# Pappus of Alexandria

Pappus (Greek Πάππος ὁ Ἀλεξανδρεύς Pappus ho Alexandreús, Latinized Pappus, and Pappus of Alexandria ) was a Greek mathematician and astronomer. He lived in Alexandria in the 4th century and was one of the last great mathematician of antiquity.

## Life

According to the Suda, a Byzantine encyclopedia, but Pappus lived at the time of the Emperor Theodosius I ( 379-395 ), according to a note in a manuscript of the 10th century under the emperor Diocletian ( 284-305 ). The only certainty is that he has observed a solar eclipse in Alexandria on 18 October 320. Since he does not mention subsequent eclipses, he was in the last decades of the fourth century, probably not scientifically active, but it is possible that he has the time of the Emperor Theodosius yet experienced.

## Mathematical Collections

His main work, the Mathematical Collections (Latin Mathematicae Collectiones ), which form a major source for our knowledge of geometry in antiquity. Essentially, it is an annotated and supplemented by findings of our own collection of older results. It contains, among other propositions about cross ratios, involutions, conic sections, their scope was not recognized until much later; also by the Jesuit Guldin anew discovered Zentrobarische rule (now Guldinsche rules ) for determining the content and the surface of bodies of revolution can already be found there. Of the eight books of Mathematical collections, only the last six and the final of the second book in manuscript available.

## Other works

In addition to the collections Pappus wrote commentaries on various older works, so to Euclid's Elements or Almagest of Ptolemy. He also wrote a geography, and it is believed that the geography of Moses by choirs is largely an Armenian translation of it. Possibly derived from Pappus a part of the comment of Porphyry to harmony of Claudius Ptolemy

## Sets of Pappus

Among the various returning to Pappos geometric rates in modern geometry especially the so-called set of Pappos Pascal important, which means that for a hexagon, the corners of which are alternately on two different lines, the intersections of the opposite sides are collinear.

## Reception

The first Latin edition of the Mathematical Collection of Pappus comes from Federico Commandino (Pesaro 1588, 1602, Venice 1589, 2nd edition Bologna 1660). Excluded was the then unknown fragment of Book 2, but John Wallis was in the Savilian Library in Oxford and its translation he published in 1688.

## Text output

- Friedrich Hultsch ( Eds.): Daddy Alexandrini Collectionis, 3 vols, Berlin 1876-1878 (Greek and Latin)
- Paul ver Eecke: Pappus of Alexandria, La Collection Mathématique, 2 volumes, Paris, Bruges 1933 ( French translation )
- Carl Immanuel Gerhardt: The Collection of Pappus of Alexandria, Greek and German, 2 volumes, Hall 1871 ( and Eisleben 1875)
- Alexander Jones ( ed.): Mathematical Collections, Book 7, Springer, 1986 ( Greek and English )
- Heike Sefrin -Weis (ed.): Pappus of Alexandria: Book 4 of the Collection, Springer, 2010
- Adolphe Rome ( ed.): Commentaires de Pappus et de Theon d ' Alexandrie sur l' Alma gesture, Volume 1, Biblioteca Apostolica Vaticana, Rome 1931
- William Thomson, Gustav Young (ed.): The commentary of Pappus on Book X of Euclid 's Elements, Cambridge (Massachusetts ), 1930, pp. 189-260 (Arabic and English)
- Heinrich Suter: The comment of Pappus to X book of Euclid, 1922, pp. 9-78 ( German translation )
- Arsène Soukry: Géographie de Moïse de Corene d'après Ptolémée. Texts arménien traduit en français, Venice 1881