Banu Musa – Family of Honor

There were three brothers Jafar Muhammad ibn Musa ibn Shakir, Ahmad ibn Musa ibn Shakir and al-Hasan ibn Musa ibn Shakir. They are almost indistinguishable but we do know that although they often worked together, they did have their own areas of expertise.

Born: about 800 in Baghdad, (now in Iraq)

The Banu Musa were the sons of Musa ibn Shakir, who had been a highwayman and later an astrologer to the Caliph al-Ma’mun. At his death, he left his young sons in the custody of the Caliph, who entrusted them to Ishaq bin Ibrahim al-Mus’abi, a former governor of Baghdad. The education of the three brothers was carried out by Yahya bin Abu Mansur who worked at the famous House of Wisdom library and translation centre in Baghdad.

Book of Ingenious Devices:
The Banu Musa brothers built a number of automata (automatic machines) and mechanical devices, and they described a hundred such devices in their Book of Ingenious Devices.

Book on the motion of the orbs:
In physics and astronomy, Muhammad ibn Musa was a pioneer of astrophysics and celestial mechanics. In the Book on the motion of the orbs, he was the first to discover that the heavenly bodies and celestial sph…eres were subject to the same laws of physics as Earth, unlike the ancients who believed that the celestial spheres followed their own set of physical laws different from that of Earth.

Astral Motion and The Force of Attraction:
In mechanics and astronomy, Muhammad ibn Musa, in his Astral Motion and The Force of Attraction, discovered that there was a force of attraction between heavenly bodies, foreshadowing Newton’s law of universal gravitation.

We now turn to the important mathematical contributions made by the Banu Musa brothers. As al-Dabbagh writes in:-

The Banu Musa were among the first Arabic scientists to study the Greek mathematical works and to lay the foundation of the Arabic school of mathematics. They may be called disciples of Greek mathematics, yet they deviated from classical Greek mathematics in ways that were very important to the development of some mathematical concepts.

The most studied treatise written by the Banu Musa is Kitab marifat masakhat al-ashkal (The Book of the Measurement of Plane and Spherical Figures). This work became well known through the translation into Latin by Gherard of Cremona entitled Liber trium fratum de geometria. The treatise considers problems similar to those considered in the two texts by Archimedes, namely On the measurement of the circle and On the sphere and the cylinder.

There are many similarities in the methods employed by the Banu Musa and those employed by Archimedes. More significant, however, is the fact that there are also many differences which, although at first sight may not seem of major importance, yet were providing the first steps towards a new approach to mathematics. The Banu Musa apply the method of exhaustion invented by Eudoxus and used so effectively by Archimedes. However, they omitted that part of the method which involves considering polygons with 2k sides as k tends to infinity. Rather they chose to use a proposition which itself required this passage to infinity in its proof. This in itself may not have been a step forward for, as the author of suggests, this may have been due to a lack of understanding of the finer points of Greek geometric thinking. As used by the Banu Musa the “method of exhaustion” loses most of its subtlety and power.

In another aspect, however, the Banu Musa made a definite step forward. 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 π as:-

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

In the text areas as described as products of linear magnitudes, so the terminology of arithmetic is perhaps for the first time applied to the operations of geometry. 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 840-41, 847-48, and 850-51.

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