A History of Greek Mathematics, Volume 2: From Aristarchus to Diophantus (Dover Books on Mathematics)
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Volume 2 of an authoritative two-volume set that covers the essentials of mathematics and features every landmark innovation and every important figure, including Euclid, Apollonius, and others.
= AD2 : DC, whether AB be greater or less than AD, then [E in the figure is a point such that ED = CD.] The algebraical equivalent is: If then ac = b 2. These lemmas are subsidiary to the next (props. 39, 40), being used in the first proofs of them. props. 39, 40 prove the following: If ACDEB be a straight line, and if then if, again, then If AB = a, BC = b, BD = c, BE = d, the algebraic equivalents are the following. VII. props. 41, 42, 43. If AD . DC = BD . DE, suppose that in
Cylinder are stated in the preface. Serenus observes that many persons who were students of geometry were under the erroneous impression that the oblique section of a cylinder was different from the oblique section of a cone known as an ellipse, whereas it is of course the same curve. Hence he thinks it necessary to establish, by a regular geometrical proof, that the said oblique sections cutting all the generators are equally ellipses whether they are sections of a cylinder or of a cone. He
point and centre to the sphere in which the moon moves’), and is a method of saying that the‘universe’ is infinitely great in relation not merely to the size of the sun but evento the orbit of the earth in its revolution about it; the assumption was necessary to Aristarchus in order that he might not have to take account of parallax.) Plutarch, in the passage referred to above, also makes it clear that Aristarchus followed Heraclides in attributing to the earth the daily rotation about its axis.
r = a + b sec θ. According to Eutocius, Nicomedes prided himself inordinately on his discovery of this curve, contrasting it with Eratosthenes’s mechanism for finding any number of mean proportionals, to which he objected formally and at length on the ground that it was impracticable and entirely outside the spirit of geometry.2 Nicomedes is associated by Pappus with Dinostratus, the brother of Menaechmus, and others as having applied to the squaring of the circle the curve invented by Hippias
setting of certain stars, and states that the predictions of weather (πισημασίαι) in calendars (παραπήγματα) are only derived from experience and observation, and have no scientific value. Chapter 18 is on the ξєλιγμός, the shortest period which contains an integral number of synodic months, of days, and of anomalistic revolutions of the moon; this period is three times the Chaldaean period of 223 lunations used for predicting eclipses. The end of the chapter deals with the maximum, mean, and