Menelaus' ``Spherics''. Early translation and al-Māhānī/al-Harawī's version
This is a definitive, monumental work on Menelaus's \textit{Spherics}. Given that the Greek original is lost, the major task is that of comparing the extant Arabic and Latin translations, of presenting the various versions, and of providing a commentary on them. Several conclusions regarding these versions include: ``(i) That there exists a fragment (about one third) of an ancient Arabic translation of the \textit{Spherics}, which is different from all the subsequent translations. The reader will find in the present volume the \textit{editio princeps} of the fragment together with its first translation. (ii) That the edition of the \textit{Spherics} which is commonly attributed to al-Harawī (10th century) is in fact due to al-Māhānī, and that it was only revised by al-Harawī. The authors also provide the \textit{editio princeps} of this other important text as well as its first translation. (iii) That the King of Saragossa, Ibn Hūd (d. 1085), in the material he borrowed for his \textit{Encyclopedia}, had at his disposal two sources: al-Māhānī's edition for what concerns the first and the second book, and al-Dimashqī's translation for the third. (iv) That the Latin translation of Gerard of Cremona (d. 1175) was not realized, as it was claimed up to now, from one and the same Arabic translation, but, exactly as is the case for Ibn Hūd's commentary, from two sources: al-Māhānī's edition for part of the work, and al-Dimashqī's translation for the rest.'' A general presentation of Menelaus's work and of his \textit{Spherics} is followed by a chapter looking at the differences in the redaction of the \textit{Spherics} by al-Māhānī and by al-Harawī, a chapter on Ibn Hūd, one on the Propositions from the \textit{Spherics} quoted in Ibn Hūd's \textit{Encyclopedia}, one on the mathematical content of the \textit{Spherics}, with the individual Proposition formulated in a language friendly to a contemporary reader, with mentions here and througout the text to later mathematicians, such as Pappus, Ibn al-Haytham, al-Tūsī, 'Umar al-Khayyām, Saccheri, who have commented on them, as well as the original Arabic of the versions referred to above and their English translation. A 45 page long postface presents a history of spherical geometry, with a particular emphasis on the role of the Propositions from Menelaus's \textit{Spherics}.
scientific article; zbMATH DE number 6908518