## Principia Mathematica, Volume 1Principia Mathematica was first published in 1910-13; this is the ninth impression of the second edition of 1925-7. The Principia has long been recognised as one of the intellectual landmarks of the century. It was the first book to show clearly the close relationship between mathematics and formal logic. Starting from a minimal number of axioms, Whitehead and Russell display the structure of both kinds of thought. No other book has had such an influence on the subsequent history of mathematical philosophy. |

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### Contents

WELLORDERED SERIES | 1 |

250 Elementary properties of wellordered series | 4 |

251 Ordinal numbers | 18 |

252 Segments of wellordered series | 27 |

253 Sectional relations of wellordered series | 32 |

254 Greater and less among wellordered series | 45 |

255 Greater and less among ordinal numbers | 58 |

A N | 65 |

Multiplication of simple ratios | 283 |

+306 Addition of simple ratios | 289 |

307 Generalized ratios | 296 |

Addition of generalized ratios | 299 |

309 Multiplication of generalized ratios | 309 |

310 The series of real numbers | 316 |

311 Addition of concordant real numbers | 320 |

312 Algebraic addition of real numbers | 327 |

256 The series of ordinals | 73 |

257 The transfinite ancestral relation | 81 |

258 Zermelos theorem | 96 |

259 Inductively defined correlations | 102 |

SECTION E FINITE AND INFINITE SERIES AND ORDINALS | 108 |

260 On finito intervals in a series | 109 |

261 Finite and infinite series | 118 |

B | 130 |

262 Finite ordinals | 131 |

263 Progressions | 143 |

264 Derivatives of wellordered series | 156 |

265 The series of alephs | 169 |

SECTION F COMPACT SERIES RATIONAL SERIES AND CONTINUOUS SERIES | 179 |

270 Compact series | 180 |

271 Median classes in series | 186 |

272 Similarity of position | 191 |

273 Rational series | 199 |

274 On series of finite subclasses of a series | 207 |

275 Continuous series | 218 |

276 On series of infinite subclasses of a series | 221 |

QUANTITY | 231 |

Summary of Part VI | 233 |

SECTION A GENERALIZATION OF NUMBER | 234 |

300 Positive and negative integers and numerical relations | 235 |

301 Numerically defined powers of relations | 244 |

302 On relative primes | 251 |

303 Ratios | 260 |

304 The series of ratios | 278 |

+313 Multiplication of real numbers | 333 |

314 Real numbers as relations | 336 |

SECTION B VECTORFAMILIES | 339 |

330 Elementary properties of vectorfamilies | 350 |

331 Connected families | 360 |

332 On the representative of a relation in a family | 367 |

333 Open families | 376 |

334 Serial families | 383 |

335 Initial families | 390 |

338 The series of vectors | 393 |

337 Multiples and submultiples of vectors | 403 |

MEASUREMENT | 407 |

350 Ratios of inembers of a family | 412 |

361 Submultipliable families | 418 |

352 Rational multiples of a given vector | 423 |

363 Rational families | 431 |

354 Rational nets | 436 |

356 Measurement by real numbers | 442 |

359 Existencetheorems for rectorfamilies | 452 |

CroLIC FAMILIES | 457 |

+370 Elementary properties of cyclic families | 462 |

371 The series of vectors | 466 |

+372 Integral sections of the series of vectors | 470 |

373 Subultiples of identity | 475 |

+374 Principal submultiples | 485 |

375 Principal ratios | 487 |

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### Common terms and phrases

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