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Al-Quhi worked chiefly in geometry and considered problems leading to quadratic or cubic equations. Nasir al-Din al-Tusi wrote:-
To construct a sphere segment equal in volume to a given sphere segment and equal in area to a second sphere segment - a problem similar to but more difficult than related problems solved by Archimedes - Al-Quhi constructed the two unknown lengths by intersecting an equilateral hyperbola with a parabola and rigorously discussed the conditions under which the problem is soluble.
Al-Quhi also described a conic compass, a compass with one leg of variable length, for drawing conic sections.
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