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 54
angleABD; draw the line DCE, which is thecommon bisectrix of the angles D and C. On DE, as a diameter, draw a semi-circle DFE, and from C erect the line CFperpendicular to DE; draw EF; andfrom E, as a centre, with EF as a radius,draw the arc FG-, cutting DE in G;through G, draw GP and GQ, parallel… … 48 KEY. From (1) and (2), we have, EG : EC : : EB : EP, or EG x EP = EC x EB; but, EG x EP is equal to the area of the equilateral triangle QGP,and EC x EB is equal to the area of the isosceles triangle ACB;hence, QGP is the required triangle. Prop. LXVI.—In a triangle ABC let two lines be drawn…
Geometry
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