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

58 files·489.1 KB···Download archive (.tar.gz)

Reader · live HTML Source files · 58 files · loading…Rendered · PDF

58 files·489.1 KB·

· 58 files

VIII.9 Proposition VIII.9

If two numbers be prime to one another, and numbers fall between them in continued proportion, then, however many numbers fall between them in continued proportion, so many will also fall in continued proportion between each of them and a unit.

Proof

Coprime extremes correspond to a least continued proportion (VIII.1); the unit extends the proportion at both ends, and VIII.2 gives the matching extension on each side.

lines 74–74 in main.tex