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The First Six Books of The Elements of Euclid
A rare and beautiful geometry primer from the 19th century
Red, yellow, blue – and of course black – are the colours that Oliver Byrne employs for the figures and diagrams in his most unusual 1847 edition of Euclid, published by William Pickering and printed by Chiswick Press, and which prompt the surprised reader to think of Mondrian. 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." Byrne is not content to trust solely in the supposed intuitive “logical” structure of Euclid’s axioms and theorems – who doesn’t know the first famous sentences of Euclid’s Elements: “I. A point is that which has no parts. II. A line is length without breadth”? –, but translates them into colourful diagrams and symbols. He thereby thinks in terms of the school classroom: he compares his colours to the dyed chalks in which figures are drawn on the blackboard.
Oliver Byrne (c. 1810–c. 1880) was an Irish author and civil engineer. Little is known about his life, though he wrote a considerable number of books. As Surveyor of Her Majesty's Settlements in the Falkland Islands, Byrne had already published mathematical and engineering works, 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 colour, sprinkled over the pages like tiny wild flowers and demanding the most meticulous alignment of the different colour plates for printing. Elsewhere, solid squares, triangles and circles are printed in bright colours, expressing a verve not seen again on the pages of a book until the era of Dufy, Matisse and Derain.
Red, yellow, blue – and of course black – are the colours that Oliver Byrne employs for the figures and diagrams in his most unusual 1847 edition of Euclid, published by William Pickering and printed by Chiswick Press, and which prompt the surprised reader to think of Mondrian. 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." Byrne is not content to trust solely in the supposed intuitive “logical” structure of Euclid’s axioms and theorems – who doesn’t know the first famous sentences of Euclid’s Elements: “I. A point is that which has no parts. II. A line is length without breadth”? –, but translates them into colourful diagrams and symbols. He thereby thinks in terms of the school classroom: he compares his colours to the dyed chalks in which figures are drawn on the blackboard.
Oliver Byrne (c. 1810–c. 1880) was an Irish author and civil engineer. Little is known about his life, though he wrote a considerable number of books. As Surveyor of Her Majesty's Settlements in the Falkland Islands, Byrne had already published mathematical and engineering works, 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 colour, sprinkled over the pages like tiny wild flowers and demanding the most meticulous alignment of the different colour plates for printing. Elsewhere, solid squares, triangles and circles are printed in bright colours, expressing a verve not seen again on the pages of a book until the era of Dufy, Matisse and Derain.
268 pages, Hardcover
First published January 1, 1847
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Displaying 1 - 25 of 25 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.
January 4, 2024
Beautiful. I teach Euclid to High Schoolers, and this is a scintillating visual aide to share with them. I especially like the color coded and diagramed “proofs” included with the propositions. This really helps them to better understand why the proposition is true.
Only downside, which really isn’t a defect, is that the text features the “f” in place of the “s”, as we read text today. But this was written in 1847, so it’s more of a feature than a bug.
Only downside, which really isn’t a defect, is that the text features the “f” in place of the “s”, as we read text today. But this was written in 1847, so it’s more of a feature than a bug.
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.
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October 11, 2024Really cool book that makes reading Euclid's Elements much easier and more comprehensible by taking abstract language and making it visual (and beautiful)!
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....
August 4, 2024
With f instead of s it’s too hard to read, but it’s lovely to dip into. The illustrations are fantastic and I want to reproduce some on larger canvases.
February 2, 2025
I read the opening sections and skimmed the rest. Just gorgeous. I'm starting to work through it with my kids.
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.
December 16, 2024
First of all I would recommend using the following website https://www.c82.net/euclid/ rather than trying to read this in book form. The website allows you to click the lines and shapes mentioned in the text and highlights them on the accompanying figure, which greatly improves the clarity of the proofs. Speaking of clarity, I found this book much more valuable as a study in logic and reasoning than as an easy to follow geometry textbook (it is not). I would recommend reading Book I on plane geometry in its entirety to see how the theorems build on each other and get a flavor for the work as a whole. These theorems are generally easier to follow and you will find a geometric proof for the famous Pythagorean theorem here. Book II on geometric algebra is incredibly difficult to follow in my opinion, using geometry to prove concepts much easier to understand algebraically. Books III and IV on circles and polygons can be skimmed. Book V on ratios and proportions I think is actually more confusing the way Byrne has presented the figures as groups of colored shapes rather than lines. Again, much of the material here is more easily represented and understood algebraically. Book VI applies the ratio concepts in Book V to polygons and is skimmable. There are actually seven more books in the complete Elements, but it seems most single volume editions leave these out, and if you’re like me and made it this far you’ve probably had more than enough already.
October 9, 2025
No lo he acabado ni lo acabaré. Libro excelente en cuanto a contenido y calidad, aunque lioso a la hora de leer por tener que ir mirando los dibujos y las letras del alfabeto griego constantemente para ver las proposiciones reflejadas en el papel, aunque eso es problema del lector, mío en este caso, falta de capacidad quizás.
Aún así, todo muy bien entendido al momento de leerlo, le di las leídas necesarias hasta entender todo. Disfruté viéndome capaz de resolver ciertas dudas y me gustó mucho ver el proceso de creación del teorema de Pitágoras, muy interesante.
Vocabulario muy técnico y complicado que ayuda a introducirte al mundo de las demostraciones matemáticas, tanto geométricas como en cualquier otro campo.
Quizás vuelva a leerlo en unos años con otra perspectiva. La valoración es baja porque me ha costado muchísimo tiempo por pereza y poco enganche.
Aún así, todo muy bien entendido al momento de leerlo, le di las leídas necesarias hasta entender todo. Disfruté viéndome capaz de resolver ciertas dudas y me gustó mucho ver el proceso de creación del teorema de Pitágoras, muy interesante.
Vocabulario muy técnico y complicado que ayuda a introducirte al mundo de las demostraciones matemáticas, tanto geométricas como en cualquier otro campo.
Quizás vuelva a leerlo en unos años con otra perspectiva. La valoración es baja porque me ha costado muchísimo tiempo por pereza y poco enganche.
October 12, 2024
Loved it; science is one thing, to communicate its findings in a way accessible to all and in the process producing a work of art is having crafted a masterpiece; was surprised to learn of the connection between Byrne's work, notably employing a use of primary colors and seemingly simple line work, and the art movements 'De Stijl' (think Mondriaan), Bauhaus and W.E. Du Bois's masterpiece W. E. B. Du Bois's Data Portraits: Visualizing Black America.
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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.
September 3, 2024
Euclid has always been one of the most interesting and significant philosopher/mathematicians for me. The fact that Euclidean geometry remains mostly unchanged is mind-blowing. Philosophy revolves around thought, and I can understand how people generate ideas. But mathematics, that's a whole different realm. Revisiting much of what I already knew, but with this new perspective, has reignited my love for math. The graphics, aesthetics, and writing are all beautifully crafted. One day I will get a physical copy of this book no matter what!
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.
December 27, 2022
It is the first 6 books of Euclid’s Elements plus a bit more. This was an early color print book and there are some interesting artifacts scattered about it. Euclid, of course, was genius and for that fact alone his Elements are worth reading. However, there are better geometry texts to use to actually learn Euclidian geometry. Byrne’s diagrams are often helpful in following the arguments.
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!
February 9, 2025
GOATED
This entire review has been hidden because of spoilers.
Displaying 1 - 25 of 25 reviews