Proposition X.11 — If four magnitudes be proportional, and the first be commens…

Proof

Commensurability

⟺

rational ratio (X.5 / X.6); rational ratios are preserved under equality of ratios.

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Depends on (2)

X.5Proposition X.5Commensurable magnitudes have to one another the ratio which a number has to a number.
X.6Proposition X.6If two magnitudes have to one another the ratio which a number has to a number, the magnitudes will be commensurable.

Required by (dependents) (2)

X.12Proposition X.12Magnitudes commensurable with the same magnitude are commensurable with one another.
X.14Proposition X.14If four straight lines be proportional, and the square on the first be greater than the square on the second by the…

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