Archimedes

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