Euclid and His Modern Rivals

by Lewis Carroll

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...

Genres: Mathematics, Nonfiction, Education, Science

58 pages, Paperback

First published January 1, 1969

About the author

The Reverend Charles Lutwidge Dodgson, better known by the pen name Lewis Carroll, was an English author, mathematician, logician, Anglican clergyman and photographer.

His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass as well as the poems "The Hunting of the Snark" and "Jabberwocky", all considered to be within the genre of literary nonsense.

Oxford scholar, Church of England Deacon, University Lecturer in Mathematics and Logic, academic author of learned theses, gifted pioneer of portrait photography, colourful writer of imaginative genius and yet a shy and pedantic man, Lewis Carroll stands pre-eminent in the pantheon of inventive literary geniuses.

He also has works published under his real name.

Reviews

[Valerie · Rating 3 out of 5]

I am a huge math nerd, and even I thought this book was boring beyond belief. I plan on subjecting my Geometry class to parts of it.

[Becky Carlan · Rating 3 out of 5]

Carroll, the math teacher of great imagination has written a play containing early Greek kings petitioned by “modern” mathematicians that their treatment of Geometry is more complete than Euclid. An imaginative apologetic for Euclid, made less enjoyable by the fact I don’t know enough about Euclid and even less about Geometry. Something good to return to later!

[Sarah · Rating 3 out of 5]

Witty and cutting, a great read if you want to do a deeper dive into Carroll, or if you're interested in education theory or the history of mathematics instruction. Not a light book, and the witty amusing sections are equal to the math-heavy bits.

[Jake Cooper · Rating 2 out of 5]

It's a cute dialogue championing Euclid's Elements -- and specifically his parallel postulate -- over then-contemporary alternative treatments. Anachronistic and dryly rigorous for 21st century pleasure reading.