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 184
tangent meet four fixed tangents,the anharmonic ratio of the four points of intersection iscalled the anharmonic ratio of the four tangents. 189. The anharmonic ratio of four fixed points on acircle is constant. Let ABCD be the four fixed points on the circumference, and0 or 0 any variable point on… … Let 0 pass to 0 between A and Bf and produce AO to A. The angles AOB and AOB are equal (III. 22), because AOBOis a quadrilateral in a circle. Therefore the two pencils 0. ABCDand 0. ABCD have their angles respectively equal. Therefore{O.ABCD} = {O.ABCD}, but the pencils O.ABCD and O.ABCDare really…
Geometry
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