Nothing here is paraphrased

Text and figures

Every proposition statement on this site is Thomas L. Heath, The Thirteen Books of Euclid's Elements (Cambridge University Press, 1908). Public domain.

All 465 propositions of all thirteen books are parsed from one source and shipped as data. There is no second kind of statement: a proposition whose enunciation is missing raises. Of the 465, 465 have been written out as programs so far; the rest are text waiting for code.

Errata

The source is a scan, and scans misread. Every correction made to it is listed here in full — what the scan says, what it was corrected to, and why. Each is a demonstrable misprint, never a reading of what Euclid meant, and the parser refuses to run if a correction stops applying.

Proposition	The scan reads	Corrected to	Why
II.13	acutc angle	acute angle	'acutc' scanned for 'acute'
VI.26	diameter with the whole	diameter with the whole.	the closing full stop is missing
XII.4	cach	each	'cach' scanned for 'each'

The figures are not Euclid's

The words are his exactly. The diagrams are not, and are not meant to be. If you hold a printed Euclid next to these pages, most figures will not match.

A figure in a book is composed. The author picks a configuration that shows the case well, draws the construction lines the argument needs and no others, and letters the points to suit the proof. Every figure here is a trace: the record of a construction that actually ran, on coordinates chosen by a sampler, containing whatever objects the code made, lettered after the parameters in the code. Three differences follow, and they are permanent:

The shapes and the lettering differ, because ours are sampled and his are chosen.
Ours often carry fewer points. Euclid needs a construction to argue steps that exact arithmetic settles outright, so his figure holds scaffolding ours has no use for.
Ours never show an impossible configuration. Where Euclid argues by contradiction his figure draws the case being refuted — I.7 shows two distinct apexes over one base. That configuration does not exist, so it cannot be constructed here; ours shows the two coincident, which is what the proposition proves.

What the figures do promise: every line and every point in them was really constructed by the program that verified the proposition, in exact arithmetic. A proposition's own work is drawn firm; the apparatus it inherited from helper constructions is drawn back in grey, still present, no longer competing.

How a misprint gets found

Two of the three above substitute a single letter and still spell a real word — acutc, cach — so no spell check or length check would catch them. What catches them is that Euclid's vocabulary is tiny and endlessly repetitive: about four hundred distinct words across all four hundred and sixty-five enunciations. The parser lists every word used exactly once, and a misprint has nowhere to hide in a list that short. Everything else in it is a genuine term of art.