:: EUCLID · PRAEFATIO ::
The Elements of Euclid
Euclid of Alexandria · the oldest engine still running, the taproot of every figure here · the first six books, Casey, 1885
It is the oldest engine still running. Picture a single page that opens with five plain sentences. A line can be drawn between two points. A circle struck from any centre. Out of those five, by nothing but patient agreement, the whole of flat space unfolds: triangles, parallels, the square on the hypotenuse, the golden cut, all of it earned, none of it assumed. Twenty-three centuries later a child still meets her first proof here, and the chain holds link for link, exactly as it held in Alexandria. Other books teach you facts; this one teaches you what it means to know a thing. Have you ever met another machine that has run that long and never once stopped?
Before the book is opened, let the terms be plain.
I keep no till here: this edition will never be sold, gated, or wrapped in advertisement. I set it down for the dissemination of knowledge and the plain love of the game.
Euclid set down the Elements in Alexandria around 300 BC — the oldest mathematical text still in daily use, and in the public domain for over two thousand years. The facsimile here is John Casey's 1885 edition of the first six books, the plane geometry, scanned by Cornell University Library and released through Project Gutenberg. I gave Casey's lettered diagrams and prose proofs a reading edition: his page set whole on the house ground on one side, and on the other the same proposition set clean and selectable for reading — with a full Book-and-Proposition index threaded through. That work is mine, and it's free — like everything here.
Provenance & Thanks
- The work
- Euclid of Alexandria (fl. c. 300 BC), Στοιχεῖα, the Elements. Thirteen books in full; here the first six, the plane geometry: the definitions, postulates and common notions, then the deductive cascade. The incommensurables are tamed in Book V, the golden ratio (extreme and mean ratio) defined in Book VI, and Book I closes on Pythagoras (I. 47). The taproot every other figure in this Scriptorium grows from.
- The edition
- John Casey, LL.D., F.R.S., The First Six Books of the Elements of Euclid, and Propositions I.–XXI. of Book XI., and an Appendix on the Cylinder, Sphere, Cone, &c., with Copious Annotations and Numerous Exercises — Dublin, printed at the University Press by Ponsonby and Weldrick, 1885. A clear, scholarly setting of the original beside the modern geometry of its day.
- The digitisation
- Cornell University Library produced the replacement volume from the deteriorated original (scanned at 600 dpi); the e-text is Project Gutenberg #21076, public domain. This edition rests on that settled ground and thanks every hand that kept the door open.
- This edition
- Casey's 216 facsimile leaves rendered to lazy-loading plates and set whole on the dark-gold ground, each page paired with its proposition text reflowed clean and selectable for reading, and a full Book/Proposition index (201 propositions across Books I–VI, Book XI, and the appendix on solids) threaded through the scroll. The reader design and the modern apparatus are mine, released for non-commercial use in the spirit of the open inheritance they draw from.
To the librarians, scanner-operators, and archivists whose patient, unglamorous work makes a deteriorated 1885 volume openable on a screen in the present — this edition bows. You are the reason any of this is possible. Thank you.