Proof
Let with side ratio .
Construct on so that (i.e.\ a third
proportional, VI.11). By VI.1 the area ratio is along
one dimension and the side ratio along the perpendicular, giving
total area ratio in the sense of Definition V.9 (duplicate
ratio).
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Depends on (3)
- VI.1Proposition VI.1Triangles and parallelograms which are under the same height are to one another as their bases.
- VI.11Proposition VI.11To two given straight lines to find a third proportional.
- 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) (2)
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