Euclid's Elements Book One with Questions for Discussion

by Euclid, Thomas Little Heath (Translation), Dana Densmore (Editor)

Presents Book One of Euclid's Elements for students in humanities and for general readers. This treatment raises deep questions about the nature of human reason and its relation to the world. Dana Densmore's Questions for Discussion are intended as examples, to urge readers to think more carefully about what they are watching unfold, and to help them find their own questions in a genuine and exhilarating inquiry.

Genres: Mathematics

102 pages, Paperback

First published August 15, 2015

About the author

Euclid (Ancient Greek: Εὐκλείδης Eukleidēs -- "Good Glory", ca. 365-275 BC) also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Stoicheia (Elements) is a 13-volume exploration all corners of mathematics, based on the works of, inter alia, Aristotle, Eudoxus of Cnidus, Plato, Pythagoras. It is one of the most influential works in the history of mathematics, presenting the mathematical theorems and problems with great clarity, and showing their solutions concisely and logically. Thus, it came to serve as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor. He is sometimes credited with one original theory, a method of exhaustion through which the area of a circle and volume of a sphere can be calculated, but he left a much greater mark as a teacher.

Reviews

[Sarah · Rating 5 out of 5]

5 stars: I loved it. More than just math (in fact, Book One contains no numbers!), Euclid's Elements is an intersection of math and logic and beauty.

I was really struck by the beauty and elegance of the construct of geometry that Euclid so meticulously presented. As I completed the first proposition, I felt myself light up with a twinkling of insight and wisdom. It made me a little emotional.

I read somewhere that no other book except the Bible has been so widely translated and circulated. The Elements is truly an extraordinary work.

[Matt Ely · Rating 4 out of 5]

Admittedly, you don't just sit down and read Euclid. It's an activity and the joy of it comes in the doing, in the recreating.

Euclid himself was synthesizing and teaching established proofs, not innovating. Why do we expect to do any differently? The knowledge is out there. Going through this text is a process of retreading millenia of already-trod paths, seeing how wisdom is constructed from its foundations or, you might say, from its elements.

This is best done with a partner or small group. That way you can look at someone else and say "Oh my gosh, we finally drew a square!!" without sounding ridiculous.

P.s. the Heath translation from Green Lion is honestly excellent. The editing is clear and concise without tons of extraneous commentary. There are other worthwhile editions, but this is a great place to start.

[Justin · Rating 5 out of 5]

This book presents the proofs well, though it is sometimes limited by including only one diagram per proposition. This can make it hard to see the original conditions or the intermediate steps that get you to the final mess of lines. Not insurmountable, but it makes you work to understand the method of presentation rather than just the material.
Supplement with “Byrne’s Euclid” website at C82 dot net for color coded diagrams that give a different perspective - each step in the proof highlights the specific lines in the diagram.
The questions at the end of most proofs are also great jumping off points and add value not found online or in other texts.

[R. · Rating 4 out of 5]

This book shines in the questions it asks. It's not really about proofs so much as... what even is pure math? And geometry? Given that it doesn't refer to spaces within reality (or does it?), what is its purpose? Math gets so weird so quickly and I think more people would get into math if it were presented in this way.