Proposition XIII.4 — If a straight line be cut in extreme and mean ratio, the squ…

Proof

A B^{2} + C B^{2} = 3 \cdot A C^{2}

where

C

cuts

A B

in extreme-and-mean ratio (greater

A C

). Use

A C^{2} = A B \cdot C B

and II.4 to verify the identity.

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Full neighborhood

Depends on (3)

II.4Proposition II.4If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the…
II.11Proposition II.11To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the…
XIII.1Proposition XIII.1If a straight line be cut in extreme and mean ratio, the square on the greater segment added to the half of the whole…

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