39. Al-Kashi
(Died in 839H/1436AD) 

Ghaiat ed-Din Massud Ibn Muhammad al-Kashi was born at the end of the 8th century H in Kashan (Iran). He studied grammar, conjugation, fiqh and logic, and learned and excelled in mathematics. No wonder since his father was one of the prominent scientists in mathematics and astronomy. He lived most of his life in Samarkand, where he built an observatory, he called as “the observatory of Samarkand”(236).

Scientific Contributions

He provided explanations for most of the output of scientists who worked with Nacir ed-Din Tussi, in the observatory of Meragha. He also revised the tables of stars devised by observers in this observatory. He gave very precise estimation of the solar eclipses during three years (between 1407 and 1409 AD / 809 and 811 H) and was the first to discover that the orbits of mercury and the moon are elliptical(237).

In mathematics, he devised the decimal fractions. Smith says in his book “The History of Mathematics”. “The discord between mathematicians is indeed bitter, but the majority of them agree that it was al-Kashi who devised the decimal fractions.”(238)

He also developed a law concerning a group of natural numbers raised to power four. Cara de Faw in his comment on the Muslin astronomers says: “Al-Kashi devised a method to add numbers of a chain, raised to power four. It is indeed a method that requires a lot of genius to find out.”(239)

Major Works

He compiled books in many sciences, here are a few :

-“Kitab Zij al-Khaquani” : It contains adjustment of the star tables developed by the astronomers at Meragha observatory;

-“Rissala fi al-Hissab” (A Treatise of Arithmetic);

-“Rissala fi al –Handassa” (A Treatise of Geometry);

-“Rissalat al-Jib wa al-Watr”

-“Rissala an Ihliligiat al Kammar wa Atarid” (A treatise on the elliptical moon and mercury)

Abdullah ad-Difaa says in his comment on the importance of al-Kashi's books, in particular “Miftah al hissab” (Key of Arithmetic), “This book was a source of inspiration for scientists either from East or West. They used it as reference in the education of their sons in schools and universities for several countries. They also used many of his theories and laws.”