Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids : to which are added, Elements of plane and spherical geometry (1826)
Playfair, John, 1748-1819, Euclid · Philadelphia : Marot & Walter · leaf 126
s ABC, DEF have the angle BAC in the one equalto the angle EDF in the other, and the sides about those angles pro^portionals; thatis,BAtoAC,asEDtoDF; the triangles ABC, DEFare equiangular, and have the angle ABG equal to the angle DBF,and ACB to DFE. At the points D, F, isthe straight line DF,… … 126 ELEMENTS the triangle ABC is equiangular to the triangle DGF; and thereforeBA : AC :: GD (4. 6.): DF. But by hypothesis,BA : AC :: ED : DF; and therefore ED : DF :: GD : (11.5.) DF; wherefore ED is equal (9. 5.)toDG: and DF is common to the two triangles EDF, GDF: there-fore the two sides ED,…
Euclid's Elements · Geometry · Trigonometry
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