Euclid's Elements
by Euclid
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Book Summary Information
Author: EuclidEditor: Dana Densmore
Translator: T.L. Heath
Edition: Paperback
Audio: English (Unknown); Ancient Greek (Original Language); English (Published)
Published: 2002-08-20
ISBN: 1888009195
Number of pages: 527
Publisher: Green Lion Press
Book Reviews of Euclid's Elements
Book Review: how could this book not be the preferred text in all high schools?
Summary: 5 Stars
This work of Euclid, made highly accessible in this edition is indeed incredible. How many people know that Euclid had a thorough grasp of the concept of a tangent line to a circle comparable to that of Newton? Certainly not me. I am currently teaching from this book and reading it in detail, to my great pleasure. In Proposition III.16, Euclid essentially shows the following 4 properties are equivalent for a line L meeting a circle C at a point P:
1) L meets C nowhere else, 2) L does not "cut" C, i.e. L contains no points interior to the circle, 3) L is perpendicular to the radius of C through P, 4) L makes angle zero with the circle C at P, i.e. the greatest lower bound of the angles between L and all secants of C through P is zero,
and his proof also shows: 5) the line L is the limit of secants of C through P as the second point of intersection approaches P, i.e. for every angle containing L as a side, there is a neighborhood of P such that all secants of C through P make with L a smaller angle than the given one.
The first property, that a tangent line should meet a circle only once, is the one I was taught in high school, and it is inadequate for discussing tangents to curves more complicated than globally convex ones. The property of not cutting the curve, or of not crossing it, is adequate for describing tangents to all locally convex curves, and the property of making an angle of zero, or of being a limit of secants is of course Newton's most sophisticated definition suited for describing tangents to all curves. I am now not surprised to learn that Newton read Euclid before producing his own work. I had no idea this was in Euclid, and I have had the same eye opening experience in several other places as I read this amazing book.
Thanks to Green Lion for this lovely edition, and to Robin Hartshorne for writing his book in such a way as to force me to read Euclid. And thanks to the commenter who pointed out I could delete an earlier erroneous review of mine.
Summary of Euclid's Elements
Green Lion Press has prepared a new one-volume edition of T.L. Heath's translation of the thirteen books of Euclid's "Elements" In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Green terms.Mathematics Books
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