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Archimedes

著者: E J Dijksterhuis
出版商: Princeton, N.J. : Princeton University Press, ©1987.
版本/格式:   图书 : 英语查看所有的版本和格式
数据库:WorldCat
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提及的人: Archimedes.; Archimède.; Archimedes.; Archimedes.
文件类型:
所有的著者/提供者: E J Dijksterhuis
ISBN: 0691084211 9780691084213 0691024006 9780691024004
OCLC号码: 15629509
注意: Includes index.
描述: 457 p. : ill. ; 25 cm.
其他题名: Archimedes.
责任: by E.J. Dijksterhuis ; translated by C. Dikshoorn ; with a new bibliographic essay by Wilbur R. Knorr.
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Preface........................................................ 7 Chapter I. The Life of Archimedes................................ 9 1. The Personality. ........................................... 9 2. ΔΟΣ ΜΟΙ ΠΟΥ ΣΤΩ . . . (Give me a place to stand on ...)....... 14 3. The Wreath Problem........................................ 18 4. Archimedes as a Mechanical Engineer. ........................ 21 α. The Cochlias............................................. 21 β. The Planetarium......................................... 23 γ. The Hydraulic Organ..................................... 25 5. The Defence of Syracuse..................................... 26 6. The Death of Archimedes.................................... 30 Chapter II. The Works of Archimedes. Manuscripts and Editions.... 33 Chapter III. The Elements of the Work of Archimedes............... 49 0.1 Notations................................................. 51 0.2 Fundamental Concepts of the Application of Areas............. 51 0.3 Fundamental Concepts of the Theory of Proportions. .......... 52 0.4 Main Operations of the Theory of Proportions................. 52 0.5 Lemma of Euclid.......................................... 54 0.6 Numerical System. ........................................ 55 1. Generation and General Properties of Conies. ................. 55 2. The Orthotome............................................ 69 3. The Oxytome. ............................................ 83 4. The Amblytome.........................................:. 94 5. Oxytome and Amblytome.................................. 97 6. Cones, Cylinders, Conoids, and Spheroids. .................... 108 7. Lemmas from Arithmetic and Application of Areas............ 118 8. The Indirect Method for Infinite Processes.................... 130 9. Νεῦσις-Constructions....................................... 133 10. Elements of Mechanics. .................................... 140 Chapter IV. On the Sphere and Cylinder. Book I.................... 141 1. Introduction............................................... 141 2. Axiomata.................................................. 143 3. Lambanomena............................................. 145 4. Introductory Propositions (1—6).............................. 149 5. Curved Surface of Cylinder and Cone. Propositions 7—20......... 154 6. Surface and Volume of the Sphere. Propositions 21-34........... 169 7. Surface of a Segment of a Sphere and Volume of a Sector of a Sphere. Propositions 35-44 .................................. 182 Chapter V. On the Sphere and Cylinder. Book II................. 188 Chapter VI. Measurement of a Circle............................ 222 Chapter VII. On Conoids and Spheroids........................... 240 Chapter VIII. On Spirals........................................ 264 Chapter IX. On the Equilibrium of Planes or Centres of Gravity of Planes. Book I .................................... 286 Chapter X. The Method of Mechanical Theorems................. 313 Chapter XI. Quadrature of the Parabola......................... 336 Chapter XII. On the Equilibrium of Planes. Book II................ 346 Chapter XIII. The Sand-Keckoner................................ 360 Chapter XIV. Floating Bodies.................................... 373 Chapter XV. Miscellaneous...................................... 398 I. The Cattle Problem....................................... 398 II. Lemmas................................................. 401 III. Semi-Regular Polyhedra................................... 405 IV. The Stomachion.......................................... 408 V. Area of the Triangle....................................... 412 VI. Construction of a Regular Heptagon......................... 414 Bibliography................................................... 417 Archimedes after Dijksterhuis: A Guide to Recent Studies, by Wilbur R. Knorr 419 Index of Names......................................................... 452 Errata................................................................. 456

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