Chapter V. _of Demonstration, and Necessary Truths._

§ 1. The Theorems of geometry are necessary truths only in the sense of necessarily following from hypotheses 251

2. Those hypotheses are real facts with some of their circumstances exaggerated or omitted 255

3. Some of the first principles of geometry are axioms, and these are not hypothetical 256

4. --but are experimental truths 258

5. An objection answered 261

6. Dr. Whewell's opinions on axioms examined 264