Proposition VI.16 — If four straight lines be proportional, the rectangle contai…

Proof

a : b = c : d

, the rectangles

a d

and

b c

are equiangular (all right-angled) and have sides reciprocally proportional, so by VI.14 they are equal. Conversely from

a d = b c

and VI.14 (its converse) we recover the proportion.

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Depends on (1)

VI.14Proposition VI.14In equal and equiangular parallelograms the sides about the equal angles are reciprocally proportional; and equiangular…

Required by (dependents) (1)

VI.17Proposition VI.17If three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the mean;…

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