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 100
erefore (VI. 2) CD isparallel to OB, and therefore the triangles ADC, ABO aresimilar, therefore AO : AG :: OB : 67), but AO, AC and OBare given lines, therefore CD the fourth proportional to them isknown (VI. 12). In like manner, if AS be cut in D in the given ratio, it isproved that CD is the… … N. B. To divide a line internally or externally in a given ratiois only a particular case of (VI. 10)* Thus, let AB be the givenline. First, for internal section, fig. 2, draw AD, and take AC,CD equal to the terms of the given ratio. Join DB, and draw CEparallel to DB. Then AB is divided in E as…
Geometry
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