# Book:Alfred North Whitehead/Principia Mathematica/Volume 3

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## Alfred North Whitehead and Bertrand Russell:

## Alfred North Whitehead and Bertrand Russell: *Principia Mathematica, Volume $\text { 3 }$*

Published $1913$, **Merchant Books**

- ISBN 978-1-60386-194-7.

### Subject Matter

### Contents

- PREFACE TO VOLUME III

- PART V. SERIES (continued).

- Section D. Well-ordered Series

- $*$250. Elementary properties of well-ordered series
- $*$251. Ordinal numbers
- $*$252. Segments of well-ordered series
- $*$253. Sectional relations of well-ordered series
- $*$254. Greater and less among well-ordered series
- $*$255. Greater and less among ordinal numbers
- $*$256. The series of ordinals
- $*$257. The transfinite ancestral relation
- $*$258. Zermelo's theorem
- $*$259. Inductively defined correlations

- Section E. Finite and Infinite Series and Ordinals

- $*$260. On finite intervals in a series
- $*$261. Finite and infinite series
- $*$262. Finite ordinals
- $*$263. Progressions
- $*$264. Derivatives of well-ordered series
- $*$265. The series of alephs

- Section F. Compact Series, Rational Series, and Continuous Series

- $*$270. Compact series
- $*$271. Median classes in series
- $*$272. Similarity of position
- $*$273. Rational series
- $*$274. On series of finite sub-classes of a series
- $*$275. Continuous series
- $*$276. On series of infinite sub-classes of a series

- PART VI. QUANTITY
- Summary of Part VI

- Section A. Generalization of Number

- $*$300. Positive and negative integers, and numerical relations
- $*$301. Numerically defined powers of relations
- $*$302. On relative primes
- $*$303. Ratios
- $*$304. The series of ratios
- $*$305. Multiplication of simple ratios
- $*$306. Addition of simple ratios
- $*$307. Generalized ratios
- $*$308. Addition of generalized ratios
- $*$309. Multiplication of generalized ratios
- $*$310. The series of real numbers
- $*$311. Addition of concordant real numbers
- $*$312. Algebraic addition of real numbers
- $*$313. Multiplication of real numbers
- $*$314. Real numbers as relations

- Section B. Vector-Families

- $*$330. Elementary properties of vector-families
- $*$331. Connected families
- $*$332. On the representative of a relation in a family
- $*$333. Open families
- $*$334. Serial families
- $*$335. Initial families
- $*$336. The series of vectors
- $*$337. Multiples and submultiples of vectors

- Section C. Measurement

- $*$350. Ratios of members of a family
- $*$351. Submultipliable families
- $*$352. Rational multiples of a given vector
- $*$353. Rational families
- $*$354. Rational nets
- $*$356. Measurement by real numbers
- $*$359. Existence-theorems for vector-families

- Section D. Cyclic Families

- $*$370. Elementary properties of cyclic families
- $*$371. The series of vectors
- $*$372. Integral sections of the series of vectors
- $*$373. Submultiples of identity
- $*$374. Principal submultiples
- $*$375. Principal ratios