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Euclid is mainly known as a mathematician, and his fame is based upon the Elements; Ptolemy's personality was far more complex and two of his books, the Almagest and the Geography, remained standard textbooks in their fields for at least fourteen centuries. The comparison of Ptolemy with Euclid is a very useful one, because the fact that their books superseded earlier ones was essentially due to the same causes. Ptolemy, like Euclid, 8 Hipparchos flourished from 161 4 in Rhodes from 146 to 127 and perhaps also to 146 in Alexandria.

It is possible to do better at present, but it is almost unbelievable that anybody could have twenty-two centuries ago. The most amazing part of Book I is Euclid's choice of postulates. Aristotle was, of course, Euclid's teacher in such matters; he had devoted much 24 attention to mathematical principles, had shown the un- EUCLID AND HIS TIME avoidability of postulates and the need for reducing them to a minimum; 16 yet, the choice of postulates was Euclid's. " ... if A person of average intelligence would say that the proposition is evident and needs no proof; a better mathematician would realize the need of a proof and attempt to give it; it required extraordinary genius to realize that a proof was yet imppssible.

The stereographic projection is the only one which is both conformal and perspective, 17 Ptolemy could not have known that unicity, but he had made a good study of projections and was lucky. 6. THE GEOGRAPHY geographical treatise or guide (geographice almost as important as the Almagest. It covered Ptolemy's hyphegesis) is the whole of mathematical geography, just as the Almagest covered the whole of mathematical astronomy, and it in- fluenced geography as deeply and as long as the Almagest influenced astronomy.

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