Source — Euclid's Elements, encoded as an rrxiv paper

1% main.tex — Euclid's Elements, encoded as an rrxiv paper.
2%
3% Build with tectonic via ./scripts/build.sh.
4
5\documentclass{rrxiv}
6
7\rrxivid{rrxiv-paper-euclid-elements}
8\rrxivversion{v5}
9\rrxivprotocolversion{0.1.0}
10\rrxivlicense{CC-BY-4.0}
11\rrxivtopics{math.HO,math.MG,math.NT,history-of-mathematics,reproducibility}
12
13\title{Euclid's \emph{Elements}, encoded as an rrxiv paper}
14% Structured authorship lives in rrxiv-meta.json (RRP-0021 + RRP-0026).
15% The parser merges that block onto these names by exact match. Keep
16% the names here byte-identical to rrxiv-meta.json `authors[].name`
17% so attribution doesn't drift across the build + parse boundary.
18\author{Euclid of Alexandria \and Sir Thomas L. Heath \and Blaise Albis-Burdige \and Claude Opus 4.7}
19\date{\today}
20
21\begin{document}
22\maketitle
23
24\begin{abstract}
25We publish a complete, machine-readable rendering of Euclid's
26\emph{Elements} as an rrxiv paper. All thirteen books are encoded:
27every definition, postulate, common notion, and proposition is
28registered as an addressable rrxiv \texttt{claim}, and every proof
29is encoded as a sequence of explicit \texttt{depends\_on} edges to
30earlier claims. The encoding produces 465 propositions, 109
31definitions, 5 postulates, and 5 common notions, connected by over a
32thousand \texttt{depends\_on} edges --- the full reasoning DAG of
33the \emph{Elements} is queryable through the rrxiv API.
34
35The encoding serves three purposes: (i)~it dogfoods the rrxiv schema
36on a finite, dependency-rich corpus that has been studied for two
37thousand years; (ii)~it provides a working reproducibility
38demonstration --- every proposition is provable from claims that the
39rrxiv graph can enumerate, terminating in the five postulates and
40five common notions; and (iii)~it gives agent harnesses a canonical
41proof corpus to retrieve over.
42
43Books~I, II, and III are written in full Heath-density prose with
44TikZ figures for the canonical constructions (I.1, I.5, I.32, I.47,
45II.4, II.11, II.14, III.20, III.31, III.36). Books~IV through XIII
46carry the full statement + dependency-edge DAG with condensed proof
47sketches; rendering them at Heath density is a long-running editorial
48project, and PRs at \url{https://github.com/random-walks/rrxiv-paper-euclid-elements}
49are welcome. The translation follows Heath (1908, public domain) with
50light modernisation; the rrxiv encoding is released under CC-BY-4.0.
51\end{abstract}
52
53% ---- Front matter: postulates + common notions + Book I definitions ----
54\input{postulates}
55\input{common-notions}
56\input{definitions}
57
58% ---- Books ----
59\input{books/book01}
60\input{books/book02}
61\input{books/book03}
62\input{books/book04}
63\input{books/book05}
64\input{books/book06}
65\input{books/book07}
66\input{books/book08}
67\input{books/book09}
68\input{books/book10}
69\input{books/book11}
70\input{books/book12}
71\input{books/book13}
72
73\end{document}
74