Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 26 - 1907  

Research Article

Examples in the Geometry of Cross Ratios

Charles Tweedie

When P is joined to four points A, B, C, D coplanar with P, a pencil of four lines is formed whose cross ratio is constant if ABCD are collinear. If A, B, C, D are not in a line the cross ratio P(ABCD) has a value which in general varies with the position of P, but which should be known when P is given in position and also A, B, C, D. A simple expression for the cross ratio is given and its utility in locus problems is illustrated by a variety of simple examples, which in several cases furnish methods for constructing a general cubic curve, with or without double point, a trinodal quartic, etc.

(Revised May 08 1907)

(Received June 02 1907)