the ſimilitude of the triangles EAF, ELI, ECH, EBG) AF is to LI as CH to BG. Likewiſe from the nature of the conic ſections, LI (or CK) is to CD as CD to CH; and therefore ex æquo perturbate) AF is to CD, as CD to BG. Q. E. D.
Cor. 1. Hence if two tangents FG, PQ meet two parallel tangents AF, BG in F and G, P and Q and cut one the other in O; AF (ex æquo pertubate) will be to BQ as AP to BG, and by diviſion, as FP to GQ and therefore as FP to OG.
Cor. 2. Whence alſo the two right lines PG, FQ drawn through the points P and G, F and Q, will meet in the right line ACB, paſſing through the centre of the figure and the points of contact A, B.
Lemma XXV.
If four ſides of a parallelogram indefinitely produced touch any conic ſection, and are cut by a fifth tangent; I ſay, that taking thosſe ſegments of any two conterminous ſide which is intercepted between the point of contact and the third ſide, is to the other ſegment. Pl. 11. Fig. 4.
Le the four ſides ML, IK, KL, MI of the parallelogram MLIK touch the conic ſection in
