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Mathematical Treasures - Qadi Zada al-Rumi's Geometry

Frank J. Swetz and Victor J. Katz


This is a page from the Sharḥ ashkāl al-taʾsīs (Commentary on the Fundamental Theorems, 1412-13) of Qāḍī Zāda Mūsā ibn Muḥammad, also known as al-Rūmī ("the Roman" or "the Byzantine") because he was born in Asia Minor in about 1364. He died in 1436. Qāḍī Zāda's book was a commentary on the Ashkāl al-taʾsīs (Fundamental Theorems), written by al-Samarandī (1250-1310) and containing a discussion of 35 of Euclid's propositions. The book shown in the image is a later copy of Qāḍī Zāda's work, probably written in the sixteenth century. At the top of the page is a discussion of Euclid's Proposition I-5, the "Bridge of Asses" proposition that the base angles of an isosceles triangle are equal. At the bottom, there is a discussion of Proposition I-6, the converse of I-5. Qāḍī Zāda was an astronomer and mathematician in the court of Ulugh Beg (1393-1449) in Samarkand. He and his colleagues compiled the first complete star catalogue since the time of Ptolemy.

Posted 5/14/2008 (or earlier); updated 5/23/17

See pages from two other copies of Qāḍī Zāda’s commentary on al-Samarḳandī’s The Fundamental Theorems (or The Forms of Foundation, based on Euclid’s Elements) in Mathematical Treasure: Commentary on The Fundamental Theorems and Mathematical Treasure: Qadi Zada’s Commentary on The Forms of Foundation.

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Qadi Zada al-Rumi's Geometry," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University