Arab mathematician and astronomer who expounded on Book V of Euclid's (c. 325-c. 250 b.c.) Elements and wrote the first treatise on spherical trigonometry. Al-Jayyani spent much of his career in the town of Jaén, capital of the Moorish principality called Jayyan; hence his name. In his On Ratio, he discussed what he identified as four types of geometrical magnitude outlined by Euclid—line, surface, angle, and solid—and added to these a fifth, number. The Book of Unknown Arcs of a Sphere approached the subject of spherical trigonometry, and provided formulas for spherical triangles. Al-Jayyani's writings would have a profound impact on European mathematics in general, and on the work of Regiomontanus (1436-1476) in particular.