An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 66
Show that any two pencils in involution have in general one andonly one pair of conjugate rays which are parallel; and show how to constructthese rays. PROPERTIES OF A PENCIL IN INVOLUTION. 49 Ex. 3. Show that the straight line joining the feet of the perpendicularsdrawn to a pair of conjugate rays… … Let any circle be drawn passing through 0, cutting the rays ofthe pencil in the points A, A, B, B, G, C. Then by § 85, AA,BR, CC will meet in the same point K. By § 84, we have KA :KA^AB.AF: AB. AB,= AG.AC:AG.AC.Therefore AB. AB: AB. AB = AG. AG: AG. AG.But if R be the radius of the circle. 2iJ= .…
Geometry
Internet Archive · Cornell University Library · Public Domain Mark 1.0. Free to use for anything.
