Practical plane and solid geometry for advanced students, including graphic statics, adapted to the requirements of the South Kensington syllabus (1899)
Harrison, Joseph, Baxandall, George Albert · London Macmillan · leaf 50
is bisected, the pencil is harmonic. Thus if OC bisect any angle A OB, and OD be taken perpendicularto OC, the pencil is harmonic because any transversal parallel to ODor OC is bisected. A cotnplete quadrilateral affords an example illustrating harmonicpencils. See the figure. Let the diagonals of… … Examples.—1. Take a and b each double the length given in thefigure above, and find the harmonic mean k. 2. Find the arithmetical mean r, and the geometrical mean e; between a and b, and vertify the theorem that /-, g, and /• are ingeometrical progression. 3. Draw any complete quadrilateral…
