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 78
is the required square. Demonstration. Because AD is a parallelogram (const.), and the angle A aright angle, the angles C, D, and B are also right (153) ; and be-cause AC is equal to AB (const.), and the sides CD and DBare equal to AB and AC (XXXIV), the four sides AB, AC,CD, D B are equal,… … On the sides AB, AC, and BC describe the squares AX,A F, and B I, and draw B E parallel to eitherC F or A D, and join B F and A I. Because the angles ICB and ACFareequal, if BCAbe added to both, the anglesI C A and B C F are equal, and the sides I C,C A are equal to the sides B C, C F, thereforethe…
Geometry
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