina, Heath, Heiberg, and Ver Eecke.
Chasles, Michel
1835-37: Apercu historique sur f’origine et le diveloppement des methodes en geometrie.
Paris. Second edition Paris 1875.
Chrzaszczewski, S.
1898: “Desargues’ Verdienste urn die Begrundung der projektivischen Geometrie”, Archiv
der Mathematik und Physik, 2. Reihe, 16, pp. 119-149 plus figures after p. 448.
Coxeter, H. S. M.
1961: Introduction to Geomerry. New York, London, John Wiley & Sons.
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1864: “Notizia Bibliografica. Oeuvres de Desargues reunies et analysees par M. Poudra”.
Annali di Matematica pura ed applicata. seria I, t.5, pp. 332-336. Reprinted in
Opere matematiche (Milano 1915) t.2, pp. 84-91.
Czwalina, A.
1926: Die Kegelschnitte des Apollonius. Miinchen-Berlin.
Desargues, see Field, Poudra, Taton, Zacharias.
Field, J. V., Gray J. J.
1987: The Geometrical Work of Girard Desargues. New York, Springer Verlag.
Fladt, K.
1965: Geschichte und Theorie der Kegelschnitte und der Flachen weiten Grades. Stuttgart,
Ernst Klett Verlag.
Heath, T. L.
1896: Apollonius of Perga. Treatise on Conic Sections. Cambridge, Cambridge University
Press.
Heiberg, J. L.
I89 1-93: Apollonii Pergaei quae graece exstant cum commentariis antiquis. 2 vols. Lripzig,
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