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News: Plato's Atlantis: Fact, Fiction or Prophecy?
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Author Topic: THE RENAISSANCE  (Read 4733 times)
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« Reply #105 on: October 17, 2008, 08:58:50 pm »

Again, it is Euclid, rather than Pythagoras, who "made a much more worthy foundation" of arithmetic because Euclid's writings actually survive, and thus form a part of the arithmetical tradition that has, in Regiomontanus's view, existed continuously until his own time (Giovanni Bianchini was a correspondent of Regiomontanus's). Boethius, Jordanus, and Jean de Murs (author of the Quadripartitum numerorum) all deserve mention in a history of arithmetic because their writings were widely read. The same pattern is apparent in Regiomontanus's history of optics, where he cites Greek works by Euclid and Archimedes, the Arabic author Alhazen, and Latin texts by Witelo and Roger Bacon, all of whom were important authorities in Regiomontanus's time.41 Diophantus's Arithmetic, which was not widely read (this was the first public mention of the text, and it would not be translated into Latin until the next century) is an interesting case, because it seems to be an example of Regiomontanus trying to establish the same kind of pattern for algebra, which until then had been considered an Arabic art.42 [End Page 55]

Paul Lawrence Rose has noted the great emphasis that Regiomontanus places on the translation and transmission of mathematical knowledge, which contribute to a vision of mathematics as existing in a continuous tradition stretching back to antiquity.43 This is true, but it should be noted that given the distinction that Regiomontanus makes between the origins of the mathematical arts and their true founders—men like Euclid and Ptolemy, whose works still survive and are used—the real continuity in the mathematical disciplines is between the earliest mathematical texts and the mathematics of the fifteenth century.   
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