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 103
s, to twice the square onOD (I. 47). Therefore the square on OC is equal to the excess of twice thesquare on the radius OD over the square on the given line OA ;therefore OC is known, and therefore the required locus is a circleconcentric with the given circle. 109. Through a given point within a… … Draw PD parallel to any side AB, meetingthe other side of the given angle in D. MakeAD : DC in the given ratio. Join CP, andproduce CP to meet AB in B. Then BC isthe required line. Because PD is parallel to AB a side ofthe triangle ABC, therefore (VI. 2) BP : PC :: AD : DC,that is, in the given…
Geometry
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