The First Six Books of the Elements of Euclid is, as weird as it sounds, one book where Oliver Byrne has recreated the process of Euclid’s geometry and arithmetic into a visual representation that’s easy to grasp. It tries to reach a wider audience and make learning more accessible by getting over the complex part of recognizing visually what the demonstration procedures are — without changing them at all.
This book was actually published in 1847, and so it is part of the Public Domain now — you can grab your own copy in the format you prefer, but I actually got a hardcover copy that looks wonderful — worth paying for.
I hadn’t read Euclid’s Elements before, so this was a double surprise for me. Once you set your mind to read over the antique English and capture the idea behind the drawings (which are not always simple), you can fully concentrate into following the logic of the demonstrations, constructions and definitions. That’s all I can say about Byrne’s adaptation but on Euclid’s books per se — they are a masterpiece indeed.
The contents of the book and the demonstrations are wonderfully ordered from most basic to most complex, and they build on top of each other, one step at a time. Some demonstrations require more mental power than others, but step by step, they are perfectly described and listed one after the other. The first books cover geometry of the line and circle, then go into surfaces, all with just a few axioms and definitions, and later on it dwelves into rations, from which proportionality, inequalities and visual resemblance can be defined mathematically.
Even if geometry is not your thing, this book (books?) is a prime example on how to proceed methodically from the most basic knowledge into the complex and useful theorems of mathematical beauty.