An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 65
l rays of the pencil. By § 84, we have KX : KX - X^ . XA: XA . XA= XB.XB:XB.XF. sinXQ.4.sinX0.4 _ sinXO.B.sinXO.Bsin XOA . sin XOA ~ sin XOB. sin XOB Therefore, since XOX is a right angle, tan XOA . tan XOA = tan XOB. tan XOB.therefore OX, OX are the principal rays. To find the double rays, draw… … Similarly we may prove that tan^ XOS = tan XOA . tan XOA. Hence, OS, OS are the double rays of the pencil. The double rays will be real or imaginary according as K lieswithout or within the circle; that is according as AA intersectsBB without or within the circle. 87. We infer from the above…
Geometry
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