. Geometry : the elements of Euclid and Legendre simplified and arranged to exclude from geomtrical reasoning the reductio ad absurdum : with the elements of plane and spherical trigonometry, and exercises in elementary geometry and trigonometry / /c By Lawrence S. Benson. + EXERCISES. 225. dicnlar and CF parallel to BD, and DGH perpendicular andBH parallel to AC. Then, because EF is equal to the perpen-dicular drawn from C to BI), and GH equal to the one drawnfrom B to AC; it would be prov-ed as before, that AP\AIv = + , and I) = + Hence, : , or (V
. Geometry : the elements of Euclid and Legendre simplified and arranged to exclude from geomtrical reasoning the reductio ad absurdum : with the elements of plane and spherical trigonometry, and exercises in elementary geometry and trigonometry / /c By Lawrence S. Benson. + EXERCISES. 225. dicnlar and CF parallel to BD, and DGH perpendicular andBH parallel to AC. Then, because EF is equal to the perpen-dicular drawn from C to BI), and GH equal to the one drawnfrom B to AC; it would be prov-ed as before, that AP\AIv = + , and I) = + Hence, : , or (V. l) AF :DII :: ^ : + But the triani^lesAFC, DIIB are equiangular, liav-in<x the rio;ht anojes Fand H, andthe angles ACF, DBH, each equal(I. 16) to ALD; therefore (V. 3) AF : AC : : DH : DB, and alternately AF : T3IT : : AC :DB. Hence (IV. 7) the foregoing analogy becomes AC : BD: : + : Wherefore, thediagonals, etc. Scho. From this proposition and the last, when the sides ofa quadrilateral inscribed in a circle are given, we can find theratio of the diagonals and their rectangle, and thence (V, 15)the diagonals themselves. Also, if the sides be given in num-bers, we can compute the diagonals. Thus, let the sides takenin succession round
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
