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 16
des of the given parallelogram. \ , Demonstration.—Let ABCD be any parallelogram, and let AS>BS, CR, and DR be the bisectrices of itsangles. Draw the diagonals PQ, RS, andprolong DA and BC to meet the bisec-trices CR and AS, in L and T. Because AS and BS are the bisec-trices of the angles A and… … 10 KEY. that each of the angles SQR, QRP and EPS is a right angle; hence,PRQS is a rectangle. Because DE and BK are parallels included between parallels, theyare equal to each other (Bk. I. Prop. 28, Cor. 1). Since AP bisects theangle DAE and is perpendicular to DE, it divides the latter line…
Geometry
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