Download E-books A History of Greek Mathematics, Volume 2: From Aristarchus to Diophantus (Dover Books on Mathematics) PDF

By Thomas Heath

Volume 2 of an authoritative two-volume set that covers the necessities of arithmetic and lines each landmark innovation and every vital determine, including Euclid, Apollonius, and others.

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C. ); ‘some of the Pythagoreans’ are for this reason the later Pythagoreans (of whom Nicomachus used to be one); the opposite order, moon, solar, Venus, Mercury, Mars, Jupiter, Saturn, was once that of Plato and the early Pythagoreans. In chap. 15 (p. 138sq. ) Theon prices verses of Alexander ‘the Aetolian’ (not fairly the ‘Aetolian’, yet Alexander of Ephesus, a modern of Cicero, or most likely Alexander of Miletus, as Chalcidius calls him) assigning to every of the planets (including the earth, although desk bound) with the sunlight and moon and the sector of the mounted stars one be aware, the periods among the notes being so prepared as to deliver the 9 into an octave, while with Eratosthenes and Plato the earth was once excluded, and the 8 notes of the octachord have been assigned to the seven heavenly our bodies and the field of the mounted stars. the total of this passage (chaps. 15 to sixteen, pp. 138–47) is not any doubt meant because the promised account of the ‘harmony within the universe’, even supposing on the very finish of the paintings Theon means that this has nonetheless to be defined at the foundation of Thrasyllus’s exposition mixed with what he has already given himself. the subsequent chapters take care of the ahead events, the desk bound issues, and the retrogradations, as they respectively seem to us, of the 5 planets, and the ‘saving of the phenomena’ by way of the choice hypotheses of eccentric circles and epicycles (chaps. 17–30, pp. 147–78). those hypotheses are defined, and the id of the movement produced via the 2 is proven by way of Adrastus relating to the sunlight (chaps. 26, 27, pp. 166–72). The facts is brought with the fascinating comment that ‘Hipparchus says it's helpful of research by means of mathematicians why, on hypotheses so varied from each other, that of eccentric circles and that of concentric circles with epicycles, an analogous effects seem to keep on with. ’ it isn't to be intended that the evidence of the id might be except effortless to a mathematician like Hipparchus; the comment might be basically means that the 2 hypotheses have been found fairly independently, and it used to be no longer until eventually later that the impact was once found to be a similar, while in fact the actual fact would appear to be curious and a mathematical facts might instantly be sought. one other passage (p. 188) says that Hipparchus most well liked the speculation of the epicycle, as being his personal. If which means Hipparchus claimed to have found the epicycle-hypothesis, it needs to be a misapprehension; for Apollonius already understood the idea of epicycles in all its generality. in accordance with Theon, the epicycle-hypothesis is extra ‘according to nature’; however it was once possibly most well liked since it was once acceptable to the entire planets, while the eccentric-hypothesis, while initially advised, utilized simply to the 3 better planets; with a purpose to make it follow to the inferior planets it is important to consider the circle defined through the centre of the eccentric to be more than the eccentric circle itself, which extension of the speculation, although recognized to Hipparchus, doesn't appear to have happened to Apollonius.

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