Byrne, Six Books of Euclid: Facsimile of the famous first edition of 1847 [Hardcover]

BYRNE'S EUCLID
Oliver Byrne's 1847 printing of Euclid's Elements, in which letters and symbols are replaced with yellow, red, blue, and black diagrams, was a tremendous technical printing feat in the mid 19th century, and remains the most unique Elements ever printed. Instead of "triangle ABC is equal to triangle ACD," the triangles are drawn out, in identifying colors, with an equals sign between. Boldly-colored shapes are queerly compared on every page, making the book as surreal as it is playful. Byrne took one of the most important works of Western thought and made a book, a physical book, as unique and memorable as its intellectual content. Edward Tufte's effusive praise for the work is well-deserved.

TASCHEN EDITION
This reprinting, for the first time in 160 years (!), is a remarkable page for page copy of the original. The corrigenda page and matching errors in the text are preserved - as they of course should be - and the last page even has the "Chiswick: printed by C. Whittingham." type at the bottom. It's such an exact replica, I don't know how they did it. The originals tend to be foxed and browned, but Taschen either found a copy in incredible condition to emulate, or they recreated the whole thing from scratch (?!). The print and paper colors are near-perfectly replicated. The only noticeable difference between this and an 1847 original is the missing thickness of the diagrams. They look thick and painted in the original, while they are flat and printed in the Taschen edition - they're no longer tactile. All in all, though, mark me down as very impressed.

The binding and clamshell case look good on the shelf, and in the case is also an informative (though dry) booklet on Byrne's work.

NOT LOOKING FOR BYRNE'S...
If you're looking for a more typical copy of Euclid's Elements, I recommend Green Lion Press's edition, which contains all 13 books in a single volume.

The Byrne book is absolutely gorgeous. Over 130 years ago, Byrne had the idea of removing almost all words from Euclid, and replacing the words with visually obvious color pictures.

His demands on the publishers were tremendous. No color printing of this magnitude had been done before (in the 1800's), and they feared the high cost of the book and the high printing cost would bankrupt them.

They were right. This book destroyed them. It remained an obscure collectors item. Most mathematicians know nothing about this book, and are stunned when they see the pages.

The pages aren't viewable here, but are available at the publisher's site. Well worth a look.

Oh... and Euclid's Elements. Most famous math book in the past 2500 years. This is arguably the best presentation of this material ever made.

Euclid's Elements played important and contradictory roles in the life of Bertrand Russell. He was introduced to them in his adolescence, and was inspired ever after to pursue mathematical knowledge. His enthusiasm for Euclid did not last, however. By the time he was thirty he had come to realize that Euclid was not the logically or mathematically perfect foundation he had hoped. He thought that it was an embarrassment that Euclid, 2000 years on, should still be used as a textbook. In an essay on Euclid, Russell was to write, "His definitions do not always define, his axioms are not always indemonstrable, his demonstrations require many axioms of which he is quite unconscious." A particular problem, Russell said, is that Euclid required figures, and the figures helped an observer hurtle over logical steps that ought to have been taken into account within the proofs they illustrate. (This is to skip over the objection to Euclid's famous Fifth Postulate, which his system demands and which equally valid non-Euclidean systems disallow.) I don't know that Russell ever got sight of _The First Six Books of the Elements of Euclid in Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners_ which was published in 1847. In it, the author Oliver Byrne concentrated on the diagrams, but in a way that no one had before. With lines, solid regions, and corners of angles colored red, yellow, blue, and black, Byrne took the diagrams, colored in the important parts, and rewrote the proofs with few words or letters, just the colored parts quoted from the diagram. The original publication with colored woodcuts is a rarity now, and if you have a spare $20,000 you might be able to get one. If you do, you will have to encase it in a protective cover and you won't be leafing through it for the instruction that Byrne wanted you to enjoy. Plus, most of the original editions have turned brown (like many books of that period), so the colored diagrams, the very heart of the work, won't be as bright. These are not concerns you will have with the reprint edition from Taschen, a lovely book that whether it would have pleased Russell or not, is a triumph of graphic design.

Byrne is identified on the title page as "Surveyor of Her Majesty's Settlements in the Falkland Islands and Author of Numerous Mathematical Works." Not much else is known about him, but he presents himself as an earnest pedagogue in his introduction. "This work," he tells us, "has a greater aim than mere illustration; we do not introduce colors for the purpose of entertainment, or to amuse by certain combinations of tint and form, but to assist the mind in its researches after truth, to increase the facilities of instruction and to diffuse permanent knowledge." Byrne is careful to specify that "colour has nothing to do with the lines, angles, or magnitudes, except merely to name them." Lines, for instance, have no breadth and thus can have no color; colored lines in this volume (and black lines in others) only stand for ideal breadthless Euclidean lines. In standard mathematical texts, a line from A to B is known as line AB. In Byrne, it is known as, say, "the red line," but even this is too many words. It is actually just a red line on the page, and where in other volumes of Euclid you might read "Line AB = line BC," in this one there are just pictures on either side of the equal sign: "[red line] = [blue line]." In most diagrams here, angles that are equal have the same color, as do lines that are equal.

Byrne says that by engaging the eye in this way, Euclid can be taught in less than a third of the time it takes with the symbol versions of the proofs. He says that memories retain such lessons better, and that he himself has done the experiments to show these successes of his system. Be that as it may, what really stands out about his book is how engagingly colorful the brilliant pages are, and how antic are the colored lines and shapes on each page. Taschen has brought the book out with more permanent paper and with a better binding than the original, in a box that includes Oechslin's essay book. It is a handsome volume to celebrate an innovation in teaching geometry and in the history of printing and graphic design.