The Archive — Notes on a piece

Euclid without letters

In 1847 an Irish engineer reprinted the first six books of Euclid with the letters torn out and pure colour put in their place. It bankrupted his publisher — and it looks a hundred years ahead of itself.
Oliver Byrne · The Elements of Euclid, Prop. I.47 · 1847 · London
Oliver Byrne’s coloured diagram of the Pythagorean theorem in red, yellow and blue
Oliver Byrne, The First Six Books of the Elements of Euclid, Prop. I.47 (the Pythagorean theorem), London, 1847. Public domain.

For two thousand years Euclid's geometry was taught in letters. An angle was "the angle ABC"; you held the diagram in one hand and chased the letters through the proof with the other. In 1847 Oliver Byrne, an Irish civil engineer, decided the letters were the problem.1

Made to name themselves

Byrne reprinted the first six books of the Elements and replaced the labels with pure colour. A line is red; the same red reappears in the demonstration, and you know, without a word, which line is meant. In his phrase, the parts "are made to name themselves, for their forms in corresponding colours represent them in the demonstration."2 The plan, he wrote, "forcibly appeals to the eye, the most sensitive and the most comprehensive of our external organs."3 Geometry, almost without language.

Proposition I.47

This plate is the book's emblem: Proposition 47 of Book I — the theorem of Pythagoras, the squares on the sides of a right triangle.4 Euclid's classic "windmill" figure, solved in blue, red and yellow, each square its own colour so the eye can walk the proof. It sits on the title page; it is the whole idea in one image.5

A beautiful failure

It was printed the hard way — not lithography but colour woodblocks, one block per colour, each pass registered by hand so the angles closed exactly where they should.6 One of the first books printed in full colour, it cost the earth: twenty-five shillings, four or five times the going rate.7 It did not sell. When the publisher William Pickering went bankrupt in 1853, three-quarters of the run was still on the shelf.8 A century on, Edward Tufte set it at the head of the history of information design, and its Pythagoras plate is now hung beside Mondrian.9

Byrne printed in flat colour with hard edges because that was the only way to make the idea work. It is the logic of the shirt exactly: red, yellow, blue and black — the diagram itself, not a picture of it.

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Notes & sources

  1. Oliver Byrne (1810–1880), Irish engineer and mathematician. Wikipedia; MacTutor.
  2. Byrne, Introduction to The First Six Books of the Elements of Euclid (1847), verbatim.
  3. Byrne, Introduction (1847), verbatim.
  4. Proposition I.47 of Book I is the Pythagorean theorem.
  5. The Prop. 47 figure appears on the title page — the emblem of the edition. Smithsonian Libraries.
  6. Printed by Charles Whittingham (Chiswick Press) for William Pickering, London, 1847, from colour woodblocks — blue, red, yellow and black — in flat tones with hard edges. Casselman (UBC).
  7. Priced at 25 shillings, several times a typical book of the day. MAA.
  8. When Pickering went bankrupt in 1853, roughly 75% of the print run was unsold. MacTutor.
  9. Edward Tufte, Envisioning Information (1990); the Prop. 47 plate is often set beside Mondrian's Composition with Red, Yellow, Black, Blue and Grey (1921). Public Domain Review.
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