Euclid's Elements - A 2,500 Year History
Bob Gardner
East Tennessee State University
Department of Mathematics and Statistics
Johnson City, TN 37614

Arabic Translations of The Elements

As Europe fell into the dark ages, the work of the classical period was preserved in the Arabic world. By the middle of the eighth century, all the important work in mathematics was being done by Islamic scholars. This would remain the case for the next several hundred years. Scholarship exploded in the Middle East, fueled in part by the availability of numerous ancient texts from Byzantium and elsewhere. In the ninth century and afterward, many of the classical works of the ancient world were translated from Greek into Arabic [Bardi, page 62]. Heath's introduction lists 31 Arabic translators of The Elements. We now mention a few of these.

The first page of an-Nairizi’s Codex Leidensis 399
(from about the year 900), commentary on Book III.
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an-Nairizi died around 922. His commentary on books I through VI survives in the Codex Leidensis, and a commentary translated into Latin in the 12th century on Books I through X also survives [Heath, page 85].

Abu l Wafa al-Buzjani
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Abu al-Buzjani (940-997), one of the greatest Arabian mathematicians, wrote a commentary on The Elements, but did not complete it. He also wrote a commentary on Diophantus [Heath, pages 85 and 86].

(cica 800–870)
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al-Kindi (died about 873), is the author (1) of a work 'on the objects of Euclid's book,' (2) of a book "on the improvement of Euclid's work," and (3) of another "on the improvement of the 14th and 15th Books of Euclid." He also wrote treatises on the work of Archimedes [Heath 86].

Thabit ibn Qurra
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Thabit Qurra (826-901) translated parts of Archimedes and Books V-VII of the Conics of Apollonius, revised a translation of Euclid's Elements, and revised a translation of the Data. He wrote: (1) On the Premises (Axioms, Postulates, etc.) of Euclid, (2) On the Propositions of Euclid, (3) On the propositions and questions which arise when two straight lines are cut by a third [Heath, page 87].

al-Hasan al-Haitham
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al-Haitham (about 965-1039) was known as an intellectual and a preeminent mathematician of his time. Among other things, he wrote a commentary and abridgement of the Elements and a collection of the elements of geometry and arithmetic drawn from the treatises of Euclid and Apollonius [Heath, page 88].

Nasiraddin al-Tusi
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Nasiraddin at-Tusi (1201-1274) wrote: (1) A treatise on the postulates of Euclid, (2) A treatise on the 5th postulate, (3) Principles of Geometry taken from Euclid, and (4) 105 problems out of The Elements. He also edited the Data [Heath, page 89].

Go to the next section: Other Translations of The Elements.

Last revised January 1, 2010.