AL-KHATĪBĪ, Shams al-Din Muhammad b. Muzaffar.

Scarce, handsomely-copied manuscript commentary of al-Salahi’s rare treatise on algebra. We have only traced one other copy at the Aja-Sofia Library (n.2751) in Istanbul (‘Kitāb’, III, p.1446). Shams al-Din Muhammad b. Muzaffar al-Khatibi al-Khalkhālī (d.745AH / 1344AD) was an imam and scholar, of whom little is known; the title calls him ‘engineer’ (muhandes). This manuscript was copied not too long after his death, in 785AH, by ‘Abd al-Karim b. Shaikh Hasan al-Rūmi. He also copied on very similar paper another scientific work – ‘Sharh al-mulakhkhas fi ‘ilm al-hay’a’ – signing the colophon AH 789 / AD 1387, in Tabriz, an important cultural center where all mathematical disciplines were studied (Brentjes), then under the tribal confederation of Aq Qoyunlu.

Al-Salahi al-Rumi al-‘Othmani al-Hasib (fl.c.735AH / 1334AD) was a scholar of mathematics of whom little is known. His work in this ms bore a nearly identical title to the founding algebra treatise by al-Khwarizmi (d.850AD). al-Khwarizmi’s treatise ‘was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as “algebraic objects”. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. […] it allowed mathematics to be applied to itself in a way which had not happened before’ (Boyer). In the course of 6 chapters, al-Salahi’s work, and its commentary, address similar topics, including algebra and the balancing and solving of quadratic equations, as well as the calculation of an area using algebra, this last part being illustrated by numerous geometrical diagrams in red ink showing, for instance, the inscription of a triangle within a semicircle and other problems. At some point, the commentator al-Khatibi also uses two lines of poetry to explain the algebraic concept of ‘mal’, i.e., the square value of a ‘thing’ in an equation. A very handsome and scarce ms. text.