Proposition VIII.14 — If a square measure a square, the side will also measure the…

Proof

a^{2} ∣ b^{2} ⟺ a ∣ b

, by Euclid's lemma (VII.30) applied prime-by-prime.

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Depends on (2)

VII.30Proposition VII.30If two numbers by multiplying one another make some number, and any prime number measure the product, it will also…
VIII.11Proposition VIII.11Between two square numbers there is one mean proportional number, and the square has to the square the ratio duplicate…

Required by (dependents) (3)

VIII.15Proposition VIII.15If a cube number measure a cube number, the side will also measure the side; and if the side measure the side, the cube…
VIII.16Proposition VIII.16If a square measure not a square, neither will the side measure the side; and if the side measure not the side, neither…
X.9Proposition X.9The squares on straight lines commensurable in length have to one another the ratio which a square number has to a…

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