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Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students (1881)

McDowell, James L · Cambridge, Deighton, Bell, and Co. · leaf 150

An illustration from Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students, 1881, leaf 150 — so that AF is half the sum of thesides, and BE half their difference (77). Therefore if AE equalsAC, BE equals FE. Draw the diameter DM, bisecting BC atright angles in G (77), and draw AN perpendicular to DM, andAF perpendicular to BC. Because FG joins the middle points ofthe sides of the triangle… … FD2 = AD.DH = ND.DG, but NG is equal to the given perpendicular AF, and FD is a givenline. Therefore also DG is a known line, and H is a fixed point.Hence the triangle DGH can be constructed. Now draw thetangent BG through G to the circle with centre A, and radiusequal to the given perpendicular,…

Geometry

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