Proposition XIII.6 — If a rational straight line be cut in extreme and mean ratio…

Proof

Solve

x^{2} + a x = a^{2}

for the greater segment

x = a (5 - 1) /2

; this is the form of an apotome relative to the rational

a

(Book X classification).

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Depends on (3)

X.73Proposition X.73If from a rational straight line there be subtracted a rational straight line commensurable with the whole in square…
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…

Required by (dependents) (2)

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