Pappus of Alexandria: Book 4 of the Collection

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If we had no other information than can be derived from a perusal of his work, we should only know that he was later than Claudius Ptolemy, whom he quotes often and with respect. Suidas states that he was of the same age as Theon of Alexandria, who wrote commentaries on Ptolemy's great work, the Almagest, and flourished in the reign of Theodosius I.


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Suidas asserts also that Pappus wrote a commentary upon the same work of Ptolemy. But it would seem incredible that two contemporaries should have at the same time and in the same style composed commentaries upon one and the same work, and yet neither should have been mentioned by the other, whether as friend or opponent. We have apparently no reason to question the statement of Suidas that Pappus wrote such a commentary. But the similarity of two such commentaries as those of Pappus and Theon may easily have led Suidas to confuse the two, and so suppose the two authors to have been contemporary.

There is, then, reason to believe that Suidas may have been mistaken; we have, however, another authority, whose statement, on the supposition that it is false, is completely incomprehensible. This is the author of certain historical glosses, which are found in the margin of a MS. Here it is stated, in connexion with the reign of Diocletian A. Except the two distinctly contradictory statements of Suidas and the scholiast, we have no evidence of the date of Pappus; and it seems accordingly best to accept the date indicated by the scholiast.

This collection, which consisted of eight books, we possess only in an incomplete form, there being no part remaining of the first book, and the rest also having suffered considerably. It is curious that no ancient writer, with the exception of the author of the appendix to book iii. The question of Pappus's commentary on Ptolemy's work is discussed by Hultsch, Pappi Collectio Berlin, , vol iii. The characteristics of Pappus's Collection are that it con-tains 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 text upon which Pappus enlarges discursively, many of his additions having no very decided points of connexion with the direct subject under discussion. Very valuable are the systematic introductions to the various books which set forth clearly in outline the contents and the general scope of the subjects to be treated. From these introductions we are able to judge of 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 texts of the many valuable treatises of earlier mathematicians of which time has deprived us.

We proceed to summarize briefly the contents of that portion of the Collection which has survived, mentioning separately certain propositions which seem, in the light of modern developments of mathematics, to be among the most important. Of book i. We can only conjecture that it, as well as book ii.

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The whole of book ii. On this subject see Nesselmann, Algebra der Griechen , Berlin, , pp. Book iii. It may be divided into five sections. Pappus gives the solutions of this problem by Eratosthenes, Nicomedes, and Heron, and finally his own solution of the more general problem of finding geometrically the side of a cube whose content is in any given ratio to that of a given one. This serves as an introduction to a general theory of means, of which Pappus distinguishes ten kinds, and gives a table repre-senting examples of each in whole numbers.

Of book iv. At the begin-ning are various theorems on the circle, leading up to the problem of the construction of a circle wdiich shall circumscribe three given circles touching each other two and two. Sell now - Have one to sell?


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