*Sharḥ ashkāl al-taʾsīs* (*Commentary on the Fundamental Theorems, *or *Commentary on the Forms of Foundation*) was written in 1413 [Youschkevitch, p. 123] by the Islamic scholar Qāḍī Zāda Mūsā ibn Muḥammad, also known as al-Rūmī ("the Roman" or "the Byzantine") because he was born in Asia Minor. His year of birth is not known; he died in 1436. The University of Michigan Library Catalog describes the manuscript (Islamic Manuscript 727) more specifically as a “commentary on the *Ashkāl al-taʾsīs* [*The Fundamental Theorems*], a compendium of geometry according to Euclid by Muḥammad ibn Ashraf al-Samarḳandī.” Al-Samarḳandī lived during the 13th century. The copy shown here was written sometime after Qāḍī Zāda wrote his commentary (in about 1413) and before 1612.

A discussion of the area of the regions resulting from the bisection of a rectangle by its diagonal (Euclid I.43):

A rendering of the “Wind Mill Proof” of the Pythagorean Theorem, one popular with Islamic authors:

*The images above are supplied through the courtesy of the University of Michigan Libraries. You may use them in your classroom; for permission to use them for any other purpose, please contact the University of Michigan Libraries. The full manuscript is available via the HathiTrust Digital Library as*

Record 002583102,* *Sharḥ ashkāl al-taʾsīs : manuscript, [between 1400? and 1611], HathiTrust Digital Library.

*Besides the two library catalog webpages (University of Michigan and HathiTrust) cited above, information for this article was obtained from the following source:*

Adolf P. Youschkevitch, *Les Mathématiques Arabes (VIIIe – XVe siècles),* Paris: Vrin, 1976.

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

Index to Mathematical Treasures