Principia Mathematica, Volume 1

Front Cover
Cambridge University Press, 1927 - Mathematics - 1907 pages
Principia 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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