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Proposition·Untested·2605.00009

Proposition X.14

If four straight lines be proportional, and the square on the first be greater than the square on the second by the square on a straight line commensurable with the first, the square on the third will also be greater than the square on the fourth by the square on a straight line commensurable with the third.

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Proof

Proportionality lifts to the squares; the deviation magnitude inherits the commensurability relation.

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Full neighborhood

Depends on (2)

Required by (dependents) (1)

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