Elements of geometry and trigonometry . scribed in a circle^ the rectangle of thetwo diagonals is equivalent to the stLtn of the rectangles of theopposite sides. In the quadrilateral ABCD, we shall - + Take the arc CO=AD, and draw BOmeeting the diagonal AC in I. The angle ABD = CBI, since the onehas for its measure half of the arc AD,and the other, half of CO, equal to AD ;the angle ADB = BCI, because they areboth inscribed in the same segmentAOB ; hence the triangle ABD is similarto the triangle IBC, and we have theproportion AD : CI : : BD : BC ; hence ^
Elements of geometry and trigonometry . scribed in a circle^ the rectangle of thetwo diagonals is equivalent to the stLtn of the rectangles of theopposite sides. In the quadrilateral ABCD, we shall - + Take the arc CO=AD, and draw BOmeeting the diagonal AC in I. The angle ABD = CBI, since the onehas for its measure half of the arc AD,and the other, half of CO, equal to AD ;the angle ADB = BCI, because they areboth inscribed in the same segmentAOB ; hence the triangle ABD is similarto the triangle IBC, and we have theproportion AD : CI : : BD : BC ; hence ^, the triangle ABl is similar to the triangle BDC ; for thearc AD being equal to CO, if OD be added to each of them,we shall have the arc AO=:DC ; hence the angle ABI DBC ; also the angle BAI to BDC, because they are in-scribed in the same segment ; hence the triangles ABI, DBC,are similar, and the homologous sides give the proportion AB :BD : : AI : CD ; hence Adding thetwo results obtained, and observing that. + =^ (AI + CI).BD=, we «hall have + 113 M GEOMETRY.
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
