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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 49

An illustration from Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre, 1875, leaf 49
he line through A and P is thethird median of the given triangle. Hence, the three medians passthrough P, which was to be proved. Prop. LVIII.— On the sides AB and AC of any triangle ABC,construct any two parallelograms ABDE and ACFG; prolong thesides DE and FG till they meet in H; draw HA, and on… … 42 KEY. Demonstration.—Let ABC be any triangle; Let AD and AF beany parallelograms constructed on AB andAC as sides; and let H be the point inwhich DE and FG meet, when prolonged;let CP be a parallelogram whose sides BPand CQ are parallel and equal to HA. Draw HA, and prolong it to S; alsoprolong…

Geometry

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