Gesammelte Werke. Band 2

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The text outlines a collection of mathematical works spanning various topics in geometry and trigonometry. It includes discussions on a new treatment of analytical spherical geometry from 1846, proofs related to Hamilton's associative principle in 1859, and the development of fundamental forms of spherical trigonometry in 1860. Other notable topics include the basic forms of third-order curves (1852), the shape of spherical curves without notable points (1848), and methods linking longimetric relations to planar geometry (1852). The author also explores new relationships between plane figures (1853) and the involution of points in a plane (1853), providing geometric proofs of Bodenmiller's theorem (1854) and presenting the theory of circle relationships (1855). Additional works discuss imaginary circles (1857), conjugate circles (1858), and the symmetry laws of crystals (1849), along with their applications to crystal classification. The collection further delves into symmetric figures (1851), higher-order involutions (1855), and the theory of collinear involutions of point pairs (1856). Concluding with the theory of elementary relationships (1863) and methods for determining the volume of polyhedra (1867), the text also includes posthumous notes on polyhedron theory and symmetric figures.