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al-Qūhī and al-Sijzī: The perfect compass and the tracing of conic sections. (al-Qūhī et al-Sijzī: Sur le compas parfait et le tracé continu des sections coniques.) (French) Zbl 1063.01006

The author has published earlier [“Geometry and geometrical optics in the 10th century”, London (2003), Chap. V] a treatise of al-Qūhīabout a mechanical device, a guided variable compas, able to trace conics, circles, and straight lines. The present paper contains text, translation, and explanation, from a single ms., of a treaty of al-Sijzī, which extends the theory and practice of this “perfect” compass to trace a conic similar to a given one. The author also points to al-Qūhī’s distinction between measurable curves (linear and quadric curves) and not-measurable curves, the latter divided into those that have order and regularity and those that are purely mechanical. He promises an investigation of the development of this classification after the 10th century.

MSC:

01A30 History of mathematics in the Golden Age of Islam
51M15 Geometric constructions in real or complex geometry

Software:

COMPAS
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