Géométrie projective / Pierre Samuel

In his charming introduction the memories of the author go back half a century ago when he was a candidate for the École polytechnique and fascinated by certain geometric issues such as the two systems of straight lines on a quadric or the Villarceau circles on a torus. He is now a specialist on algebra and algebraic geometry but every now and then there is an opportunity to introduce young people into projective geometry and "to open their minds". This booklet is the result of these lectures; it is intended not only for students but for amateurs as well. In view of the character of the work it is not possible to give a systematic account of its rich contents and therefore we restrict ourselves to some topics. Projective spaces over a general field (finite or infinite) are dealt with and so are affine and Euclidean geometries. Axiomatics (incidence, Desargues, Pappos) are made use of. We meet rational curves, classification of quadrics, some topology, inversion, homogeneous coordinates, Poncelet polygones and an interesting appendix on (2,2) correspondences. A minor point: in all figures illustrating theorems on conics they are intentionally drawn as circles. (Zentralblatt)

Bibliogr. p. [174]. Index