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Pappus of Alexandria, Greek geometer, flourished about the end of the 3rd century CE. In a period of general stagnation in mathematical studies, he stands out as a remarkable exception. How far he was above his contemporaries, how little appreciated or understood by them, is shown by the absence of references to him in other Greek writers, and by the fact that his work had no effect in arresting the decay of mathematical science. In this respect, the fate of Pappus strikingly resembles that of Diophantus of Alexandria. In his Collection, Pappus gives no indication of the date of the authors whose treatises he makes use of, of the time at which he himself wrote. If we hand no other information than can be derived from his work, we should only know that he was later than Claudius Ptolemy whom he often quotes. Suidas states that he was of the same age as Theon of Alexandria, who wrote commentaries on Ptolemy’s great work, the Syntaxis mathematica, and flourished in the reign of Theodoxius I. (379-395 CE). Suidas says also that Pappus wrote a commentary upon the same work of Ptolemy. But it would seem incredible that two contemporaries should have it at the same time and in the came style composed commentaries upon one and the same work, and yet neither should have been mentioned by the other, either as friend or opponent. It is more probable that Pappus’s commentary was written long before Theon’s, but was largely assimilated by the latter, and that Suidas, through failure to disconnect the two commentaries, assigned a like date to both. A different date is given by the marginal notes to a 10th century MS., where it is stated, in connection with the reign of Diocletian (284-305 CE), that Pappus wrote during that period; and in the absence of any other testimony it seems best to accept the date indicated by the scholiast.<./P>

The great work of Pappus, in eight books and entitled sunagoge or Collection, we possess only in an incomplete form, the first book being lost, and the rest having suffered considerably. Suidas enumerates other works of Pappus as follows: Chrographia oikoumenike, eis ta tessara Biblia tes Ptolemaiou begales suntazeos upomnema, poramous tous en Dibue, oneirokritika. The question of Pappus’s commentary on Ptolemy’s work is discussed by Hultsch, Pappi collectio, (Berlin, 1878), vol. iii. p. xiii. squ. Pappus himself refers to another commentary, of which nothing is known. He also wrote commentaries on Euclid’s Elements (of which fragments are preserved in Proclus and the Scholia, while the tenth Book has been found in an Arabic MS.), and on Ptolemy's Armonika.

The characteristics of Pappus's Collection are that it contains an account, systematically arranged, of the most important results obtained by his predecessors, and, secondly, notes explanatory of, or extending, previous discoveries. These discoveries form, in fact, a test upon which Pappus enlarges discursively. Very valuable are the systematic introductions to various books which set forth clearly in outline the contents and general scope of the subjects to be treated. From these introductions we are able to judge the style of Pappus’s writing, which is excellent and even elegant the moment he is free from the shackles of mathematical formulae and expressions. At the same time, his characteristic exactness makes his collection a most admirable substitute for the test of the many valuable treatises of earlier mathematicians of which time has deprived us.

From the eleventh edition of The Encyclopedia, 1911. Public domain. Some editing has been done for the sake of clarity.

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