Davies, Charles, 1798-1876 · New York and Chicago, A. S. Barnes and company · leaf 97
lso proportional to the partsAD, AE, or to BD, CE. For, by composition (Bk. III. Th. vii), we have AD+BD : BD :: AE+EC : EC.Then, by alternation (Bk. 111. Th. iv).AB : AC : : BD : EC, hence, also, AB : AC : : AD : AE 96 G EOMETRY. Proportions of T riant: lei THEOREM XIV. A line which bisects the… … For, draw BE parallel toCD and produce A C to E. Then, since CB cuts the two B D A parallels CD, EB, the alternate angles BCD and CBE areequal (Bk. I. Th. xii) : hence, CBE is equal to angle A CD. But, since AE cuts the two parallels CD, BE, the angleACD is equal to GEB (Bk. I. Th. xiv):…
Geometry · Plane trigonometry
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