The Principles of Mathematics (1903)

Chapter XLVII. Metrical Geometry
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Chapter XLVII. Metrical Geometry

Table of Contents

  1. § 388. Metrical geometry presupposes projective or descriptive geometry
  2. § 389. Errors in Euclid
  3. § 390. Superposition is not a valid method
  4. § 391. Errors in Euclid (continued)
  5. § 392. Axioms of distance
  6. § 393. Stretches
  7. § 394. Order as resulting from distance alone
  8. § 395. Geometries which derive the straight line from distance
  9. § 396. In most spaces, magnitude of divisibility can be used instead of distance
  10. § 397. Meaning of magnitude of divisibility
  11. § 398. Difficulty of making distance independent of stretch
  12. § 399. Theoretical meaning of measurement
  13. § 400. Definition of angle
  14. § 401. Axioms concerning angles
  15. § 402. An angle is a stretch of rays, not a class of points
  16. § 403. Areas and volumes
  17. § 404. Right and left
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