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 171
salsPAC, PBD. Join PO, meeting the givenlines in E and F. Because the trianglesDOC and AOB are similar, therefore DO : OA :: CD : AB, but the trianglesDOFand AOEare similar, therefore DO : OA :: FO : OE. Therefore FO : OE :: CD : AB. Also, because CD and AB are parallel, CD : AB :: DP : PB :: FP :… … Fig. 3- 179.] AND IN MODERN GEOMETRY. 143 N.B. In finding the locus of 0, when the two given lines areparallel, we have proved the case of (169), in which one of thelines joining the points of intersection of two sides is parallel tothe third side of the triangle. For the three lines drawn through…
Geometry
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