Proposition VI.22 — If four straight lines be proportional, the rectilineal figu…

Proof

Apply VI.20: figures similar on proportional sides have areas in the duplicate ratio of the sides. Equality of those duplicate ratios is equivalent to equality of the original side ratios.

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Depends on (2)

VI.20Proposition VI.20Similar polygons are divided into similar triangles, equal in multitude and in the same ratio as the wholes; and the…
V.9Definition V.9When three magnitudes are proportional, the first is said to have to the third the duplicate ratio of that which it has…

Required by (dependents) (3)

X.9Proposition X.9The squares on straight lines commensurable in length have to one another the ratio which a square number has to a…
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…
XI.37Proposition XI.37If four straight lines be proportional, the similar and similarly described parallelepipedal solids upon them will also…

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