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

VII.30 Proposition VII.30

If two numbers by multiplying one another make some number, and any prime number measure the product, it will also measure one of the original numbers.

Proof

If a prime

p ∣ ab

but

p ∤ a

, then by VII.29

p

is coprime to

a

; by VII.24 (taking

b

as the multiplicand)

p

must divide

b

.

lines 74–74 in main.tex