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 44
ertex, on the other side of the line. Solution.—Let P be the given point and ABC the given triangle. Draw the median AD, and on itlay off DO == £DA; draw PO, andprolong it till it meets DC prolonged,in S; upon this line let fall the per-pendiculars CG, AF, DK and BE. Because D is the middle of… … 38 KEY. whence, by composition SC : SC + SB : : CG : CG + BE . . . (3). From the similar triangles SCG and SDK, we have SC : SD : : CG : DK . . . (4). Because the antecedents in (3) and (4) are equal, each to each,we have, SC + SB : SD : : CG + BE : DK . . . (5). But, SC + SB = 2SD, hence, CG + BE…
Geometry
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