Ibn Sahl (mathematician)

Ibn Sahl (full name Abū Saʿd al-ʿAlāʾ ibn Sahl أبو سعد العلاء ابن سهل; c. 940–1000) was a mathematician and physicist of the Islamic Golden Age, associated with the Buwayhid court of Baghdad. Nothing else about his person is known.

He is known to have written an optical treatise around 984. The text of this treatise was reconstructed by Roshdi Rashed from two manuscripts (edited 1993).: Damascus, al-Ẓāhirīya MS 4871, 3 fols., and Tehran, Millī MS 867, 51 fols. The Tehran manuscript is much longer, but it is badly damaged, and the Damascus ms. contains a section missing entirely from the Tehran ms. The Damascus ms. has the title Fī al-'āla al-muḥriqa "On the burning instruments", the Tehran ms. has a title added in a later hand Kitāb al-harrāqāt "The book of burners".

Ibn Sahl is the first Muslim scholar known to have studied Ptolemy's Optics, and as such an important precursor to the much more influential Book of Optics by Ibn Al-Haytham (Alhazen), written some thirty years later. The treatise deals with the optical properties of curved mirrors and lenses and the law of refraction (Snell's law). Ibn Sahl uses the law of refraction to derive lens shapes that focus light with no geometric aberrations, known as anaclastic lenses. In the remaining parts of the treatise, Ibn Sahl dealt with parabolic mirrors, ellipsoidal mirrors, biconvex lenses, and techniques for drawing hyperbolic arcs.

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