DUPIN, Développements de Géométrie, 1813
DUPIN, Charles.
Développements de géométrie, avec des applications à la stabilité des vaisseaux, aux déblais et remblais, au défilement, à l'optique, etc.
Paris, Courcier, 1813.
4to (253x200 mm), xx-373-(1) pages and 11 plates. binding : Contemporary full sheep, gilt flat spine. Binding rubbed. Waterstains.
First edition.
references: DSB [IV, p.257 : " His 'Applications de géométrie et de mécanique' (1822) was a continuation of the 'Développements' but placed greater stress on applications. (.) The 'Développements' contains many contributions to differential geometry, notably the introduction of conjugate and asymptotic lines on a surface, the so-called indicatrix of Dupin, and "Dupin's theorem," that three families of orthogonal furfaces intersect in the lines of curvature. A particular case Dupin investigated consisted of confocal quadrics. In the 'Applications' we find an elaboration of Monge's theory of deblais et remblais -- and, hence, of congruences of straight lines, with applications to geometrical optics. Here Dupin, improving on a theorem of Malus's (1807), stated that a normal congruence remains normal after reflection and refraction. He also gave a more complete theory of the cyclids as the envelopes of the spheres tangent to three given spheres and discussed floating bodies"].
Price : 350 €
