An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 285
=-k\ In this case the points may be said to form a bivalent range. 419. If OA, OB, OC, OB be any four rays of a pencil, theratio of sin AOG . sin BOD : sin BOG . sin AOD is called thecross ratio of the pencil 0 {AB, GD]. \i A, B, G, D be any four points on the same straight line, thepencil 0 {AB,… … For, if ON be perpendicular to the line AB, we have, ON .AB = OA . OB sin AOB.Therefore AG .BD:BG. AD = sm AOG. sin BOD : sin BOG . sin AOD. CONSTRUCTION OF A GIVEN RANGE. 269 420. Ex. 1. If {ABCD} be any range, and if the circles described on AB,CD, as diameters intersect at the angles %6, shew…
Geometry
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