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Ueber die Biegung gewisser Flächen.
Berlin, G. Reimer, 1838. 4to. In ""Journal für die reine und angewandte Mathematik, 18. Band, 4 Heft, 1838"". In the original printed wrappers, without backstrip. Fine and clean. [Minding:] Pp. 297-302. [Entire issue: Pp. 281-376, (2) + 1 folded plate.].
First printing of Minding's first work on the deformation of general ruled surfaces into ruled surfaces and showed that any ruled surface can be developed on another whose direction vectors form a circular cone. This was subject in which he was to make his most important discoveries. ""Minding's most important discoveries were in the dilierential geometry of surfaces"" in these works he brilliantly continued the researches of Gauss, which had been published in 1828. In his first paper (1830), which dealt with the isoperimetric problem of determining on a given surface the shortest closed curve surrounding a given area (on the plane it is the circumference of a circle), he introduced the concept of geodesic curvature. It was independently discovered in 1848 by O. Bonnet, and it was he who named it geodesic curvature. Minding soon proved, as did Bonnet after him, the invariance of the geodesic curvature under bending of the surface. Neither of them knew that the same results had been presented in an earlier, unpublished paper of Gauss's (1825)."" (DSB).
Ueber die Bestimmung des Grades einer durch Elimination hervorgehen den Gleichung.
Berlin, G. Reimer, 1841. 4to. In ""Journal für die reine und angewandte Mathematik, 22. Band, 2 Heft, 1841"". In the original printed wrappers, without backstrip. Fine and clean. [Minding:] Pp. 178-83. [Entire volume: Pp. 97-192, (2)].
First printing of Minding's important paper in which he presents his theorem representing the first (implicit) appearance of the BKK bound and some of its extensions in the amthematical literature. ""Minding's most important discoveries were in the dilierential geometry of surfaces"" in these works he brilliantly continued the researches of Gauss, which had been published in 1828. In his first paper (1830), which dealt with the isoperimetric problem of determining on a given surface the shortest closed curve surrounding a given area (on the plane it is the circumference of a circle), he introduced the concept of geodesic curvature. It was independently discovered in 1848 by O. Bonnet, and it was he who named it geodesic curvature. Minding soon proved, as did Bonnet after him, the invariance of the geodesic curvature under bending of the surface. Neither of them knew that the same results had been presented in an earlier, unpublished paper of Gauss's (1825)."" (DSB).
