On a Group of Parabolas associated with the Triangle

§1. The general theorem underlying the subject of this paper is as follows:—If through c1, c2, c3, … points on AB, a side of ΔABC, rays be drawn from two vertices O1, O2, the former meeting AC in b1, b2b3, …, and the latter meeting BC in a1, a2, a3, …, then the lines a1b2, a2b2, … envelope a conic touching the sides AC and BC. This follows since the ranges a1a2a3 …, b1b2b3 …, are homographic.