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The First Six Books of the Elements of Euclid
Primary elements. Euclid in living color
Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th century mathematician Oliver Byrne employed the color scheme for the figures and diagrams in his most unusual 1847 edition of Euclid's Elements. The author makes it clear in his subtitle that this is a didactic measure intended to distinguish his edition from all others: “The Elements of Euclid in which coloured diagrams and symbols are used instead of letters for the greater ease of learners.” As Surveyor of Her Majesty’s Settlements in the Falkland Islands, Byrne had already published mathematical and engineering works previous to 1847, but never anything like his edition on Euclid. This remarkable example of Victorian printing has been described as one of the oddest and most beautiful books of the 19th century.
Each proposition is set in Caslon italic, with a four-line initial, while the rest of the page is a unique riot of red, yellow, and blue. On some pages, letters and numbers only are printed in color, sprinkled over the pages like tiny wild flowers and demanding the most meticulous alignment of the different color plates for printing. Elsewhere, solid squares, triangles, and circles are printed in bright colors, expressing a verve not seen again on the pages of a book until the era of Dufy, Matisse, and Derain.
Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th century mathematician Oliver Byrne employed the color scheme for the figures and diagrams in his most unusual 1847 edition of Euclid's Elements. The author makes it clear in his subtitle that this is a didactic measure intended to distinguish his edition from all others: “The Elements of Euclid in which coloured diagrams and symbols are used instead of letters for the greater ease of learners.” As Surveyor of Her Majesty’s Settlements in the Falkland Islands, Byrne had already published mathematical and engineering works previous to 1847, but never anything like his edition on Euclid. This remarkable example of Victorian printing has been described as one of the oddest and most beautiful books of the 19th century.
Each proposition is set in Caslon italic, with a four-line initial, while the rest of the page is a unique riot of red, yellow, and blue. On some pages, letters and numbers only are printed in color, sprinkled over the pages like tiny wild flowers and demanding the most meticulous alignment of the different color plates for printing. Elsewhere, solid squares, triangles, and circles are printed in bright colors, expressing a verve not seen again on the pages of a book until the era of Dufy, Matisse, and Derain.
395 pages, Hardcover
First published January 1, 1847
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Displaying 1 - 14 of 14 reviews
April 19, 2018
I bought this book on impulse, on the grounds that it was beautiful and surprisingly inexpensive. It then sat unread on the top shelf of our science and mathematics bookcase for several years; but I've recently become interested in geometry, thanks to the good offices of our mathematician friend T, and this week I finally opened it. I finished it in a few days.
The book consists of a facsimile of Oliver Byrne's unusual 1847 edition of Euclid's first six books, followed by a long critical essay by the Swiss art historian and architect Werner Oechslin where he compares Byrne with Plato, Goethe, Frege, Einstein and various others of the usual suspects. I imagine Oechslin is saying some worthwhile things here, but to me he seems to be missing the main point, which is a very simple one. Byrne has found a way of presenting Euclid, a notoriously dry and inaccessible author, which makes him fun to read. He does this by using colours instead of letters. Instead of saying "the angle ACD" or "the line MN", which means your eye is continually flicking back and forth between the text and the diagram trying to find those damn angles and lines and losing the thread of the argument, Byrne just marks everything in colour. He doesn't say "the angle ACD" and "the line MN"; he draws a yellow angle and a blue line in the diagram, and then in the text he shows you the same yellow angle and blue line. Evolution has tuned our eyes to make them very good at noticing coloured objects, so you immediately see what the text refers to and you can read at a more or less normal speed. To give you the flavour of it, here are the two pages showing the proof of Pythagoras's Theorem.
It really is remarkably pleasurable: you soon pick up Euclid's logical-visual way of thinking, and you see how he methodically advances from the obvious (two circles can intersect in at most two points) to the almost obvious (a triangle inscribed in a circle, one of whose sides is a diameter, is a right-angled triangle) to the not obvious at all (if you draw two lines through a circle that intersect inside it, the products of the lengths of the two segments of each line are the same). Some of it is familiar from college math, and some of it, at least to me, is bizarrely alien. In particular, Euclid loves to use the lemma which we now would write as "(a + b)² = a(a + 2b) + b²", but which he thinks of as dividing the line with length 2(a + b) first into the unequal pieces of lengths a and (a + 2b), and then into two equal pieces of length (a + b), comparing the products and squares. It's amazing how many tricks he can do with this simple result.
If you're too cheap to buy a paper copy, Byrne's Euclid is available online here. Have fun getting in touch with your inner geometer!
The book consists of a facsimile of Oliver Byrne's unusual 1847 edition of Euclid's first six books, followed by a long critical essay by the Swiss art historian and architect Werner Oechslin where he compares Byrne with Plato, Goethe, Frege, Einstein and various others of the usual suspects. I imagine Oechslin is saying some worthwhile things here, but to me he seems to be missing the main point, which is a very simple one. Byrne has found a way of presenting Euclid, a notoriously dry and inaccessible author, which makes him fun to read. He does this by using colours instead of letters. Instead of saying "the angle ACD" or "the line MN", which means your eye is continually flicking back and forth between the text and the diagram trying to find those damn angles and lines and losing the thread of the argument, Byrne just marks everything in colour. He doesn't say "the angle ACD" and "the line MN"; he draws a yellow angle and a blue line in the diagram, and then in the text he shows you the same yellow angle and blue line. Evolution has tuned our eyes to make them very good at noticing coloured objects, so you immediately see what the text refers to and you can read at a more or less normal speed. To give you the flavour of it, here are the two pages showing the proof of Pythagoras's Theorem.
It really is remarkably pleasurable: you soon pick up Euclid's logical-visual way of thinking, and you see how he methodically advances from the obvious (two circles can intersect in at most two points) to the almost obvious (a triangle inscribed in a circle, one of whose sides is a diameter, is a right-angled triangle) to the not obvious at all (if you draw two lines through a circle that intersect inside it, the products of the lengths of the two segments of each line are the same). Some of it is familiar from college math, and some of it, at least to me, is bizarrely alien. In particular, Euclid loves to use the lemma which we now would write as "(a + b)² = a(a + 2b) + b²", but which he thinks of as dividing the line with length 2(a + b) first into the unequal pieces of lengths a and (a + 2b), and then into two equal pieces of length (a + b), comparing the products and squares. It's amazing how many tricks he can do with this simple result.
If you're too cheap to buy a paper copy, Byrne's Euclid is available online here. Have fun getting in touch with your inner geometer!
April 17, 2018
Hot tip for anyone reading this who's currently sleeping with a math geek: give your lover a copy of Oliver Byrne, and you will get good sex. Though not immediately.
June 21, 2012
Clever, gorgeous, inspiring, personal, mondrianesque.
Science, art, and love.
I wish to print all pages of this book and hang them on my hallway wall.
Science, art, and love.
I wish to print all pages of this book and hang them on my hallway wall.
February 17, 2020
I only read the first four books.
Fun to read, However, the language gets too verbose sometimes, and relying solely on colored diagrams is partly to blame.
Also, there is a good online reproduction available here : https://www.c82.net/euclid/
I think it doesn't make much sense to read Euclid on it's own these days, and so I'm planning on reading Geometry: Euclid and Beyond For a modern interpretation of what I'd just read. But I'm not sure if it's worthwhile to spend that much time on Classical Geometry at all.
Fun to read, However, the language gets too verbose sometimes, and relying solely on colored diagrams is partly to blame.
Also, there is a good online reproduction available here : https://www.c82.net/euclid/
I think it doesn't make much sense to read Euclid on it's own these days, and so I'm planning on reading Geometry: Euclid and Beyond For a modern interpretation of what I'd just read. But I'm not sure if it's worthwhile to spend that much time on Classical Geometry at all.
June 22, 2010
Easily the most beautiful math book I own (sorry, Annotated Flatland). A stunning example of what can be done with lines and logic. One of the foundational achievements of our species presented with true elegance. Worth it for any single diagram, though the essays are pitch-perfect as well. Go buy this book right now.
May 9, 2016
this book is a series of math proofs from two thousand years ago -- no explanations, few words. it isn't for reading. it's a work of art, an homage to a 19th century printing feat, and the most important text in math. but don't get it to read.
July 12, 2013
Էրեխեքիս երկրաչափություն էս գրքով եմ սովորացնելու, հաստատ։ Էս ինչ լավն էր
August 21, 2017
All of Euclid's proofs and constructions demonstrated with colourful diagrams. A gorgeous book.
October 15, 2020
You can use all pages to decorate your house.... If all math books had this quality....
July 17, 2021
Let me preface this review by stating that I am not reviewing Euclid's Elements - a book so fundamental to our mathematical framework - but rather Oliver Byrne's work of illustrating his first six books. Still, being the first time that I looked at Euclid's work, I found it to be more enjoyable and accessible than I would have thought.
This is a must have for any math geek out there, the quality of the book outweigh greatly the cost, in my opinion, and most of the proofs do benefit from the illustrative approach. The pages are sturdy and the writing is minimal leaving all the room to the visual interpretation.
However it doesn't work at the same level for all of Euclid's work. I tought Book I-III did an exceptionnal job of setting the foundation of a curriculum that is still mostly followed more than 2 millenia later.
Book IV eased most of the comprehensive proofs, but failed in my opinion to digest correctly some of the harder ones. That's not to say that there's a better way to illustrate it, only that visuals only go so far.
Book V was the weakest, only because it enhanced very little of Euclid's work being a algebra focused book; and Book VI was a mixed bag similar to Book IV.
Still, if you a have a love for mathematics you are going to find a theorem every few pages that reminds you of one that you may have known on simpler terms or named differently.
A small note on the second part which criticizes Byrne's work through a pure philosophical approach (in three different languages I must say) - I feel very uninformed about the reason why it is there, but at face value it felt lukewarm and redundant.
Still amazing work.
This is a must have for any math geek out there, the quality of the book outweigh greatly the cost, in my opinion, and most of the proofs do benefit from the illustrative approach. The pages are sturdy and the writing is minimal leaving all the room to the visual interpretation.
However it doesn't work at the same level for all of Euclid's work. I tought Book I-III did an exceptionnal job of setting the foundation of a curriculum that is still mostly followed more than 2 millenia later.
Book IV eased most of the comprehensive proofs, but failed in my opinion to digest correctly some of the harder ones. That's not to say that there's a better way to illustrate it, only that visuals only go so far.
Book V was the weakest, only because it enhanced very little of Euclid's work being a algebra focused book; and Book VI was a mixed bag similar to Book IV.
Still, if you a have a love for mathematics you are going to find a theorem every few pages that reminds you of one that you may have known on simpler terms or named differently.
A small note on the second part which criticizes Byrne's work through a pure philosophical approach (in three different languages I must say) - I feel very uninformed about the reason why it is there, but at face value it felt lukewarm and redundant.
Still amazing work.
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August 19, 2016Lior Silberman, Assistant Professor, Mathematics recommends . . .
First six books of of the elements of Euclid by Euclid
Why is this a favourite book?
This has been the standard "introduction to mathematics" book for more than two thousand years, a marvel of cultural continuity. Then as now it furnishes one of the cornerstones of a general education. I also think of it as the connecting thread of research mathematics, showing that today's modern discipline is the same one studied in Greece 2300 years ago.
First six books of of the elements of Euclid by Euclid
Why is this a favourite book?
This has been the standard "introduction to mathematics" book for more than two thousand years, a marvel of cultural continuity. Then as now it furnishes one of the cornerstones of a general education. I also think of it as the connecting thread of research mathematics, showing that today's modern discipline is the same one studied in Greece 2300 years ago.
March 21, 2013
A reissue by Taschen of a book from 1847 by Oliver Byrne in which the proofs of theorems by Euclid are given in few words and a lot of nice figures with colours turning the book in a Mondriaan one. Unfortunately character recognition went wrong and 80% of the letters "s" is printed as "f", very disturbing. Shame on Taschen who should have made more effort to make this book amusing. A 5-star for Byrne, but due to Taschen it becomes a 2-star book.
June 3, 2015
Great edition & great art. Euclid's books are greatly transformed by Oliver Byrne's illustrations. The accompanying text explaining the reception at the time (1856) of this book was a very illuminating read.
December 7, 2014
Looking forward to getting re-acquainted with my 5th grade math class and Miss Veronica Piper!
Displaying 1 - 14 of 14 reviews