Machine summary:
We shall focus on his mathematical works, which are as follows: The Works - Establishing Points on Lines in the Ratio of Areas - Answers to Questions Posed by Other Geometers - Discourse Embellishing Archimedes’ Lemmata - Filling a Lacuna in Book II of Archimedes’ Sphere and Cylinder - On Centers of Gravity - Division of the Sphere by Planes - The Elements, According to the Model of the Book of Euclid To begin with evidence from Kūhī’s works in al-Sijzī’s writings we have ten substantial fragments from Sijzī’s Geometrical Annotations.
Finally, it is related to the first problem in Kūhī’s Two Geometrical Questions (Berggren and Van Brummelen, 2001), which is a special case of a theorem in Apollonius’s On Plane Loci.
Fragment 4 [Fig. 3] gives an analysis of the following general problem from Apollonius’s Cutting-Off a Ratio: (View the image of this page) Fig. 3 Given straight lines AB and GD, and points A and G on AB and GD respectively, let E be a third given point somewhere in the plane.
This work of Apollonius was translated into Arabic, and Abū Ishāq al-Sābī, in his correspondence with Kūhī, reminds him that he had promised to send him “the remaining theorems of the second book of Apollonius’ treatise The Determinate Section” (Berggren, 1983).
There is a second book in which Kūhī also refers to his Establishing Points on Lines, and that is his Perfect Compass (Rashed, cf.
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