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Elements of geometry and trigonometry (1835)

Legendre, A. M. (Adrien Marie), 1752-1833, Brewster, David, Sir, 1781-1868, Davies, Charles, 1798-1876 · New York, Wiley & Long · leaf 120

An illustration from Elements of geometry and trigonometry, 1835, leaf 120
of AO, r/o,the radii of thecircumscribed circles, or as the squares of OD, of/, the radii ofthe inscribed circles. PROPOSITION XI. THEOREM. The (ti( urnjrrrmr.s ijj <[/(irs (tic ta Idch other as thr.ir radiifand the areas are to each other as the squares of their radii. ^Wf| 120 GEOMETRY Let us… … Inscribe within the circles two reguJar polygons of the samenumber of sides. Then, whatever be the number of sides,their perimeters will be to each other as the radii CA and OB(Prop. X.). Now, if the arcs subtending the sides of the polygons be continually bisected, until the number of sides of…

Trigonometry · Geometry

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