Applications de géométrie et de méchanique, a la marine, aux ponts et chaussées, etc., pour faire suite aux développements de géométrie.

Paris, Bachelier, 1822. Large 4to (27.0 x 21.5 cm). xxxv, 330, [iv] pp., 17 large, folded, engraved plates. Contemporary marbled limp boards. = First edition of the first work on nonspherical surfaces with circular curvature. The author, Charles Dupin (1784-1873) was a French naval engineer and mathematician (both professions reflected in the title of this work) after whom the Dupin cyclide (discussed in this work) and Dupin indicatrix are named. "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" (DSB). The last four pages are a publisher's catalogue, dated April 1822). Uncut, broad-margined copy. The spine cover has perished and the boards are worn and detached, the outer margin of a few pages with a small dampstain, otherwise a very good, clean copy. DSB 4, p. 257.