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 140
or alternately, AB : BD :: BE : BC; but the angles ABD and CBE are equal, therefore (YI. G) the tri-angles ABD and CAE are similar, and therefore AD : BD :: CE : BC, therefore AD.BC = BD.CE. Therefore the sum of the rectangles under the opposite sidesis equal to the rectangle under BD and the sum… … 112 EXERCISES ON EUCLID [149. Cor. Hence, if the rectangle under the diagonals of a quadri-lateral is equal to the sum of the rectangles under the oppositesides, it is circumscribable by a circle; for if it be not circum-scribable, the rectangle under its diagonals will be less than thesum of the…
Geometry
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