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
... proofs ; ( 3 ) New Propositions to be added . Proposed changes which , if proved to be essential , would necessitate such abandonment : - . ( 1 ) Separation of Problems and Theorems ; ( 2 ) Different treatment of Parallels . 13 . 15 ...
... proofs ; ( 3 ) New Propositions to be added . Proposed changes which , if proved to be essential , would necessitate such abandonment : - . ( 1 ) Separation of Problems and Theorems ; ( 2 ) Different treatment of Parallels . 13 . 15 ...
Side xix
... proof of Euclid's ( tacitly assumed ) Axiom , that two Lines cannot have a common segment Treatment of Angle . دو Parallels Assumption of R. Simpson's Axiom Euclid's 12th Axiom replaced by a Definition , two Axioms , and five Theorems ...
... proof of Euclid's ( tacitly assumed ) Axiom , that two Lines cannot have a common segment Treatment of Angle . دو Parallels Assumption of R. Simpson's Axiom Euclid's 12th Axiom replaced by a Definition , two Axioms , and five Theorems ...
Side xx
... proof of Playfair's Axiom discussed وو دو General survey of book : - Enormous amount of new matter Two non - sequiturs ' . An absurdity proved à la Henrici Motion ' per saltum ' denied A strange hypothesis . A new kind of open question ...
... proof of Playfair's Axiom discussed وو دو General survey of book : - Enormous amount of new matter Two non - sequiturs ' . An absurdity proved à la Henrici Motion ' per saltum ' denied A strange hypothesis . A new kind of open question ...
Side xxii
... proofs List of Euclid's Propositions which are omitted General survey of book : - A false Corollary A plethora of negatives A superfluous datum Cumbrous proof of Euc . I. 24 An unintelligible Corollary A unique Theorem of equality ' A ...
... proofs List of Euclid's Propositions which are omitted General survey of book : - A false Corollary A plethora of negatives A superfluous datum Cumbrous proof of Euc . I. 24 An unintelligible Corollary A unique Theorem of equality ' A ...
Side xxviii
... proof for Ax . 10 accepted • 217 218 • 33 219 • § 6. Omissions , alterations , and additions , suggested by Modern Rivals . Omission of I. 7 suggested 220 APPENDICES . I. ( 6 Extract from Mr. Todhunter's essay xxviii ARGUMENT OF DRAMA .
... proof for Ax . 10 accepted • 217 218 • 33 219 • § 6. Omissions , alterations , and additions , suggested by Modern Rivals . Omission of I. 7 suggested 220 APPENDICES . I. ( 6 Extract from Mr. Todhunter's essay xxviii ARGUMENT OF DRAMA .
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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