989-after c. 1079

Spanish Moor mathematician and astronomer who made important contributions to geometrical mathematics. Born in Córdoba, Spain, Ibn Muadh was evidently in Cairo from 1012 to 1017 and moved to Jaén in Spain where he wrote his most important works. On ratio was a defense of the fifth book of Euclid's Elements in which he introduced the concept of "number" as one of the five mathematical magnitudes essential to defining ratio. His The Book of Unknown Arcs of Sphere was evidently the first treatise on spherical trigonometry. In his On the Dawn or On Twilight and the Rising of Clouds he determined by refraction that the sun was 18° below the horizon at dawn and end of twilight, providing a means of estimating the height of the atmosphere.