The first six books of the elements of Euclid : with a commentary and geometrical exercises ; to which are annexed a treatise on solid geometry, and short essays on ancient geometrical analysis, and the theory of transversals (1861)
Lardner, Dionysius, 1793-1859 · London : Print. for Taylor and Walton · leaf 222
et the other be c : d, and let c : d =■ b : x, then a : b\ (a : b\ But (hyp.) a : x is a ratio of equality, *. * x := a. Hence b : x is thereciprocal of a : 6, and •. • c : d is the reciprocal of a : b. (599) By (519) it was proved that triangles and parallelograms are ina ratio compounded of their… … BOOK THE SIXTH. 203 Hence the sides of equal rectangles are four proportionals, the meansbeing the sides of one and the extremes of the other, and vice versa therectangle under the means is equal to the rectangle under the ex-tremes. Thus the sixteenth proposition follows immediately from thefirst.…
Geometry
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