Muhammad bin Musa

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Ǧa‘far Muḥammad ibn Mūsā ibn Šākir (800 - 873), was a 9th century Persian mathematician and astronomer from Baghdad, the eldest of the Banu Musa brothers.

In addition to making major contributions to geometry texts, Jafar Muhammad also wrote Premises of the book of conics which was a critical revision of Apollonius's Conics.

However, Jafar Muhammad was also the most politically active of the brothers, particularly in the last part of his life when the Turks were gaining control of the empire. It appears that he had an active dispute with al-Kindi.

He, along with his two brothers, were instrumental in translating many scientific Greek and Pahlavi manuscripts into Arabic for al-Ma'mun. The Banu Musa brothers were among the first group of mathematicians to begin to carry forward the mathematical developments begun by the ancient Greeks (See House of Wisdom).

The Banu Musa brothers took a definite step forward, where the Greeks had not; The Greeks had not thought of areas and volumes as numbers, but had only compared ratios of areas etc. The Banu Musa's concept of number is broader than that of the Greeks. For example they describe pi as:

:"... the magnitude which, when multiplied by the diameter of a circle, yields the circumference."

The Banu Musa also introduce geometrical proofs which involve thinking of the geometric objects as moving. In particular they used kinematic methods to solve the classical problem of 'trisecting an angle'.

In astronomy the brothers made many contributions. They were instructed by al-Ma'mun to measure a degree of latitude and they made their measurements in the desert in northern Mesopotamia. They also made many observations of the sun and the moon from Baghdad. Muhammad and Ahmad measured the length of the year, obtaining the value of 365 days and 6 hours. Observations of the star Regulus were made by the three brothers from their house on a bridge in Baghdad in 840-41AD, 847-48AD, and 850-51AD.

Sources

Golden Age of Persia, Richard Nelson Frye, p162-163.
D El-Dabbah, The geometrical treatise of the ninth-century Baghdad mathematicians Banu Musa (Russian), in History Methodology Natur. Sci., No. V, Math. Izdat. (Moscow, 1966), 131-139.

Muhammad bin Musa

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