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

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By Thomas Heath

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

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Astronomy offers, no longer with reasons, yet with evidence; as a result it usually proceeds by means of hypotheses, mentioning yes expedients wherein the phenomena will be stored. for instance, why do the sunlight, the moon and the planets seem to stream irregularly ? to provide an explanation for the saw evidence we could suppose, for example, that the orbits are eccentric circles or that the celebs describe epicycles on a sporting circle; after which we need to cross farther and look at alternative routes during which it's attainable for the phenomena to be led to. ‘Hence we really discover a yes individual [Heraclides of Pontus] coming fomvard and announcing that, even at the assumption that the earth strikes in a undeniable manner, whereas the solar is in a undeniable manner at leisure, the obvious irregularity on the subject of the sunlight should be stored. ’ Philological issues in addition to the opposite notices which we own approximately Heraclides make it essentially yes that ‘Heraclides of Pontus’ is an interpolation and that Geminus acknowledged τις easily, ‘a yes person’, with none identify, notwithstanding he no doubt intended Aristarchus of Samos. 33 Simplicius says that Alexander quoted this extract from the epitome of the ξήγησις via Geminus. because the unique paintings used to be it seems that made the topic of an abridgement, we assemble that it should have been of substantial scope. it's a query even if ξήγησις skill ‘commentary’ or ‘exposition’; i'm prone to imagine that the latter interpretation is the right kind one, and that Geminus reproduced Posidonius’s paintings in its entirety with elucidations and reviews; this turns out to me to be steered through the phrases additional by way of Simplicius instantly after the extract ‘this is the account given by means of Geminus, or Posidonius in Geminus, of the adaptation among physics and astronomy’, which turns out to indicate that Geminus in our passage reproduced Posidonius textually. ‘Introduction to the Phaenomena’ attributed to Geminus. There is still the treatise, purporting to be through Geminus, which has come all the way down to us below the name Γєμίνου єσαγωγєς τ Φαινόμєνα. 34 What, if any, is the relation of this paintings to the exposition of Posidonius’s Meteorologica or the epitome. of it simply pointed out ? One view is that the unique Isagoge of Geminus and the ξήγησις of Posidonius have been one and an analogous paintings, notwithstanding the Isagoge as we've it's not by means of Geminus, yet via an unknown compiler. The objections to this are, first, that it doesn't include the extract given by way of Simplicius, which might have are available in usefully firstly of an advent to Astronomy, nor the opposite extract given by way of Alexander from Geminus and on the subject of the rainbow which turns out likewise to have come from the ξήγησις35; secondly, that it doesn't wherever point out the identify of Posidonius (not, might be, an insuperable objection); and, thirdly, that there are perspectives expressed in it which aren't these held via Posidonius yet opposite to them. back, the author understands the way to provide a valid judgement as among divergent perspectives, writes in sturdy sort by and large, and will hardly ever were the mere compiler of extracts from Posidonius which the view in query assumes him to be.

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