The First Six Books
of the Elements of Euclid

Some books are not read. They are seen.

Oliver Byrne's 1847 interpretation of Euclid's Elementsis one of those rare moments when mathematics becomes image. Theorems that had been taught for over two thousand years using letters and symbols were retold, by Byrne, entirely in colour: red, yellow, blue, and black. A line segment was no longer labelled “BC” — it was a yellow line. An angle was no longer expressed as a sequence of letters — it was a blue triangle.

The result remains astonishing today: the most abstract corners of mathematics translated into a visual language the eye can grasp before the mind has even caught up.

One thing must be understood about Euclid's Elements: this is the second most printed book in history. For centuries it was studied not merely as a mathematics text but as a model of correct thinking — of how to build a sound argument, how to prove something step by irrefutable step. Newton read it. Spinoza wrote his entire philosophy in geometric proof form. Lincoln studied the Elements from cover to cover before becoming a lawyer — because he wanted to learn how to demonstrate that something was true. (The Indiana Pi Bill of 1897 is a good reminder of what happens when legislators lose sight of Euclid's standard of proof.)

Euclid's Elements has never stopped inspiring visual reinvention. Henry Billingsley's 1570 English edition included paper pop-up solids that readers could fold out of the page — three-dimensional geometry rendered tactile. Byrne's question, in 1847, was different and no less radical: what if all of this could simply be shown?

Before Mondrian, Byrne. Before the Bauhaus, Byrne. A mathematics textbook from 1847 that looks like it was designed last year.

Designers speak of Byrne's book with reverence today because its red-yellow-blue-black palette, flat geometric forms, and the precision living inside apparent simplicity look uncannily like the most important design movements of the twentieth century — movements that would not arrive for another eighty years. Perhaps beauty and truth really do draw from the same source. The proof that √2 is irrational, which Euclid himself established, carries exactly that same quality: once seen, it cannot be unseen.

TASCHEN's edition presents the original in its full large format, with complete fidelity. William Rankin's introduction places Byrne in context — mathematically, visually, culturally. But again: you do not open this book for the words.

Once you are inside, you get lost. You follow a theorem: a red line begins here, a blue area intersects it, a yellow segment extends beyond. The steps are so clear, so visible, that instead of saying “I understand” you find yourself saying “I see.” And the distance between those two things is the whole point of Byrne's project.

Two thousand years of thought, given back to the eye. That is what this book does. And every time you open it at a random page and find yourself surprised that something so old can feel so immediate — you understand exactly what Byrne was after. Mathematics was always visible. It was only ever being told in the wrong language.

Oliver Byrne — The First Six Books of the Elements of Euclid
TASCHEN, 2010  ·  Original edition: London, 1847  ·  abakcus.com