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Mathematical Treasure: Qadi Zada’s Commentary on the Forms of Foundation

Frank J. Swetz (The Pennsylvania State University)

In 1412, Qāḍīzāda (or Qāḍī Zāda) Ṣalāh al-Din Mūsā ibn Muḥammad, also known as al-Rūmī (1364-1436), wrote Sharḥ ashkāl al-ta’sīs (Commentary on Forms of Foundation). Ashkāl al-ta’sīs (Forms of Foundation, often translated as Fundamental Theorems) was a geometric tract written by the earlier mathematician Shams al-Dīn Muḥammad ibn Ashraf al-Ḥusaynī al-Samarandī, who died in about 1303. Qāḍīzāda was an important astronomer at the Samarkand observatory and dedicated his work to the founder and director of the observatory, Ulugh Beg. Since Ashkāl al-ta’sīs focused on 35 “postulates” from Euclid’s Elements, so, too, did Qāḍīzāda's Commentary. The Commentary was widely studied and copied throughout the Islamic world from the 15th century onward, especially in North Africa. The copy featured here was made in 1714-15.  The opening pages provide an introduction:

Important points within the discussions are written in red ink. Diagrams are provided in the page margins:

These images are obtained through the courtesy of the World Digital Library, where the entire manuscript can be viewed. The manuscript itself is held by the Qatar National Library.

Source: Qāḍīzāda's Commentary on Forms of Foundation via World Digital Library:

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 Treasures - Qāḍī Zāda’s Geometry and Mathematical Treasure: Commentary on The Fundamental Theorems. 

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Qadi Zada’s Commentary on the Forms of Foundation," Convergence (July 2017)