Which translation to read of Euclid Elements

I have three recommendations based on three different motivations for reading Euclid.

1: Interest in the history and philosophy of mathematics

In this case I'm assuming you want to read Euclid in a direct translation that preserves all of the details of his original thought and presentation as much as possible.

As an analogy, if you didn't speak English but wanted to read and study a play by Shakespeare you might want a version of the play that translated everything quite literally with helpful footnotes and commentaries so that you could have the greatest chance of catching on to the kind of wordplay he uses. It could also give you context for the metaphors and references that would otherwise have gone over your head.

Go with the Dover books Heath translation in three volumes, ISBN: 978-0486600888

If you want mostly that but don't want footnotes interrupting the bliss of reading the actual text itself, then I'd recommend the Green Lion Press Heath translation. This also has much more space in the margin for you to interact with the text and write notes. I have an old copy from school that I am intimate with because the text is so clean and I was able to make it my own with my notes and reactions.

ISBN: 978-1888009194

Use the awesome web version presented by Dr. Joyce (the one you linked) for references and explanations when you actually need or want them.

Speaking of web versions, there's also these two which are not as complete as the one above, but are also high quality. I recommend them to my students when they are getting started.

http://math.furman.edu/~jpoole/euclidselements/euclid.htm http://www.themathpage.com/aBookI/plane-geometry.htm

2: Desire to learn a lot of Euclidean geometry in the most accessible and delightful way

In this case, I'm assuming you want to work through an entirely proof-based 5 postulate course in geometry that will wow you with a fireworks display of amazing and wonderful theorems without getting bogged down in inappropriate rigor (from the perspective of someone relatively new to such a course). You also want to avoid having clear ideas become obscured through archaic ways of speaking.

You do still want something that resembles 85% of what Euclid did in form and content though. And you would enjoy being teased by puzzles and exercises that extend your understanding of each proposition.

I recommend this free web textbook by Michael Augros. Each of the chapters correspond closely to the 13 books of Euclid's elements :

Search google for: Arts of Liberty Geometry course (I guess I can't post more than 2 links since I'm new to the site).

If you want to experience geometry from the perspective of discovery rather than experiencing it only from the perspective of proof, then I also strongly recommend Lockhart's Measurement

ISBN: 978-0674284388

3: Appreciation of mathematical beauty

Elegant proofs are beautiful. Many of Euclid's proofs are quite beautiful when the wordiness of the argument falls away and you get to experience that feeling of insight, that feeling of looking through the diagram like looking through a window and seeing a piece of the world on the other side, or comprehending the many steps of the argument in a single blissful moment.

If you want to smooth the way to Euclidean Nirvana with a textbook, then order a copy of Oliver Byrne's edition of the Elements where the names of figures have been replaced by colored lines and diagrams.

His graphical way of representing the proofs removes the alphabet soup phenomenon of reading a geometric proof.

There are scans of this book online for free, but I have a velvety hardcover copy of it that is reprinted and sold on Amazon. It makes a great coffee table book.