Being given a fixed line (the directrix) and two fixed points S, s (Fig. 15), then, if z and Z are two points on the directrix, the lines zp and ZP are said to correspond if zp be parallel to SZ and 8zsz be parallel to ZP.

Theorem 1. If pairs of corresponding lines meet in p and P respectively, then sp is parallel to SP ; and, if any line goes through p, the corresponding line goes through P.