The Abridged Commentary on "The Apple in the Science of Measurement"


This manuscript is a commentary on the treatise Al-Tuffāḥa fi ‘ilm al-Misāḥa (The apple in the science of measurement), which was written at the beginning of the 12th century by the mathematician Aḥmad ibn Muḥammad al-Ašh‘ari. The study of measures and measurement techniques (‘ilm al-misāha) was of great interest to Arabic mathematicians during the Middle Ages, both from theoretical and practical points of view. The ability to calculate the dimensions of landholdings was extremely important when it came to determining the correct amounts for inheritances and to calculating taxes. This work deals mainly with the definition of solid and plane figures and the description of rules for the calculation of lengths, areas, and volumes in elementary plane and solid geometry. The author of the commentary, ‘Abd al-Laṭīf ibn Aḥmad al-Dimašhqī, arranges his explanation according to a classical template common to many similar geometrical treatises. The rubricated headings and the quotations from al-Ašh‘arī's work lead the reader from a general introduction to geometry to more detailed explanations of how to calculate areas of simple and complex figures. Drawings in the margins of the manuscript, which was made in 1887, are used to explain the problems presented in the main text.

Date Created


Title in Original Language

شرح مختصر التفاحة في علم المساحة

Type of Item

Physical Description

22 leaves (20 lines), bound : paper ; 25 x 18 centimeters


  • Paper: yellowed cream, with watermarks; edges of first 5 leaves torn, first and last leaves repaired. Text of al-Tuffāḥah written in pink, with the commentary in black, framed in a double pink line. Diagrams and notes in the margins. Catchwords on rectos. Maghribi script; 20 lines in written area, 19 x 10 centimeters.


Last updated: March 16, 2012