**al-Jawhari**'s life except that he was associated with the remarkable House of Wisdom that was set up in Baghdad by the Caliph al-Ma'mun. It is worth looking at the events which led up to the founding of this important centre for learning.

Harun al-Rashid became the fifth Caliph of the Abbasid dynasty on 14 September 786, and ruled from his court in the capital city of Baghdad over the Islam empire which stretched from the Mediterranean to India. He brought culture to his court and tried to establish the intellectual disciplines which at that time were not flourishing in the Arabic world. He had two sons, the eldest was al-Amin while the younger was al-Ma'mun. Harun died in 809 and there was an armed conflict between the brothers.

Al-Ma'mun won the armed struggle and al-Amin was defeated and killed in 813. Following this, al-Ma'mun became Caliph and ruled the empire from Baghdad. He continued the patronage of learning started by his father and founded an academy called the House of Wisdom where Greek philosophical and scientific works were translated. He also built up a library of manuscripts, the first major library to be set up since that at Alexandria, collecting important works from Byzantium. In addition to the House of Wisdom, al-Ma'mun set up observatories in which Muslim astronomers could build on the knowledge acquired by earlier peoples.

Al-Jawhari was employed in the service of al-Ma'mun in Baghdad, although we do not know exactly when he began his work there. Mathematicians such as al-Kindi, al-Khwarizmi, Hunayn ibn Ishaq, Thabit ibn Qurra and the Banu Musa brothers were also appointed by al-Ma'mun to the House of Wisdom, so a truly remarkable collection of scholars worked there. There are very few instances in the history of mathematics when a larger number of world class mathematicians gathered together and took part in research. Al-Jawhari, although best known as a geometer, made observations in Baghdad from 829 to 830 while working for al-Ma'mun. He left Baghdad before the death of al-Ma'mun in 833, for he was observing in Damascus in 832-33.

The main work by al-Jawhari was *Commentary on Euclid's Elements* which is listed in the *Fihrist* (Index), a work compiled by the bookseller Ibn an-Nadim in 988. *Commentary on Euclid's Elements* is almost the same work described by Nasir al-din al-Tusi (although al-Tusi gives a slightly different title for al-Jawhari's work: *Emendation of the Elements*). This work contained nearly fifty propositions additional to those given by Euclid and included an attempt by al-Jawhari to prove the parallel postulate. The proof followed similar lines to that attempted by Simplicius but it is certainly not a copy of Simplicius's proof, containing several original ideas. Al-Tusi quotes six of the nearly fifty propositions which together form what al-Jawhari believed was a proof of the parallel postulate. This means that, as far as we are aware, al-Jawhari was the first Arabic mathematician to attempt such a proof. The fact that the proof fails was certainly noted by al-Tusi.

The paper [3] discusses a thirteenth century commentary on a short treatise by al-Jawhari. In the short treatise al-Jawhari presents three additions to Book V of Euclid's *Elements*, which are meant prove Definition 5 which defines equal ratio, and Definition 7 which defines greater ratio. Al-Jawhari's "proofs" are examples of early attempts by Muslim mathematicians to understand the difficult concepts in Euclid's *Elements*. Berggren, reviewing [3], expresses surprise, not at al-Jawhari's fallacious arguments, but rather the fact that they were still being repeated 400 years later:-

One can only wonder, however, at the survival of such ill-conceived alterations of Euclid's "Elements" and their incorporation, so many centuries later, in an Arabic edition of the "Elements" composed late in the thirteenth century.

**Article by:** *J J O'Connor* and *E F Robertson*

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