Euclid’s Elements – Oliver Byrne’s Geometric Masterpiece

By Emily Gillis

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Despite being printed over a century ago, Oliver Byrne’s stunning edition of Euclid’s Elements continues to be one of the most beautiful expositions in the world of mathematical publishing. Scattered across each page in brilliant reds, yellows and blues are triangles, squares and circles in a myriad of combinations with intersecting lines and numbers. These intricate figures express the mathematical proofs of many iconic geometric equations that form the bedrock of mathematical study. 

The History of Euclid’s Elements

First published in 1847 and uniquely beautiful in its presentation, Byrne’s edition of The First Six Books of the Elements of Euclid was the first attempt to illustrate the classic books of mathematical theorems written by ancient Greek mathematician Euclid of Alexandria, originally penned around 300BC. Euclid’s original treatise on geometry and mathematical theory laid the foundation for the modern study of geometry and have since become cornerstone works in the history of mathematics. They have proved influential in the sciences, used by Galileo Galilei, Albert Einstein, and Sir Isaac Newton, who implemented the theories within Elements to aid their discoveries. The thirteen books of Euclid’s Elements continue to be considered a masterpiece in the practice and application of mathematics.

While the artfully compact diagrams within this volume can be appreciated as artworks in their own right, Byrne’s intention surpassed the visual, aiming to aid the mind in attaining such complex mathematical knowledge. The visual, educational elements in Byrne’s nineteenth-century edition encouraged learning by physical example, provided in the colourful compounds formed of shapes, angles, and edges. This stunning example of numerical visual study has influenced the history of mathematics the world over; however, it has also proven to be an indispensable inspiration for twentieth-century art movements. With avant-garde groups like De Stijl and The Bauhaus using Byrne’s iconic colour, line work and form in many of their works. 

Translated from Greek, Euclid means ‘renowned’ or ‘glorious’ – a fitting name for the legacy to which the scholar is attributed, now often named ‘the father of geometry’. The thirteen books produced by Euclid in 300BC equated to a comprehensive geometrical system that was, for many following centuries, considered the only geometry possible. Euclid deduced many theorems of geometry, mathematical proofs, and number theory within the works, and although many theorems originated from earlier mathematicians, Euclid’s Elements was pioneering in its age because of how the hypotheses were presented. The single, logical framework was easy to reference as it included a system of rigorous mathematical proofs to help aid the reader. His work included the now-famous geometry theorems like Pythagoras and circular theory, which have become integral to the logical development of subjects like mathematics and science. Euclid’s axiomatic approach of application and proof of geometry has enabled his work to remain the basis of mathematical study for over 2000 years. In the modern age, this ancient system is often referred to as Euclidean geometry to separate it from other forms of non-Euclidean geometry discovered from the nineteenth century onwards. When Oliver Byrne’s edition was published in 1847, Euclid’s Elements was still used as the basis for geometric study in the classroom.

Oliver Byrne’s edition of Euclid

Oliver Byrne was a mathematician, civil engineer, and prolific author, born in Ireland at the beginning of the nineteenth century. He wrote numerous works on mathematics, geometry, and engineering; however, he is most famous for his creative adaptation of Euclid’s Elements – illustrating the first six books in his edition: 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. With little about his early life being known, Byrne first appeared on record in Dublin aged twenty with the publication of his first book, A Treatise on Diophantine Algebra, 1830, which was co-authored by his younger brother, John. Byrne embarked on a prolific writing career penning over forty works in his lifetime – mostly on educational subjects such as mathematics and engineering, and a well-known work on the Irish Independence of the 1850s. He was also a significant contributor to Spon’s Dictionary of Engineering. In 1839, Byrne spent two years as Professor of Mathematics at the College for Civil Engineers in Putney, Southwest London.

Byrne’s Euclid was his most ingenious educational work. By accompanying Euclid’s original geometric theories with expressive, colourful proofs, Byrne turned what was already a cornerstone academic text into a pedagogical work of art. Working as an aid to understanding Euclid’s complex equations, Byrne’s fascinating and carefully considered graphics added an appealing visual element for many who struggle to make sense of complex mathematics with numbers alone. The compelling explanations in vibrant red, yellow, and blue float across the book’s pages, bringing the ancient theorems to life, in an attempt as he expressed: ‘to teach people how to think, and not what to think.’ Each wash of colour, shape, form, angle, and line were carefully contemplated to create visually stunning and easily conceivable graphics.

Byrne’s mathematical masterpiece was one of the first multicolour printed books after the invention of the printing press. The multiple colours of the proofs, text, and intricate letter plates were a feat of printing technology previously unseen in the century. The First Six Books of the Elements of Euclid was designed and printed by Charles Whittingham of the Chiswick Press in 1847. Each page features a sophisticated initial designed by the printer’s daughters to complement the typed propositions and coloured shapes. The complex nature of the illustrations must have presented a significant challenge due to the early printing methods of the time. As a consequence of the extravagant nature of the printing, Byrne’s book was sold for a much higher price than other books of the time, at 25 shillings. Unfortunately, the high cost led to the book being much less successful than hoped, with only 100 copies being printed. 

Despite pricing his work out of the hands of the educators for which it was intended, Byrne’s vibrant geometric feat made its debut at the Great Exhibition of 1851 in London. The international exhibition aimed to showcase the work and technologies of Great Britain to cement its role as an industry leader on the world stage. The First Six Books of the Elements of Euclid was celebrated for its elegance and artistry within the printing world, with the fascinating intricacies of Byrne’s illustrations proving as evocative in the Victorian age as they are today. 

Euclid and the Art World

The influence of Byrne’s work on the classroom is apparent; however, his illustrations have created a legacy within the art world. The colour and form of Byrne’s original illustrations profoundly affected the world of art and design after they were picked up by art groups in the early twentieth century. Their influence can be seen in the avant-garde work of the Bauhaus School and art group De Stijl (meaning ‘the style’ in Dutch), responsible for pushing aesthetic boundaries and creating minimalist, abstract works. The order and conformity of Byrne’s geometric proofs appealed to these groups in the wake of the First World War – they were committed to rebelling against the chaos and destruction of the war, looking for a ‘return to order’. The neat squares of primary colours produced by Dutch pioneers like Piet Mondrian, and other leading artists in the De Stijl movement like Theo Van Doesburg, are a short leap from the delicate shapes and stark lines of Byrne’s Euclid. His influence can also be seen later in the twentieth century in the colourful intersectional work of Wassily Kandinsky, whose combinations of shapes and lines hark back to the geometric constructions first created by Byrne in the mid-1800s. In more recent times, Byrne’s pioneering visual work has been the subject of study in graphic design, featuring in many contemporary works on the subject. 

Restoring this Euclid’s Elements

While Euclid’s original theorems stand alone as the foundation of modern mathematics and continue to be used as a practical mathematical guide, it is through Byrne’s enchanting illustrations that this work continues to intrigue readers centuries on.

Republished by Read & Co. Books for our Art Meets Science imprint, a facsimile edition of this legacy work has been painstakingly restored for a new generation to enjoy. Taking special care to conserve the colours, shapes, and text as they were printed on publication in the hope to recapture the magic of this beautiful volume for future readers, both inside and outside of the classroom. 

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