×

The Arabic version of Ptolemy’s Planisphere or flattening the surface of the sphere: text, translation, commentary. (English) Zbl 1137.01005

Ptolemy’s Planisphere is the earliest known work on the construction of a plane diagram of the celestial sphere by means of methods related to stereographic projection. Both in style and in level it shows similarities to the Almagest, to which it frequently refers. The Planisphere is not extant in the original Greek, but an Arabic translation presumably deriving from the 9th-century translation activities in Baghdad and a 12th-century Latin translation by Hermann of Carinthia of an Arabic version revised by Maslama al-Majrīṭī (ca. AD 1000) have survived. The Latin version was edited by Heiberg (1907) and translated into German by Drecker (1927). One of the two available manuscripts of the Arabic translation (Istanbul, Aya Sofia 2671) was published in facsimile, translated into English and studied by Anagnostakis in his doctoral dissertation (1984). The other (Tehran, Khān Malik Sāsānī) was briefly described by P. Kunitzsch [“The second Arabic manuscript of Ptolemy’s Planisphaerium”, Z. Gesch. Arab.-Islam. Wissen. 9, 83–89 (1994)].
The present article contains in Section IV a full edition of both extant Arabic manuscripts of the Planisphere, also taking into account the notes on the treatise by Maslama and the Latin translation by Hermann. Furthermore it presents an English translation with technical explanations in footnotes (Section V), as well as an extensive commentary placing the contents of the treatise in the context of ancient mathematical methods (Section VI). The commentary shows in particular that it is often more useful to explain Ptolemy’s procedures in terms of solid geometry, conic sections, and analemma methods than by means of the projective geometry as it was developed by medieval and early modern mathematicians. It thus brings our understanding of the text some significant steps further than the earlier studies by J. L. Berggren [Arch. Hist. Exact Sci. 43, No. 2, 133–144 (1991; Zbl 0778.01001)], R. P. Lorch [Arch. Hist. Exact Sci. 49, No. 3, 271–284 (1995; Zbl 0838.01004)], and others.
The article contains a careful discussion of the editorial and translation procedures that were followed (Sections I and II), the latter including an extensive treatment of the most important astronomical, geographical, mathematical, as well as non-technical terminology. Section III analyses the structure of the treatise, which was originally one continuous piece of prose, and justifies the division in sections used in the edition and translation.

MSC:

01A20 History of Greek and Roman mathematics
01A30 History of mathematics in the Golden Age of Islam
01A75 Collected or selected works; reprintings or translations of classics

Biographic References:

Maslama al-Majrīṭī; Ptolemy
PDFBibTeX XMLCite