A History of Greek Mathematics and Astronomy

Page 27

Hypsicles (second half of second century B. C.) wrote what became known as 'Book XIV' of the Elements containing supplementary propositions on the regular solids (partly drawn from Aristaeus and Apollonius); he seems also to have written on polygonal numbers. A mediocre astronomical work (Αναφορικος {Anaphorikos}) attributed to him is the first Greek book in which we find the division of the zodiac circle into 360 parts or degrees.

Posidonius the Stoic (about 135-51 B. C.) wrote on geography and astronomy under the titles On the Ocean and περι μετεωρων {peri meteôrôn}. He made a new but faulty calculation of the circumference of the earth (240,000 stades). Per contra, in a separate tract on the size of the sun (in refutation of the Epicurean view that it is as big as it looks), he made assumptions (partly guesswork) which give for the diameter of the sun a figure of 3,000,000 stades (39-1/4 times the diameter of the earth), a result much nearer the truth than those obtained by Aristarchus, Hipparchus, and Ptolemy. In elementary geometry Posidonius gave certain definitions (notably of parallels, based on the idea of equidistance).

Geminus of Rhodes, a pupil of Posidonius, wrote (about 70 B. C.) an encyclopaedic work on the classification and content of mathematics, including the history of each subject, from which Proclus and others have preserved notable extracts. An-Nairīzī (an Arabian commentator on Euclid) reproduces an attempt by one 'Aganis', who appears to be Geminus, to prove the parallel-postulate.

But from this time onwards the study of higher geometry (except sphaeric) seems to have languished, until that admirable mathematician, Pappus, arose (towards the end of the third century A. D.) to revive interest in the subject. From the way in which, in his great Collection, Pappus thinks it necessary to describe in detail the contents of the classical works belonging to the 'Treasury of Analysis' we gather that by his time many of them had been lost or forgotten, and that he aimed at nothing less than re-establishing geometry at its former level. No one could have been better qualified for the task. Presumably such interest as Pappus was able to arouse soon flickered out; but his Collection remains, after the original works of the great mathematicians, the most comprehensive and valuable of all our sources, being a handbook or guide to Greek geometry and covering practically the whole field. Among the original things in Pappus's Collection is an enunciation which amounts to an anticipation of what is known as Guldin's Theorem.

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T. L. Heath
A History of Greek Mathematics and Astronomy

Learned Freeware

T. L. Heath A History of Greek Mathematics and Astronomy

Learned Freeware

T. L. Heath
A History of Greek Mathematics and Astronomy