Synopsis
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1885 edition. Excerpt: ... Rivals: it is in quality, not in quantity, that they claim to supersede you. Your methods of proof, so they assert, are antiquated, and worthless as compared with the new lights. Eue. It is to that very point that I now propose to address myself: and, as we are to discuss this matter mainly with reference to the wants of beginners, we may as well limit our discussion to the subject-matter of Books I and II. Min. I am quite of that opinion. Euc. The first point to settle is whether, for purposes of teaching and examining, you desire to have one fixed logical sequence of Propositions, or would allow the use of conflicting sequences, so that one candidate in an examination might use X to prove J, and another use Y to prove X--or even that the same candidate might offer both proofs, thus 'arguing in a circle.' Min. A very eminent Modern Rival of yours, Mr. Wilson, seems to think that no such fixed sequence is really necessary. He says (in his Preface, p. 10) 'Geometry when treated as a science, treated inartificially, falls into a certain order from which there can be no very wide departure; and the manuals of Geometry will not differ from one another nearly so widely as the manuals of algebra or chemistry; yet it is not difficult to examine in algebra and chemistry.' Euc. Books may differ very 'widely' without differing in logical sequence--the only kind of difference which could bring two text-books into such hopeless collision that the one or the other would have to be abandoned. Let me give you a few instances of conflicting logical sequences in Geometry. Legendre proves my Prop. 5 by Prop. 8, 18 by 19, 19 by 20, 27 by 28, 29 by 32. Cuthbertson proves 37 by 41. Reynolds proves 5 by 20. When Mr. Wilson has produced similarly conflicting...
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Book Description
Euclid and His Modern Rivals is a humorously constructed, yet deeply convincing testament to the Greek mathematician's teachings of elementary geometry. Published in 1879, it appeared in the form of an intentionally unscientific dramatic comedy - Charles Dodgson's attempt to entertain his audience beyond the confining realm of mathematics.
About the Author
Lewis Carroll is a pseudonym of the Rev. Charles Lutwidge Dodgson, who was born on January 27, 1832, and died on January 14, 1898. His most famous works are Alice's Adventures in Wonderland; its sequel, Through the Looking-Glass and What Alice Found There; and The Hunting of the Snark.
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