Download A History of Greek Mathematics, Volume II: From Aristarchus by Sir Thomas Heath PDF

By Sir Thomas Heath

ISBN-10: 0486240746

ISBN-13: 9780486240749

"As it truly is, the e-book is integral; it has, certainly, no severe English rival." — Times Literary Supplement
"Sir Thomas Heath, best English historian of the traditional targeted sciences within the 20th century." — Prof. W. H. Stahl
"Indeed, considering loads of Greek is arithmetic, it's controversial that, if one could comprehend the Greek genius absolutely, it'd be a great plan to start with their geometry."
The point of view that enabled Sir Thomas Heath to appreciate the Greek genius — deep intimacy with languages, literatures, philosophy, and the entire sciences — introduced him probably towards his loved matters, and to their very own perfect of expert males than is usual or perhaps attainable this day. Heath learn the unique texts with a serious, scrupulous eye and taken to this definitive two-volume background the insights of a mathematician communicated with the readability of classically taught English.
"Of all of the manifestations of the Greek genius none is extra striking or even awe-inspiring than that that is printed via the heritage of Greek mathematics." Heath files that historical past with the scholarly comprehension and comprehensiveness that marks this paintings as evidently vintage now as whilst it first seemed in 1921. The linkage and cohesion of arithmetic and philosophy recommend the description for the complete historical past. 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 heritage and research of recognized difficulties: squaring the circle, attitude trisection, duplication of the dice, and an appendix on Archimedes's facts of the subtangent estate of a spiral. The insurance is all over thorough and sensible; yet Heath isn't really content material with simple exposition: it's a illness within the current histories that, whereas they kingdom usually the contents of, and the most propositions proved in, the nice treatises of Archimedes and Apollonius, they make little try and describe the method during which the implications are bought. i've got hence taken pains, within the most important circumstances, to teach the process the argument in adequate aspect to let a reliable mathematician to know the tactic used and to use it, if he'll, to different comparable 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 customary reference; readers usually will locate, relatively within the full of life discourses on Euclid and Archimedes, precisely what Heath potential by way 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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New York This Dover edition, first published in 1981, is an unabridged republication of the work first published in 1921 by the Clarendon Press, Oxford. For this edition the errata of the first edition have been corrected. International Standard Book Number: 0–486-24074–6 Library of Congress Catalog Card Number: 80–70126 Manufactured in the United States of America Dover Publications, Inc. 31 East 2nd Street, Mineola, N. Y. 11501 CONTENTS OF VOL II XII. ARISTARCHUS OF SAMOS XIII. 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.

APOLLONIUS OF PERGA The text of the Conics Apollonius’s own account of the Conics Extent of claim to originality Great generality of treatment Analysis of the Conics Book I Conics obtained in the most general way from oblique cone New names, ‘parabola’ ‘ellipse’ ‘hyperbola’ Fundamental properties equivalent to Cartesian equations Transition to new diameter and tangent at its extremity First appearance of principal axes Book II Book III Book IV Book V Normals as maxima and minima Number of normals from a point Propositions leading immediately to determination of evoluta of conic Construction of normals Book VI Book VII Other works by Apollenius (α) On the Cutting off of a Ratio (), two Books (β) On the Cutting-off of an Area (), two Books (γ) On Detemninate Section (), two Books (δ) On Contacts or Tangencies (), two Books (ε) Plane Loci, two Books (ζ) (Vergings or Inclinations), two Books (η) Comparison of dodecahedron with icosahedron (θ) General Treatise (ι) On the Cochlias (κ) On Unordered Irrationals (λ) On the Burning-mirror (μ) Astronomy XV.

The main results obtained in Book I are shortly stated in a prefatory letter to Dositheus. Archimedes tells us that they are new, and that he is now publishing them for the first time, in order that mathematicians may be able to examine the proofs and judge of their value. The results are (1) that the surface of a sphere is four times that of a great circle of the sphere, (2) that the surface of any segment of a sphere is equal to a circle the radius of which is equal to the straight line drawn from the vertex of the segment to a point on the circumference of the base, (3) that the volume of a cylinder circumscribing a sphere and with height equal to the diameter of the sphere is of the volume of the sphere, (4) that the surface of the circumscribing cylinder including its bases is also of the surface of the sphere.

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