Homographic Ranges—Elementary Principles

Extract

My object is to indicate what seem to be the fundamental ideas connected with homography which would be readily understood and appreciated by a beginner.

If a pencil of concurrent rays is cut by any transversal, the ratios between the parts into which it is divided are the same as for any parallel transversal. This is not the case when the two transversals are not parallel, and it becomes an important problem to find out what property of the segments is common to both transversals in such a case. To the Greeks, who so exhaustively studied the properties of the conic sections as sections of a cone, this problem must have presented itself quite early, and it appears that not only Pappus, but also Euclid, and therefore probably Apollonius, knew the solution.