Read e-book online A History of Greek Mathematics, Volume II: From Aristarchus PDF

By Sir Thomas Heath

ISBN-10: 0486240746

ISBN-13: 9780486240749

"As it really is, the e-book is crucial; it has, certainly, no critical English rival." — Times Literary Supplement
"Sir Thomas Heath, most excellent English historian of the traditional distinctive sciences within the 20th century." — Prof. W. H. Stahl
"Indeed, considering the fact that a lot of Greek is arithmetic, it really is debatable that, if one could comprehend the Greek genius absolutely, it might be an outstanding plan firstly their geometry."
The viewpoint that enabled Sir Thomas Heath to appreciate the Greek genius — deep intimacy with languages, literatures, philosophy, and all of the sciences — introduced him probably in the direction of his loved topics, and to their very own excellent of informed males than is usual or maybe attainable this day. Heath learn the unique texts with a severe, scrupulous eye and taken to this definitive two-volume historical past the insights of a mathematician communicated with the readability of classically taught English.
"Of the entire manifestations of the Greek genius none is extra awesome or even awe-inspiring than that that's published by means of the heritage of Greek mathematics." Heath documents that heritage with the scholarly comprehension and comprehensiveness that marks this paintings as evidently vintage now as while it first seemed in 1921. The linkage and solidarity of arithmetic and philosophy recommend the description for the full heritage. Heath covers in series Greek numerical notation, Pythagorean mathematics, Thales and Pythagorean geometry, Zeno, Plato, Euclid, Aristarchus, Archimedes, Apollonius, Hipparchus and trigonometry, Ptolemy, Heron, Pappus, Diophantus of Alexandria and the algebra. Interspersed are sections dedicated to the background and research of well-known difficulties: squaring the circle, attitude trisection, duplication of the dice, and an appendix on Archimedes's evidence of the subtangent estate of a spiral. The assurance is far and wide thorough and really apt; yet Heath isn't content material with undeniable exposition: it's a illness within the present histories that, whereas they country mostly the contents of, and the most propositions proved in, the good treatises of Archimedes and Apollonius, they make little try to describe the method in which the consequences are acquired. i've got for this reason taken pains, within the most important instances, to teach the process the argument in enough element to permit a reliable mathematician to understand the strategy used and to use it, if he'll, to different related investigations.
Mathematicians, then, will have a good time to discover Heath again in print and obtainable after a long time. Historians of Greek tradition and technology can renew acquaintance with a typical reference; readers in most cases will locate, rather within the lively discourses on Euclid and Archimedes, precisely what Heath capacity by means of impressive and awe-inspiring.

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Additional info for A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus

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2 None of the champions of Heraclides have been able to meet this positive statement. But we have conclusive evidence in favour of the claim of Aristarchus; indeed, ancient testimony is unanimous on the point. Not only does Plutarch tell us that Cleanthes held that Aristarchus ought to be indicted for the impiety of ‘putting the Hearth of the Universe in motion’2 ; we have the best possible testimony in the precise statement of a great contemporary, Archimedes. In the Sand-reckoner Archimedes has this passage.

Solution of the of Archimedes, On Spirals, Prop. 8, by means of conics Book V. Preface on the sagacity of Bees Section (1). Isoperimetry after Zenodorus Section (2). Comparison of volumes of solids having their surfaces equal. Case of sphere Section (3). Digression on semi-regular solids of Archimedes Section (4). Propositions on the lines of Archimedes, On the Sphere and Cylinder Section (5). Of regular solids with surfaces equal, that is greater which has more faces Book VI Problem arising out of Euclid’s Optics Book VII.

4 (i) Archimedes’s own solution (ii) Dionysodorus’s solution (iii) Diocles’s solution of original problem Measurement of a Circle On Conoids and Spheroids On Spirals On Plane Equilibriums, I, II The Sand-reckoner (Psammites or Arenarius) The Quadmture of the Parabola On Floating Bodies, I, II The problem of the crown Other works (α) The Cattle-Problem (β) On semi-regular polyhedra (γ) The Liber Assumptorum (δ) Formula for area of triangle Eratosthenes Measurement of the Earth XIV. CONIC SECTIONS.

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A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus by Sir Thomas Heath


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