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Topic: Euclid and his Modern Rivals

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	Euclid or Einstein, Chapter II
		Euclid’s difficulty and that of his predecessors was that he was unable to make this proof independent of the parallel theory.
		His work on Euclid was printed in Arabic in Rome in 1594, and a Latin translation of the part concerning the fifth postulate is to be found in the second volume of Walls, which was published at Oxford in 1651.
		It is this tendency of raising the opposite assumption as a challenge to Euclid’s statements that marked Saccheri’s method, and later culminated in the Geometry of Bolyai and Lobatschewsky.
	www.reciprocalsystem.com /euclid/callahan/callah2.htm (12348 words)

	EUCLID (Site not responding. Last check: 2007-10-14)
		Euclid's Elements, an introductory work on elementary geometry and other topics, superseded other works of its kind to such an extent that they are now known only by indirect reference.
		Euclid's Elements is remarkable for the clarity with which the theorems and problems are selected and ordered.
		While Euclid is not known to have made any original discoveries, and the Elements is based on the work of his predecessors, it is assumed that some of the proofs are his own and that he is responsible for the excellent arrangement.
	www.engr.iupui.edu /~orr/webpages/cpt120/mathbios/euclid.htm (261 words)

	Euclid (c. 300 BC) : Library of Congress Citations (Site not responding. Last check: 2007-10-14)
		Title: The first six books of the elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners.
		Author: Holleman, Euclid C. Title: In-flight evaluation of the lateral handling of a four-engine jet transport during approach and landing, by Euclid C. Holleman and Glenn B. Gilyard.
		Euclidis Elementorum libri XV Graecae & Latinae Euclid.
	www.mala.bc.ca /~mcneil/cit/citlceuclid1.htm (1477 words)

	Euclid and his modern rivals by Lewis Carroll - book review
		Dedicated fans of Lewis Carroll might might be interested in reading it, as well as those interested in his psychological state, but I can't recommend it for general readership.
		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.
	www.chronon.org /Science/Euclid_and_his_modern_rivals.php (377 words)

	Charles Lutwidge Dodgson Biography \| World of Scientific Discovery
		His complex and, in the view of some modern scholars, controversial friendships with the children of his many friends inspired Dodgson to write under the nom de plume he had used previously as a writer of verse-- Lewis Carroll.
		Dodgson, however, did not follow the progress of modern mathematics as it was being formulated in his day, though he wrote a number of sophisticated papers on mathematical topics.
		The flaw in Euclid's reasoning would have been less a surprise to Dodgson had he been aware of the work of Georg Riemann and others who had already formulated the techniques of non-Euclidean geometry.
	www.bookrags.com /biography/charles-lutwidge-dodgson-wsd (508 words)

	Dodgson biography
		None of his mathematics books have proved of enduring importance except for Euclid and his modern rivals (1879) which is of historical interest.
		Dodgson wrote it to defend using Euclid's Elements as a means of teaching geometry.
		The book is written in the form of a play in which the ghost of Euclid returns to defend his book to modern geometers.
	www-history.mcs.st-andrews.ac.uk /Biographies/Dodgson.html (2796 words)

	[No title]
		The book “on which his reputation as a mathematician largely rests” was Euclid and His Modern Rivals (1879) (The 1911 Edition Encyclopedia website).
		The book is a comedy “about a mathematics lecturer, Minos, in whose dreams Euclid debates his original Elements with such modernizers as Legendre and J.M. Wilson and, naturally, routs the opposition,” (Dictionary of Scientific Biography, 1971, p.
		Euclid and His Modern Rivals (1879) and Charles’ mathematical puzzles proved that learning mathematics could be done in a very innovative way.
	www-math.cudenver.edu /~wcherowi/courses/m4010/s05/abeyta.doc (3061 words)

	Euclid and His Modern Rivals
		Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; classica...
		Volume 2 of three-volume set containing complete English text of all 13 books of the Elements plus critical apparatus analyzing each definition, postulate and proposition in great detail.
		Over 350 ingenious problems involving classical logic: logic expressed in symbols; syllogisms and the sorites diagrammed; logic as a game played with 2 diagrams and a set of counters.
	store.doverpublications.com /0486495663.html (310 words)

	A201/A597/I210 Introduction to Programming I (4/3 cr.) - Spring Semester 2004
		None of his math books have proved of enduring importance except for Euclid and his modern rivals (1879) which is of historical interest.
		Euclid's most famous work is his treatise on mathematics The Elements.
		The book was a compilation of knowledge that became the centre of mathematical teaching for 2000 years.
	www.cs.indiana.edu /classes/a201-dger/spr2004/notes/Fifteen.html (725 words)

	CARROLL, LEWIS. The Columbia Encyclopedia: Sixth Edition. 2000 (Site not responding. Last check: 2007-10-14)
		He did, however, lecture in mathematics at Christ Church from 1855 until 1881.
		Among his mathematical works, now almost forgotten, is Euclid and His Modern Rivals (1879).
		Carroll is chiefly remembered as the author of the famous children’s books Alice’s Adventures in Wonderland (1865) and its sequel, Through the Looking Glass (1872), both published under his pseudonym and both illustrated by Sir John Tenniel.
	www.bartleby.com /aol/65/ca/CarrollL.html (359 words)

	The Tribune...Sunday Reading
		The next year saw yet another book on geometry — The Formulae of Plane Geometry, Alice’s Adventures in Wonderland appeared only later in 1865, to be followed by An Elementary Treatise on Determinants, the book that gave birth to the famous story already mentioned.
		In it he projected his appreciation of the basic foundations on which Euclidean geometry is based, and he sought to defend that for their sheer invincible simplicity, Euclid’s axioms, definitions and methods could simply not be improved upon.
		In Pillow Problems, one of his less serious efforts, he gives an interesting collection of puzzles which require application of algebra, geometry and trigonometry but which one is expected to solve in bed itself without the help of pencil or paper.
	www.tribuneindia.com /1998/98nov22/sunday/head5.htm (651 words)

	Cordula's Web. Lewis Carroll
		He also wrote many short pieces, including Euclid and his Modern Rivals and The Alphabet Cipher.
		It has been ignored, even by the most recent and reputed of modern biographers in all but its briefest outline.
		It is undisputed that throughout his growing wealth and fame, he continued to teach at Christ Church until 1881, and that he remained in residence there until his death.
	www.cordula.ws /authors/carrolll.html (2250 words)

	Poets.org - Poetry, Poems, Bios & More - Lewis Carroll (Site not responding. Last check: 2007-10-14)
		He was successful in his study of mathematics and writing, and remained at the college after graduation to teach.
		His mathematical writings include An Elementary Treatise on Determinants (1867), Euclid and His Modern Rivals (1879), and Curiosa Mathematica (1888).
		Supplement to "Euclid and His Modern Rivals" (1885)
	www.poets.org /poet.php/prmPID/78 (548 words)

	Euclid - new and used books (Site not responding. Last check: 2007-10-14)
		The work was reconstructed by R. Archibald in 1915' (D. EUCLID: - Euclid's Book on Divisons of Figures.
		506.An attempt to reconstruct the lost book of Porisms of Euclid, which 'Chales felt were essentially the equations of curves and that many of the results utilized the concept of the cross ratio.
		Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; classical, medieval, Renaissance and modern commentators; refutations, supports, extrapolations, reinterpretations and historical notes.
	www.isbn.pl /A-Euclid (824 words)

	The Hindu : He spoke their language
		His imagination danced on the border of dreams and waking.
		He produced works like Euclid and His Modern Rivals, a masterpiece of nonsensical verse.
		He wrote on social issues favoring the education of women, invented puzzles, word games and became the foremost Victorian photographer of children.
	www.hinduonnet.com /thehindu/2000/01/29/stories/13291101.htm (661 words)

	Free Books > Tags > Rivals
		Euclid And His Modern Rivals by Lewis Carroll
		The Rivals Of Acadia: An Old Story Of The New World by H. Cheney
		The Tom Swift And His Motor-Boat, or Rivals Of Lake Carlopa by Victor Appleton
	2020ok.com /tags/rivals.htm (190 words)

	Amazon.com: Euclid and His Modern Rivals (Dover Phoenix Editions): Books: Lewis Carroll (Site not responding. Last check: 2007-10-14)
		Amazon.com: Euclid and His Modern Rivals (Dover Phoenix Editions): Books: Lewis Carroll
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		Euclid and His Modern Rivals (Dover Phoenix Editions) (Hardcover)
	www.amazon.com /Euclid-Modern-Rivals-Phoenix-Editions/dp/0486495663 (663 words)

	BookHq: Compare New & Used Books and College Textbooks Prices
		0913228222 : Euclid Beach Park Is Closed for the Season
		0935408010 : Euclid Beach Park--a Second Look, Vol.
		0815304935 : Euclid's Phaenomena:A Translation and Study of a Hellenistic Treatise in Spherical Astronomy
	www.bookhq.com /history/e_15000.html (735 words)

	Down the Rabbit Hole and Onto the Web: Lewis Carroll Etexts
		It saves time.") and memorable phrases that have enriched the lexicon ("curiouser and curiouser"; "of cabbages and kings"), the Alice books on one level are a child's fantasy, but they are also multilayered tales chockful of logic puzzles, word plays, and sly jokes and puns for adult readers.
		Born in Daresbury, Cheshire, England on January 27, 1832, Carroll attended Oxford University, where he became a professor of mathematics; he published several books on mathematics, including Euclid and His Modern Rivals, which is available as an etext.
		He originally wrote the Alice stories for a little girl named Alice Liddell, the daughter of a colleague.
	www.elliemik.com /carrolletexts.html (487 words)

	The Brindisi Bronzes: Classical Castoffs reclaimed from the Sea (Site not responding. Last check: 2007-10-14)
		Yet his imagination danced on the boundary between dreams and waking.
		His prolific mind produced learned works like Euclid and His Modern Rivals; a masterpiece of nonsensical verse, The Hunting of the Snark; poetry in Phantasmagoria and Other Poems; a novel about fairies, Sylvie and Bruno.
		He wrote on social issues, invented puzzles and word games, and became the foremost Victorian photographer of children.
	storysyn.ngs.org /yearofpub/1991/lewiscarroll.html (162 words)

	Carroll Lewis 1832 1898 Euclid and his modern rivals, by Charles L. Dodgson ... AIP Niels Bohr Library (Site not responding. Last check: 2007-10-14)
		Carroll Lewis 1832 1898 Euclid and his modern rivals, by Charles L. Dodgson...
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		Euclid and his modern rivals, by Charles L. Dodgson...
	www.aip.org /history/catalog/books/11194.html (44 words)

	Chronology of Works of Lewis Carroll (Site not responding. Last check: 2007-10-14)
		1868 - The Fifth Book of Euclid Treated Algebraically, so far as it Relates to Commensurable Magnitudes
		1873 - The Enunciations of Euclid I-VI, Together with Questions on the Definitions, Postulates, Axioms, &c.
		1885 - Supplement to Euclid and His Modern Rivals
	www.lewiscarroll.org /works.html (192 words)

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