Schmall, Charles Nelson. [from old catalog] · New York, D. Van Nostrand company · leaf 39
ll rectangles of a given area, the square has the leastperimeter. Let a, and 6, be the sides of any one of the rectangles.Let X be the side of the equivalent square. Then x = s/ab.Hence we must prove 2 x <; a + 6, or 2\/ab <; a + 6.Now(a-6)2>o, .-. a2 +52^2a&, .-. a2 + 62+… … D B G Fig. 26. parallel to DE. 6 and 0 are the angles required. By Trigonometry,sin ^ : sin 0 : : BD : BE. 8. So that their tangents may have a given ratio. Take any two linesAD, DB in the given ratio. On AB describe a segment to contain an C y \ \ / y1 y^ ^~ V 1 y^ 1 y \ \ A D B Fig. 27.angle…
Geometry, Analytic
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