Advanced geometry for high schools : synthetic and analytical (1919)
McDougall, A. H. (Alexander Hiram), 1859-1946 · Toronto : Copp, Clark · leaf 33
Note.—Ptolemy, a native of Egypt, flourished in Alexandria inA.l>.) SYNTHETIC GEOMETRY 16. The sum of the rectangles contained by theopposite sides of a quadrilateral is not less than therectangle contained by the diagonals. ABCD is a quadrilateral,AC, BD its diagonals. Required to show thatAB.… … ABBE ACCD From the similar As BAC,BC EDAC ~ AD id .*. BC EAD,AD = AC . ED. Consequently AB . CD + BC . AD = AC (BE 4- ED)but BE + ED is not < BD;.*. AB , CD 4 BC . AD is not < AC . BD, EXERCISES 21 J&^l 17.—Exercises (a) 1. If the exterior vertical Z A of A ABC be bisected bya line -which…
Geometry · Geometry, Analytic
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