帕普斯

Pappus of Alexandria ( ; Ancient Greek: Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c.  350 AD) was a Greek mathematician of late antiquity known for his Synagoge (Ancient Greek: Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria, where he worked as a mathematics teacher to higher level students, one of whom was named Hermodorus.

The Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics that were part of the ancient mathematics curriculum, including geometry, astronomy, and mechanics.

Pappus was active in a period generally considered one of stagnation in mathematical studies, where, to some, he stands out as a remarkable exception and, to others, as an exemplar of ills that halted the progress of Greek science. In many respects, his fate strikingly resembles that of Diophantus', originally of limited importance but becoming very influential in the late Renaissance and Early Modern periods.

Dating

In his surviving writings, Pappus gives no indication of the date of the authors whose works he makes use of, or of the time (but see below) when he himself wrote. If no other date information were available, all that could be known would be that he was later than Ptolemy (died c. 168), whom he quotes, and earlier than Proclus (born c. 411), who quotes him.

The 10th century Suda states that Pappus was of the same age as Theon of Alexandria, who was active in the reign of Emperor Theodosius I (372–395).……

Works

The great work of Pappus, in eight books and titled Synagoge or Collection, has not survived in complete form: the first book is lost, and the rest have suffered considerably. The Suda enumerates other works of Pappus: Description of the Inhabited World (Ancient Greek: Χωρογραφία οἰκουμενική, romanized: Chorographia oikoumenike), a commentary on the thirteen books of Ptolemy's Almagest (of which the part on books 5 and 6 survives), The Rivers in Libya (Ancient Greek: Ποταμοὺς τοὺς ἐν Λιβύῃ), and The Interpretation of Dreams (Ancient Greek: Ὀνειροκριτικά). Pappus himself mentions another commentary of his own on the Ἀνάλημμα (Analemma) of Diodorus of Alexandria.……

Collection

Pappus's Collection contains an account, systematically arranged, of the most important results obtained by his predecessors and notes explanatory of, or extending, previous discoveries. These discoveries form, in fact, a text upon which Pappus enlarges discursively. Heath considered the systematic introductions to the various books valuable, for they set forth clearly an outline of the contents and the general scope of the subjects to be treated. In these introductions, the style of Pappus's writing is excellent and even elegant the moment he is free from the shackles of mathematical formulae and expressions.……

Book I

Book I has been lost.……

Book II

The whole of Book II (the former part of which is lost, the existing fragment beginning in the middle of the 14th proposition) discusses a method of multiplication from an unnamed book by Apollonius of Perga.……

Legacy

Pappus's Collection was relatively unknown in medieval Europe, but exerted great influence on 17th-century mathematics after being translated to Latin by Federico Commandino. Diophantus's Arithmetica and Pappus's Collection were the two major sources of Viète's In artem analyticam isagoge (1591). The Pappus's problem and its generalization led Descartes to the development of analytic geometry. Fermat also developed his version of analytic geometry and his method of Maxima and Minima from Pappus's summaries of Apollonius's lost works Plane Loci and On Determinate Section.……