Davies, Charles, 1798-1876 · New York and Chicago, A. S. Barnes and company · leaf 96
BOOK IV. 95 Of Triangle Sides cut Proportionally.THEOREM XIII. If a line be drawn parallel to the base of a triangle, it will dividethe other two sides proportionally. Let ABC be any triangle, and DE astraight line drawn parallel to the baseBC: then will AD : DB : : AE : EC. … For, draw BE and DC. Then, thetwo triangles BDE and DCE have thesame base DE, and the same altitude, B C since their vertices B and C, lie in the lin< BC parallel toDE : hence, they are equivalent (Th. ii). Again, the triangles ADE and BDE, ha\e a common ver-tex E, and the same altitude;…
Geometry · Plane trigonometry
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