Modern geometry . ?. Cross-ratio of a pencil of parallel lines. If the vertex of a pencil retreats to infinity, the rays becomeparallel, and the angles of the pencil become zero. By theprinciple of continuity, we may be assured that all transversalsstill cut the pencil in equicross ranges; this property is, however,obvious from the fact that any two transversals are dividedsimilarly by a pencil of parallel lines. The angles of the pencil being zero, it would not appear, atfirst sight, that the ordinary definition of the cross-ratio of apencil has no application to this case. This difficulty ma
Modern geometry . ?. Cross-ratio of a pencil of parallel lines. If the vertex of a pencil retreats to infinity, the rays becomeparallel, and the angles of the pencil become zero. By theprinciple of continuity, we may be assured that all transversalsstill cut the pencil in equicross ranges; this property is, however,obvious from the fact that any two transversals are dividedsimilarly by a pencil of parallel lines. The angles of the pencil being zero, it would not appear, atfirst sight, that the ordinary definition of the cross-ratio of apencil has no application to this case. This difficulty may beavoided by defining the cross-ratio of a pencil of parallel lines asthe cross-ratio of the range in which any transversal cuts thepencil. We may use the property Lt ——- = 1 to illustrate the case of a pencil of parallel lines. For suppose that a circle be drawn with centre O so thatthe pencil intercepts arcs AB, BC, CD. A
Size: 1743px × 1433px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauth, bookcentury1900, bookdecade1900, bookidcu31924001083090
