Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre (1875)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York, Chicago [etc.] A.S. Barnes & company · leaf 47
40 KEY. Solution.—Let ABC be the given triangle. Lay off AE equal toAC, and complete the parallelogram ACFE.Draw FA cutting BC in 0; draw OP par-allel to FC, and OQ parallel to FE. From the similar triangles AFC andAOP, we have, AF : AO : : FC : OP . . . (1). From the similar triangles AFE andAOQ,… … (2)- Prop. LYI.—Show that the line drawn from the middle point ofthe base, of any triangle, through the middle point of any line of thetriangle parallel to the base, will pass through the opposite vertex, ifsufficiently produced. Demonstration.—Let ABC be any triangle, SR a line parallel tothe base…
Geometry
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