Leçons sur les applications du calcul infinitésimal à la géométrie

	Author Augustin-Louis Cauchy Title Leçons sur les applications du calcul infinitésimal à la géométrie Year of publication 1826 Subject mathematics Language French Source Library of Sobolev Institute of Mathematics SB RAS

Augustin Louis Cauchy (21 August 1789 - 23 May 1857) was a French mathematician. He started the project of formulating and proving the theorems of calculus in a rigorous manner and was thus an early pioneer of analysis. He also gave several important theorems in complex analysis and initiated the study of permutation groups. A profound mathematician, Cauchy exercised by his perspicuous and rigorous methods a great influence over his contemporaries and successors. His writings cover the entire range of mathematics and mathematical physics.

The genius of Cauchy was illustrated in his simple solution of the problem of Apollonius - describing a circle touching three given circles-which he discovered in 1805, his generalization of Euler's formula on polyhedra in 1811, and in several other elegant problems. More important is his memoir on propagation, which obtained the Grand Prix of the Institut in 1816. His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced. These are mainly embodied in his three great treatises, Cours d'analyse de l'École Polytechnique (1821); Le Calcul infinitésimal (1823); Leçons sur les applications de calcul infinitésimal; La géométrie (1826-1828); and also in his Courses of mechanics (for the École Polytechnique), Higher algebra (for the Faculté des Sciences), and of Mathematical physics (for the Collège de France).

Leçons sur les applications du calcul infinitésimal à la géométrie

Title-page

Works of A.Cauchy edited in this edition

Tome I

Title page of edition of 1826

Preface, p. v

Preface, p. vi

Contents of volume I, p. vij

Contents of volume I, p. viij

Preliminaries

Preliminaries, p. 1	p. 2	p. 3	p. 4	p. 5	p. 6
p. 7	p. 8	p. 9	p. 10	p. 11	p. 12
p. 13	p. 14	p. 15	p. 16	p. 17	p. 18
p. 19	p. 20	p. 21	p. 22	p. 23	p. 24
p. 25	p. 26	p. 27	p. 28	p. 29	p. 30
p. 31	p. 32	p. 33	p. 34

The first lecture

Lecture First, p. 35	p. 36	p. 37	p. 38	p. 39	p. 40
p. 41	p. 42	p. 43	p. 44	p. 45	p. 46

The second lecture

Lecture Second, p. 47	p. 48	p. 49	p. 50	p. 51	p. 52
p. 53	p. 54

The third lecture

Lecture Third, p. 55	p. 56	p. 57	p. 58	p. 59	p. 60
p. 61	p. 62	p. 63

The four lecture

Lecture Fourth, p. 64	p. 65	p. 66	p. 67	p. 68	p. 69
p. 70	p. 71	p. 72	p. 73	p. 74	p. 75
p. 76

The fifth lecture

Lecture Fifth, p. 77	p. 78	p. 79	p. 80	p. 81	p. 82
p. 83	p. 84	p. 85	p. 86	p. 87	p. 88

The sixth lecture

Lecture Sixth, p. 89	p. 90	p. 91	p. 92	p. 93	p. 94
p. 95	p. 96	p. 97	p. 98	p. 99	p. 100

The seventh lecture

Lecture Seventh, p. 101	p. 102	p. 103	p. 104	p. 105	p. 106
p. 107	p. 108	p. 109	p. 110	p. 111	p. 112
p. 113	p. 114	p. 115

The eighth lecture

Lecture Eighth, p. 116

p. 117

p. 118

p. 119

p. 120

The ninth lecture

Lecture Ninth, p. 121	p. 122	p. 123	p. 124	p. 125	p. 126
p. 127	p. 128	p. 129	p. 130	p. 131	p. 132
p. 133	p. 134	p. 135	p. 136	p. 137	p. 138
p. 139	p. 140	p. 141	p. 142	p. 143	p. 144

The tenth lecture

Lecture Tenth, p. 145	p. 146	p. 147	p. 148	p. 149	p. 150
p. 151	p. 152	p. 153	p. 154	p. 155

The eleventh lecture

Lecture Eleventh, p. 156	p. 157	p. 158	p. 159	p. 160	p. 161
p. 162	p. 163	p. 164	p. 165	p. 166	p. 167
p. 168	p. 169	p. 170	p. 171	p. 172	p. 173

The twelfth lecture

Lecture Twelfth, p. 174	p. 175	p. 176	p. 177	p. 178	p. 179
p. 180	p. 181	p. 182	p. 183	p. 184	p. 185
p. 186	p. 187	p. 188	p. 189

The thirteenth lecture

Lecture Thirteenth, p. 190	p. 191	p. 192	p. 193	p. 194	p. 195
p. 196	p. 197	p. 198	p. 199	p. 200	p. 201
p. 202

The fourteenth lecture

Lecture Fourteenth, p. 203	p. 204	p. 205	p. 206	p. 207	p. 208
p. 209	p. 210	p. 211	p. 212	p. 213	p. 214
p. 215	p. 216	p. 217	p. 218	p. 219	p. 220
p. 221	p. 222	p. 223	p. 224	p. 225	p. 226
p. 227	p. 228	p. 229	p. 230	p. 231	p. 232

The fifteenth lecture

Lecture Fifteenth, p. 233	p. 234	p. 235	p. 236	p. 237	p. 238
p. 239	p. 240	p. 241	p. 242	p. 243	p. 244
p. 245	p. 246	p. 247	p. 248	p. 249	p. 250
p. 251	p. 252	p. 253	p. 254	p. 255	p. 256
p. 257	p. 258	p. 259	p. 260	p. 261	p. 262
p. 263	p. 264	p. 265	p. 266	p. 267	p. 268
p. 269	p. 270	p. 271	p. 272	p. 273	p. 274
p. 275

The sixteenth lecture

Lecture Sixteenth, p. 276	p. 277	p. 278	p. 279	p. 280	p. 281
p. 282	p. 283	p. 284	p. 285	p. 286	p. 287
p. 288	p. 289	p. 290

The seventeenth lecture

Lecture Seventeenth, p. 291	p. 292	p. 293	p. 294	p. 295	p. 296
p. 297	p. 298	p. 299	p. 300	p. 301	p. 302
p. 303	p. 304	p. 305	p. 306

The eighteenth lecture

Lecture Eighteenth, p. 307	p. 308	p. 309	p. 310	p. 311	p. 312
p. 313	p. 314	p. 315	p. 316	p. 317	p. 318
p. 319	p. 320	p. 321	p. 322	p. 323	p. 324
p. 325	p. 326	p. 327	p. 328

The nineteenth lecture

Lecture Ninetieth, p. 329	p. 330	p. 331	p. 332	p. 333	p. 334
p. 335	p. 336	p. 337	p. 338	p. 339	p. 340
p. 342	p. 343	p. 344	p. 345	p. 346	p. 347
p. 348	p. 349	p. 350	p. 351	p. 352	p. 353
p. 354

The twentieth lecture

Lecture Twentieth, p. 355	p. 356	p. 357	p. 358	p. 359	p. 360
p. 361	p. 362	p. 363	p. 364	p. 365

The twenty-first lecture

Lecture Twenty First, p. 366	p. 367	p. 368	p. 369	p. 370	p. 371
p. 372	p. 373	p. 374	p. 375	p. 376	p. 377
p. 378	p. 379	p. 380	p. 381	p. 382	p. 383

The twenty-second lecture

Lecture Twenty Second, p. 384	p. 385	p. 386	p. 387	p. 388	p. 389
p. 390	p. 391	p. 392	p. 393

Errata

Errata, p. 394	p. 395	p. 396	p. 397	p. 398	p. 399
p. 400

Tome II

Volume II. Title page

Works of A.Cauchy edited in this edition

Title page of edition of 1828, Volume II

Table of contents

The first lecture (tome II)

Lecture First, p. 1	p. 2	p. 3	p. 4	p. 5	p. 6
p. 7	p. 8	p. 9	p. 10	p. 11	p. 12
p. 13	p. 14	p. 15	p. 16	p. 17	p. 18
p. 19	p. 20	p. 21	p. 22	p. 23	p. 24
p. 25

The second lecture (tome II)

Lecture Second, p. 26	p. 27	p. 28	p. 29	p. 30	p. 31
p. 32	p. 33	p. 34	p. 35	p. 36	p. 37
p. 38	p. 39	p. 40	p. 41	p. 42	p. 43
p. 44	p. 45	p. 46	p. 47	p. 48	p. 49
p. 50	p. 51	p. 52	p. 53

The third lecture (tome II)

Lecture Third, p. 54	p. 55	p. 56	p. 57	p. 58	p. 59
p. 60	p. 61	p. 62	p. 63	p. 64	p. 65
p. 66	p. 67	p. 68	p. 69	p. 70	p. 71
p. 72	p. 73	p. 74	p. 75	p. 76	p. 77
p. 78	p. 79	p. 80	p. 81	p. 82	p. 83
p. 84	p. 85	p. 86	p. 87	p. 88	p. 89
p. 90

The eleventh lecture (tome II)

Lecture Eleventh, p. 91	p. 92	p. 93	p. 94	p. 95	p. 96
p. 97	p. 98	p. 99	p. 100	p. 101	p. 102
p. 103	p. 104	p. 105	p. 106	p. 107	p. 108
p. 109	p. 110	p. 111	p. 112	p. 113	p. 114
p. 115	p. 116	p. 117	p. 118	p. 119	p. 120
p. 121	p. 122