Nasir al-Din al-Tusi, Tahrir kitab al-kura wa'l-ustuwanali Arshimidis ('Sphere and Cylinder', a commentary on geometry), and Maqalah fi taksir al-kura li Arshimides (a treatise on measuring the sphere), Persia, Timurid, 15th century

Arabic manuscript on paper, 80 leaves plus 2 flyleaves, 19 lines to the page, written in black ink, catchwords, astronomical diagrams throughout, brown leather binding with tooled decoration

Seal impression of Qiwam al-Din Muhammad al-Husaini, dated 1097 AH/1685-86 AD

In good overall condition, pages slightly cropped, spine repaired, minor paper repairs to top corners throughoutminor smudges, as viewed.
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This treatise describes and explains one of the most famous of Archimedes' mathematical theories, that of the 'Sphere and the Cylinder'. Addressed to Dositheus, Archimedes obtained the result of the relationship between the sphere and circumscribed cylinder of the same height and diameter. The sphere has a volume two-thirds that of the circumscibed cylinder, and similarly the sphere has an area two-thirds that of the cylinder (including the bases). This particular mathematical proof was so close to Archimedes' heart that a sculpted sphere and cylinder were placed on top of his tomb at his request.

Rosenthal and Ihsanoglu list other copies of this work in various libraries including Berlin, Florence, Rampur, Manchester, London, Mashhad and Paris, see Mathematicians, Astronomers & Other Scholars of Islamic Civilisation and their Works (7^th-19^th c.), Istanbul, 2003, pp. 211-219, no 606, M4.

See also A. Mingana, Catalogue of the Arabic Manuscripts in the John Rylands Library, Manchester, 1934, p.550, no.350. where the author states that “the editor, Nasir al-Din al-Tusi, informs us in the preface that the version which he used was revised by Thabet Ibn Qurrah who died in 901 AD, and was first translated by Hunayn Ibn Ishaq Hunayn who died in 873 AD, while his researches were facilitated by the commentary of Eutocius of Ascalon. The work has two maqalahs”. This information also appears in the preface of the present manuscript.

The great scholar and polymath Nasr al-Din al-Tusi (1201-74 AD) was responsible for editions of most of the Greek astronomical and mathematical works that had been translated into Arabic in the eighth-tenth centuries. His enormous output in such editions or recensions was almost matched by his own independent works on those subjects.