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 331
equivalent the rectangle G H x G I,together with the square of G C, the remainders, the rectangles C Ix I K and G I xl H are equal. Hence we have GI:IC=IK :IH.Therefore, in the triangles C I G and H I K the angle I is common,and the sides which include it are proportional, and therefore the… … APPENDIX III. 325 Multiplying the homologous terms we obtain, a o v : a N b c — c p c : p c c• .* ab c = a bcIf the transversal be pa-rallel to a side C, the seg-ments c c become infinite,their difference C beingfinite. They are thereforeto be considered as equal.Dividing the one productby c, and…
Geometry
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