The measurement of the circle in Naṣīr al-Dīn al-Ṭūsī's Revision of the 'middle books' (Taḥrīr al- mutawassiṭāt)

The mathematical treatises known as Taḥrīr al-mutawassiṭāt, “Revision of the Middle

books”, are a collection of Greek and Arabic treatises which were re-edited by Naṣīr

al-Dīn al-Ṭūsī. This paper explores the nature of the editorial work Ṭūsī did, showing

that it is not a simple rendering of the original text but that it involves major

revisions and in fact original additions. For the first time, a collated version of

Ṭūsī’s revision on the treatise on the measurement of the circle (by Archimedes) is

provided. A translation of the Arabic text is put side by side with a rendition of the

treatise as it was circulated before Ṭūsī’s time. An in-depth analysis of the text

elucidates the nature of Ṭūsī’s contributions to the text. This article also provides

modest corrections to earlier studies by W. R. Knorr and P. Luckey.