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(fl. 320)

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(fl. ad 320),

mathematical commentator. The most important of his surviving works is Sunagōgē (Collection), a compilation (probably made after his death) in eight books of eight originally separate treatises and commentaries on different parts of the mathematical sciences. Book 8, an introduction to mechanics, is referred to as a distinct work by Eutocius, and exists as such in Arabic translation (in a fuller version than the Greek). Book 1 is missing, but was perhaps Pappus' commentary on Euclid, Elements 10 (see below). Book 2, of which the first part is also missing, contains number games based on a lost work of Apollonius of Perge with a notation for expressing large numbers. Book 3 is a miscellany of geometrical problems for the use of students, book 4 on higher geometry and special curves, book 5 on isoperimetric problems and the regular and semi-regular polyhedra, book 6 a commentary on the collection of astronomical treatises known as the ‘Little [Domain] of Astronomy’ (Mikros Astronomoumenos). Book 7, the longest and most interesting, entitled Domain of Analysis (Analouomenos topos), is a commentary on Hellenistic works of higher geometry, mostly lost. The Collection is invaluable (and of considerable influence in European mathematics) as a source for lost works from the great period of Greek mathematics. Pappus' own contributions, in the form of ‘lemmas’ and proofs, are mostly trivial, and it is probable that all significant theorems are taken from earlier works, even when unattributed.

Pappus wrote a commentary to Ptolemy (Claudius Ptolemaeus)'s Almagest, of which the part on books 5 and 6 survives. This is superficial, but provides valuable information on lost works of Hipparchus. His commentary to Euclid Elements 10, which survives in Arabic translation, is of interest because of its discussion of ‘unordered irrationals’, with references to a work of Apollonius on the same topic and to Theaetetus. Among other lost works are Chōrographia oikoumenikē, a universal geography used in an early Armenian text, and commentaries on the Planispherium of Ptolemy (Claudius Ptolemaeus) and the Analemma of Diodorus of Alexandria.

G. J. Toomer

Subjects: Classical studies

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