Abū ḥāmid Aḥmad ibn Muḥammad al‐Ṣāghānī al‐Asṭurlābī was an Arabic astronomer and mathematician. He was born in Chagaian (Central Asia) and worked in Baghdad.
His main work was the Kitāb fī'l‐tasṭīh al‐tāmm(Book of the Perfect Projection on to a Plane) which is extant in two manuscripts. The treatise is devoted to a generalization of the stereographic projection of a sphere on to a plane, usually used in the making of astrolabes. This concerns the projection from a pole of the sphere on to the equatorial plane or a plane parallel to it. Under this projection, circles on the sphere are imaged on to the plane as circles or straight lines. The “perfect projection” invented by al‐Ṣāghānī is the projection of the sphere from any point of its axis on to a plane orthogonal to the axis. Under this projection, circles on the sphere are imaged on the plane as conic sections (ellipses, hyperbolas, and parabolas) or straight lines. These descriptions of methods for conics construction are...
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