دانلود کتاب The works of Archimedes. Vol. 1 The two books on the sphere and the cylinder

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COVER......Page 1
HALF-TITLE......Page 3
TITLE......Page 5
COPYRIGHT......Page 6
DEDICATION......Page 7
CONTENTS......Page 9
ACKNOWLEDGMENTS......Page 11
1 goal of the translation......Page 13
2.1 Some special conventions of Greek mathematics......Page 17
2.2 Special conventions adopted in this translation......Page 18
2.3 Purpose and practices of the critical edition of diagrams......Page 20
3.1 Archimedes and his works......Page 22
3.2 The text of Archimedes......Page 25
3.3 The two books On the Sphere and the Cylinder......Page 30
TRANSLATION AND COMMENTARY......Page 41
/Introduction: general/......Page 43
Introduction: the genre......Page 45
/“Axiomatic” introduction/......Page 46
/Definitions/......Page 47
Definitions 1–4......Page 48
Postulates 1–2: about what?......Page 49
Unpacking Postulate 3......Page 50
The overall structure of Definitions 1–4, Postulates 1–4......Page 51
Postulate 5......Page 52
/1/......Page 53
The use of the axiomatic introduction......Page 54
/2/......Page 55
textual comments......Page 56
Existence and realism......Page 57
/3/......Page 58
textual comments......Page 60
/4/......Page 61
Repetition of text, and virtual mathematical actions......Page 63
/5/......Page 64
textual comments......Page 65
/6/......Page 66
Meta-mathematical interests displayed in the text......Page 68
/7/......Page 69
The “grounds” for a claim......Page 71
/8/......Page 72
textual comments......Page 73
The significance of different ways of naming objects......Page 74
/9/......Page 75
Ambiguities and their implication for the author/audience attitude......Page 78
/10/......Page 79
What is the sequence of actions inside a construction?......Page 82
The role of the axiomatic discussion......Page 83
/11/......Page 84
textual comments......Page 86
Operations on phrases as a tool for argumentation......Page 88
/12/......Page 89
textual comments......Page 91
The operation of “imagination”......Page 92
/Sequel to sequence 9–12/......Page 93
textual and general comments......Page 94
/13/......Page 95
textual comments......Page 99
Arguments based on division of logical space......Page 100
Relations between parts of text......Page 101
Some notes on operations with ratios......Page 102
/14/......Page 103
Different layers of imagination......Page 106
/15/......Page 107
Reference to Proposition 14......Page 108
/16/......Page 109
textual comments......Page 111
Non-pictorial diagrams......Page 112
/Interlude recalling elementary results/......Page 113
general comments......Page 114
/17/......Page 115
Underspecification of diagram by text......Page 116
/18/......Page 117
textual comments......Page 118
Overall structure of transformations of proportions......Page 119
/19/......Page 120
textual comments......Page 121
Relations between parts of the proposition......Page 122
/20/......Page 123
Formulaic expression and definitions......Page 124
/21/......Page 125
textual comments......Page 126
The strange nature of the proposition......Page 127
/22/......Page 128
Other aspects of the brevity of the proof......Page 129
/23/......Page 130
textual and general comments......Page 131
The internal structure of the proposition......Page 132
/24/......Page 134
The absence of algebraic and logical conventions......Page 136
/25/......Page 137
On “that is,” and the nature of the proposition......Page 139
/26/......Page 140
textual comments......Page 141
A move to a more general space......Page 142
/27/......Page 143
The creativity of formulaic language......Page 144
/28/......Page 145
Proposition I.23 gave rise to a locally established form......Page 146
Quotations and other textual procedures......Page 147
/30/......Page 148
Reduced setting-out......Page 149
/Corollary/......Page 150
/32/......Page 151
A fully fledged proposition, finally......Page 154
Letters used as indices......Page 155
/33/......Page 156
A sense of accomplishment......Page 158
Elegance of expression......Page 159
/34/......Page 160
/Corollary/......Page 162
Why state the result in a corollary?......Page 163
Various ways of “taking as obvious”......Page 164
/35/......Page 165
textual comments......Page 166
The nature of the final “chapter 6”......Page 167
Ambiguous language, its significance and its practical resolution......Page 168
textual and general comments......Page 169
/37/......Page 170
Another look at the history of “the obvious”......Page 171
/38/......Page 172
/Corollary/......Page 173
Archimedean carelessness as regards detail......Page 174
/39/......Page 175
textual comments......Page 176
Backwards-looking structure and its significance for how the proposition is to be read......Page 177
/40/......Page 178
/Corollary 2/......Page 179
textual comments......Page 180
Limits on visualization......Page 181
/41/......Page 182
A sketchy proposition, with objects sketchily described......Page 185
/42/......Page 186
Meager diagrams, rich verbal formulations......Page 188
/43/......Page 189
Relations between propositions become even more direct......Page 190
/44/......Page 191
textual comments......Page 194
Haste......Page 195
/Introduction/......Page 197
Practices of mathematical communication......Page 198
/1/......Page 199
Does “analysis” find solutions?......Page 202
/2/......Page 203
/Corollary/......Page 206
textual comments......Page 208
The two cones and the generality of the argument......Page 209
The operation of “imagination:” the border between the conceptual and spatial......Page 210
/3/......Page 211
textual comments......Page 212
The strange nature of “being given”......Page 213
/4/......Page 214
textual comments......Page 218
The use of interim results......Page 219
/5/......Page 220
Relying on informal intuitions......Page 224
/6/......Page 225
textual comments......Page 228
The relation between analysis and synthesis......Page 229
/7/......Page 230
textual comments......Page 232
/8/......Page 233
textual comments......Page 236
“Exponent” ratios......Page 237
Archimedes takes off......Page 238
/In another way/......Page 239
textual comments......Page 242
Structural properties of the proof......Page 243
Extensions of plane geometry to solid figures......Page 244
/9/......Page 245
The double figure, a preliminary discussion......Page 248
Textual and mathematical problems other than the double figure......Page 249
How can the proof be seen to apply to both cases?......Page 251
conclusion......Page 253
TO BOOK 1......Page 255
To the definitions......Page 256
To Theorem 2......Page 262
To 3......Page 264
To 6......Page 266
To 8......Page 267
To 9......Page 268
To 10......Page 269
To 13......Page 270
To 14......Page 272
To 23......Page 274
To 32......Page 275
To 34......Page 277
To 39......Page 278
To 41......Page 279
To 42......Page 280
To 44......Page 281
EUTOCIUS’ COMMENTARY TO ON THE SPHERE AND THE CYLINDER II......Page 282
To the synthesis of the 1st......Page 284
As Plato......Page 285
As Hero in the Mechanical Introduction and in the Construction of Missile-Throwing Machines......Page 287
As Philo the Byzantine......Page 289
As Apollonius......Page 290
As Diocles in On Burning Mirrors......Page 291
As Pappus in the Introduction to Mechanics......Page 293
As Sporus......Page 297
As Menaechmus......Page 298
In another way......Page 300
Archytas’ solution, according to Eudemus’ History......Page 302
As Eratosthenes......Page 306
As Nicomedes in On Conchoid Lines......Page 310
To the second theorem......Page 318
To 3......Page 321
To 4......Page 322
As Dionysodorus......Page 342
As Diocles in On Burning Mirrors......Page 346
To the synthesis of 4......Page 355
To 5......Page 357
To the synthesis of 5......Page 359
To the synthesis of 6......Page 360
To 7......Page 361
To 8......Page 362
Lemma to the following......Page 367
To the alternative of 8......Page 369
To 9......Page 376
BIBLIOGRAPHY......Page 381
INDEX......Page 383