### Chapter XIX. The Meaning of Magnitude

- § 149. Previous views on the relation of number and quantity
- § 150. Quantity not fundamental in mathematics
- § 151. Meaning of magnitude and quantity
- § 152. Three possible theories of equality to be examined
- § 153. Equality is not identity of number of parts
- § 154. Equality is not an unanalyzable relation of quantities
- § 155. Equality is sameness of magnitude
- § 156. Every particular magnitude is simple
- § 157. The principle of abstraction
- § 158. Summary
- Note to Chapter XIX.

### Chapter XX. The Range of Quantity

### Chapter XXI. Numbers as Expressing Magnitudes: Measurement

- § 164. Definition of measurement
- § 165. Possible grounds for holding all magnitudes to be measurable
- § 166. Intrinsic measurability
- § 167. Of divisibilities
- § 168. And of distances
- § 169. Measure of distance and measure of stretch
- § 170. Distance-theories and stretch-theories of geometry
- § 171. Extensive and intensive magnitudes

### Chapter XXII. Zero

### Chapter XXIII. Infinity, the Infinitesimal, and Continuity

- § 179. Problems of infinity not specially quantitative
- § 180. Statement of the problem in regard to quantity
- § 181. Three antinomies
- § 182. Of which the antitheses depend upon an axiom of finitude
- § 183. And the use of mathematical induction
- § 184. Which are both to be rejected
- § 185. Provisional sense of continuity
- § 186. Summary of Part III

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.