The Book on the Measurement of Plane and Spherical Figures (Arabic: كتاب معرفة مساحة الأشكال البسيطة والكريّة, Kitāb maʿrifah masāḥat al-ashkāl al-basīṭah wa-al-kuriyyah)[note 1] was the most important of the works produced by the Banū Mūsā.[2] A Latin translation by the 12th century Italian astrologer Gerard of Cremona was made, entitled Liber trium fratrum de geometria and Verba filiorum Moysi filii Sekir. The original work in Arabic was edited by the Persian polymath Naṣīr al‐Dīn al‐Ṭūsī in the 13th century.[3] The original work in Arabic is not extant, but its contents are known from later translations.[4]
The treatise, which is about geometry, was similar to two books by Archimedes, On the measurement of the circle and On the sphere and the cylinder.[3] It was used extensively in the Middle Ages, and was quoted by authors such as Thābit ibn Qurra, Ibn al‐Haytham, Leonardo Fibonacci (in his Practica geometriae), Jordanus de Nemore, and Roger Bacon.[5] It deals with the geometrical concepts of area and volume, angle trisection, construction, and conic sections.[6] It includes theorems not known to the Greeks.[7]
The book was re-published in Latin with an English translation by the American historian Marshall Clagett, who has also summarized how the work influenced mathematicians during the Middle Ages.[8]
