Non Euclidean Geometry a Critical And Historical Study of Its Development
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Beltrami's Direct Proof of this Independence 234—236 S 9. Klein's Direct Proof of this Independence .. 236— -237 Appendix V.
The Impossibility of proving Euclid's Postulate. An Elementary Demonstration of this Impossibility founded upon the Properties of the System of Circles orthogonal to a Fixed Circle.
§ I. Introduction 238 S 2 — 7. The System of Circles passing through a Fixed Point 239 250 S 8 — 12. The System of Circles orthogonal to a Fixed Circle - 250—264 Index of Authors .. 265 Chapte...r I.
The Attempts to prove Euclid's Parallel Postulate The Greek Geometers and the Parallel Postulate, § I. Euclid (circa 330 — 275, B. C. ) calls two straight lines parallel, when they are in the same plane and being produced indefinitely in both directions, do not meet one another in either direction (Def. XXIII. ).^ He proves that two straight lines are parallel, when they form with one of their transversals equal interior alternate angles, or equal corresponding angles^ or interior angles on the same side which are supplementary.
What to read after Non Euclidean Geometry a Critical And Historical Study of Its Development?
You can find similar books in the "Read Also" column, or choose other free books by Roberto Bonola to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Beltrami's Direct Proof of this Independence 234—236 S 9. Klein's Direct Proof of this Independence .. 236— -237 Appendix V.
The Impossibility of proving Euclid's Postulate. An Elementary Demonstration of this Impossibility founded upon the Properties of the System of Circles orthogonal to a Fixed Circle.
§ I. Introduction 238 S 2 — 7. The System of Circles passing through a Fixed Point 239 250 S 8 — 12. The System of Circles orthogonal to a Fixed Circle - 250—264 Index of Authors .. 265 Chapte...r I.
The Attempts to prove Euclid's Parallel Postulate The Greek Geometers and the Parallel Postulate, § I. Euclid (circa 330 — 275, B. C. ) calls two straight lines parallel, when they are in the same plane and being produced indefinitely in both directions, do not meet one another in either direction (Def. XXIII. ).^ He proves that two straight lines are parallel, when they form with one of their transversals equal interior alternate angles, or equal corresponding angles^ or interior angles on the same side which are supplementary.
What to read after Non Euclidean Geometry a Critical And Historical Study of Its Development?
You can find similar books in the "Read Also" column, or choose other free books by Roberto Bonola to read onlineMoreLess
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