Alexandria, c. 300 BC
Euclid's Elements is the most influential textbook ever written: thirteen books and four hundred and sixty-five propositions that built all of geometry from five postulates and a handful of definitions. Nothing is asserted; everything is constructed, step by step, with a compass and a straightedge. The first six books — plane geometry, from the equilateral triangle of Proposition 1 to the similar figures of Book VI — contain one hundred and seventy-three propositions. Euclid never measured an angle in degrees; he counted in right angles. The Elements is a book about what can be drawn, and proven, from almost nothing.
London, 1847
Oliver Byrne, a mathematician and surveyor, published The First Six Books of the Elements of Euclid, in which Coloured Diagrams and Symbols are used instead of Letters with William Pickering, printed at the Chiswick Press. His idea was radical: delete the letters. Where Euclid wrote "the square on AB," Byrne printed a small coloured square. Equal things share a colour; the proof of the Pythagorean theorem becomes red, yellow and blue areas you can simply see are equal. The book used exactly four inks on cream paper, was shown at the Great Exhibition of 1851, sold poorly in a small print run — reportedly around a thousand copies — and helped sink its publisher. Design historians now treat it as roughly seventy years ahead of its time, anticipating De Stijl, Mondrian and the Bauhaus. It is one of the most beautiful books of the nineteenth century, and it is long in the public domain.
The palette, measured
The colours here are not picked from a swatch book. They were measured from photographs of the book's pages — each page white-balanced against its own paper, the inks read in reflectance space, the medians taken across a forty-eight page sample. The result is warmer and earthier than modern primaries: a burnt vermilion, a golden ochre, a slate ultramarine, and a near-black with brown in it, on cream.
The collection
Geometric Foundations is 1,730 constructions: one canon plate for each of the 173 propositions of the first six books, and nine generated variations of each — the same theorem, instantiated on different inputs, because a theorem is true for every triangle, not one. Each token belongs to a single book and inherits its visual grammar: triangles and their angle sectors in Book I, dissected squares and gnomons in Book II, circles in Book III, inscribed figures in Book IV, magnitudes as rows of coloured units in Book V, similarity and the golden section in Book VI. The books are the traits, and the rarity curve was set 2,300 years ago: Book II has only fourteen propositions, so its 140 tokens are the scarcest in the edition.
The art is deliberately light. Flat fills, four inks, no gradients: an average of 0.92 kilobytes of SVG per token, generated deterministically from a seed, which is what makes storing the entire edition on-chain practical rather than aspirational. Full-colour plates are the common ground of the collection; duotones are uncommon, single-ink plates rare, inverted night plates very rare, and twenty-six uncoloured plates — pure black construction linework, the way every other edition of Euclid ever looked — are the scarcest of all.
The numbers
173 propositions in Books I–VI, and 173 is prime. Ten tokens per proposition gives the edition of 1,730. The golden ratio that fixes Book VI's proportions is Euclid's own "extreme and mean ratio," defined in the book itself. And Byrne's year, 1847, is prime too. None of this is decoration; the structure of the collection is the structure of the source.
The chain
The collection deploys to Robinhood Chain, an Ethereum Layer 2, with each token's SVG assembled on-chain from its seed. Secondary trading is visible anywhere the chain is supported, including OpenSea. Byrne's book was public infrastructure that arrived a century early; putting it on a public chain, permanently, feels like the ending it was owed.
A project by [Owner] & Bart · MMXXVI