# Proposition: Prop. 10.009: Commensurability of Squares

### (Proposition 9 from Book 10 of Euclid's “Elements”)

Squares on straight lines (which are) commensurable in length have to one another the ratio which (some) square number (has) to (some) square number. And squares having to one another the ratio which (some) square number (has) to (some) square number will also have sides (which are) commensurable in length. But squares on straight lines (which are) incommensurable in length do not have to one another the ratio which (some) square number (has) to (some) square number. And squares not having to one another the ratio which (some) square number (has) to (some) square number will not have sides (which are) commensurable in length either.

### Modern Formulation

(not yet contributed)

Proofs: 1 Corollaries: 1

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Propositions: 18 19 20 21 22 23 24 25 26 27 28 29

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