Proposition XI.36 — If three straight lines be proportional, the parallelepipeda…

Proof

For

a : b = b : c

(with

b

the mean),

ab c = b^{3}

and the parallelepipeds on

a, b, c

versus

b, b, b

have equal volumes by XI.34 / XI.33.

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Depends on (3)

VI.17Proposition VI.17If three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the mean;…
XI.32Proposition XI.32Parallelepipedal solids which are of the same height are to one another as their bases.
XI.34Proposition XI.34In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal…

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