Euclid and His Modern RivalsCourier Corporation, 1. jan. 2004 - 275 sider From the Oxford don who created 'Alice in Wonderland' comes a fanciful play that takes a hard look at late-nineteenth-century interpretations of Euclidean geometry. 'Euclid and His Modern Rivals' takes place in Hell, where the Infernal Judges are examining and passing judgment on contemporary theories of geometry. Books that reject Euclid's treatment of parallels receive first consideration (infinite series, angles made by transversals, equidistances, revolving lines, 'directions,' infinitesimals), followed by books that adopt Euclid's treatment, and ultimately, Euclid's own works. |
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Side xiv
... Proposed changes which , even if proved to be essential , would not necessitate the abandonment of Euclid's Manual : - . ( 1 ) Propositions to be omitted ; ( 2 ) 39 to be replaced by new proofs ; ( 3 ) New Propositions to be added .
... Proposed changes which , even if proved to be essential , would not necessitate the abandonment of Euclid's Manual : - . ( 1 ) Propositions to be omitted ; ( 2 ) 39 to be replaced by new proofs ; ( 3 ) New Propositions to be added .
Side xvii
... proposed as Axioms ( 1 ) Euclid's Axiom ; ( 2 ) T. Simpson's Axiom ; ( 3 ) Clavius ' وو PAGE 37 ( 4 ) Playfair's دو ( 5 ) R. Simpson's Axiom . It will be shown ( in Appendix III ) that III ) that any Theorem of Table II is sufficient ...
... proposed as Axioms ( 1 ) Euclid's Axiom ; ( 2 ) T. Simpson's Axiom ; ( 3 ) Clavius ' وو PAGE 37 ( 4 ) Playfair's دو ( 5 ) R. Simpson's Axiom . It will be shown ( in Appendix III ) that III ) that any Theorem of Table II is sufficient ...
Side xviii
... Proposal tested by comparing Euc . II . 4 , with Mr. Wilson's version of it ACT II . [ MINOS and NIEMAND . ] Manuals which reject Euclid's treatment of Parallels . SCENE I. Introductory SCENE II . Treatment of Parallels by methods ...
... Proposal tested by comparing Euc . II . 4 , with Mr. Wilson's version of it ACT II . [ MINOS and NIEMAND . ] Manuals which reject Euclid's treatment of Parallels . SCENE I. Introductory SCENE II . Treatment of Parallels by methods ...
Side 8
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Side 14
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adjacent angles alternate angles angles are equal assert assume axiomatic beginners Cambridge Mathematical Tripos Certainly coincide coincidental Lines common point Contranominal Cor Cor course curve CUTHBERTSON deduce define Definition demonstration different directions different Lines drawn edition Elementary Geometry equal angles equally inclined equidistant equidistantial Euclid examining Felix Klein figure finite Lines given Line given point grant H. S. M. COXETER HENRICI interior angles interpolated intersectional Lines Legendre magnitude Manual mathematical mean meet if produced method Modern Rivals NIEMAND reads old proof Pair of Lines parallel perpendicular Petitio Principii phrase Plane Playfair's Axiom position Pr Pr Problems Prop Propositions prove right angles right Line separate point separational Lines sepcodal side straight angle straight Line suppose Syllabus teaching text-book Th Th Theorem tion transversal treatise Triangle true Unabridged republication undisputed Axioms Wilson words writer دو وو