A treatise on special or elementary geometry (1877)
Olney, Edward, 1827-1887, Olney, Edward, 1827-1887. Elements of trigonometry, plane and spherical · New York : Sheldon · leaf 166
onsequently similar. To prove that the sides opposite theequal angles are proportional, place thetriangle DEF upon ABC, so that F shallcoincide with its equal C, CE=FE, andCD=FD. Draw AE, and DB. Since angle CED=CBA, DE is parallel toAB,and as the triangles DEA and DEB have a common base DE and… … Fig. 231. For like reason CDE : DEA : : CD : DA.CDE : DEB : : CE : EB. Then, since DEA and DEB are equivalent, the two proportions have a com-mon ratio, and we may write CD : DA : : CE : EB. By composition CD: CD+ DA : : CE : CE + EB, or CD : CA : : CE : CB, or FD : CA : : FE : CB. In a similar…
Geometry · Trigonometry
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