Generalised Metrical Theorems

Extract

It is well known that Euclidean metric geometry is a special case of projective geometry, inasmuch as it refers to transformations which leave the line at infinity and the circular points invariant. Every projective theorem will thus have one or more Euclidean counterparts according to which line and which points on it are taken to be the line at infinity and the circular points. It is, on the other hand, also possible to translate any theorem into projective language by removing every trace of metrical properties. A theorem of projective geometry is thus obtained of which the original theorem is a special case. This principle will be illustrated by applying it to the following elementary