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 183
po int. 188. If two circles cut one another orthogonally, anystraight line drawn through the centre of either and meetingboth circles is cut harmonically by the two circumferences. 154 EXERCISES ON EUCLID [189. Let the two circles whose centres are 0 and 0 cut orthogonallyat E. Then shall any… … Because 0E0 is a right angle (hyp.), therefore (III. 16) OEis a tangent to the circle CED, and therefore (III. 36) OG. OD= OE2 = OB2. Therefore (163) A, C, B, D form an harmonic range. Q. E. D. N. B. The converse is also true, viz. If a line be cut harmonic-ally, any circle through one pair of…
Geometry
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