Smart, Edward Howard · London : Macmillian and Co. · leaf 221
pointsto any fifth point not collinearwith the other four points. A pencil of four concurrent rays,taken in a given order, has a cross-ratio equal to that of the rangedetermined by cutting these raysby any transversal not concurrentwith the other four rays. Eanges or Pencils which have the same… … Fig. 100. Draw the transversal XBY parallel to the ray d.Then, by §4, {ABCD} = {XBYx}- But Yoo : = 1, Xx . YB XBhence {ABCD} Xco ■ ^ YB This form is useful for constructing ranges and pencils having a given cross-ratio, and also for quickly determining the sign of a given cross-ratio. For in the…
Geometry, Projective
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
![An illustration from Works. Popular edition.] 2 series (1886)](https://img.insideoutlibrary.com/img/200/bl-bl_003191336_9-290-1.webp)
