Euclid's Elements, Book I, as a graph.

What Pythagoras needs

Proposition I.47 cites I.4, I.14, I.41 and I.46 directly, and Axiom 6. Followed all the way back, it rests on 25 propositions, 7 axioms, 5 definitions, and 3 postulates: 40 items out of the 142 in Book I.

The longest chain of citations back to a first principle is 16 steps:

1. I.47
2. I.41
3. I.37
4. I.35
5. I.34
6. I.26
7. I.16
8. I.15
9. I.13
10. I.11 (construction)
11. I.8
12. I.7
13. I.5
14. I.3 (construction)
15. I.2 (construction)
16. I.1 (construction)
17. Post. 3

The result cited most often in Book I is I.34 (in a parallelogram, opposite sides and opposite angles are equal), cited 17 times.

How this was made

The text is Project Gutenberg's edition of John Casey's The First Six Books of the Elements of Euclid (1885), which is in the public domain. Casey's commentary, exercises and figures were removed, and every item became a LaTeX environment. The links are Casey's explicit citations, such as “[I.4]” or “(Post. 3)”, plus each corollary's link to its proposition.

That makes this a lower bound on what each proof uses, not the complete logical structure: a step Casey didn't cite is not here. His English is from 1885 ("right line" means straight line), the figures the proofs refer to are missing, and some corollaries are Casey's additions rather than Euclid's.

The prepared file is euclid-book-1.tex. Import it into a Manifield project to browse Book I in the library, or import it as a source and cite it.