A Treatise on the Sector-Figure and the Composition of Ratios


This manuscript preserves a three-page fragment from Risālatun fī al-shakl al-qiṭāʻ wa al-nisbati al-muʼallafah (A treatise on the sector-figure, and the composition of ratios), an essay that deals with Menelaus’s Theorem and spherical astronomy. The treatise is attributed to Thabit ibn Qurrah al-Harrani (died 901), a Sabian from the ancient city of Harran (in present-day Turkey). Thabit was an important mathematician, translator, physician, philosopher, and the court astronomer for the Abbasid caliph al-Muʿtadid (reigned 892–902). Thabit is known, among other things, for his early reform of the Ptolemaic system, his work on statics, his remarkable estimation of the sidereal year, and the Thabit number, named in his honor. Thabit's native tongue was Syriac. He knew Greek but wrote his important works in Arabic. In Baghdad, he worked with a well-known family of mathematicians and astronomers known as the Banu Musa, great intellectuals in the scholarly life of Baghdad in the ninth century. His work was divided between translation and research. He translated the works of Archimedes, Apollonius, and others. The text presented here is incomplete, with several pages missing at the beginning and the end. It is taken from a longer essay on the sector-figure, in which Thabit attempts to provide a “shorter and easier proof than that of Ptolemy” on the sector-figure. The manuscript was copied in black, undotted naskh script in the month of Rajab 698 AH (circa April 1299). It contains a total of four geometrical figures (three drawn in red ink), and bears a stamp of “the Hijazi Repository” of “Fuad Salim al-Hijazi”, who might be the late-19th and early-20th century Egyptian nationalist and intellectual of the same name.

Date Created

Subject Date


Title in Original Language

رسالة فى الشكل والقطاع والنسبة المؤلفة

Type of Item

Physical Description

3 pages ; 17 x 22 centimeters


  1. Glen Van Brummelen. "On the Sector-Figure and Related Texts." Mathematical Association of America Reviews. January 26, 2010. http://www.maa.org/press/maa-reviews/on-the-sector-figure-and-related-texts.

Last updated: April 3, 2018