Cas. 3. Let ACB [in Fig. 6.] be the refracting Surface of any Sphere whose Centre is E. In any Radius thereof EC produced both ways take ET and Ct equal to one another and severally in such Proportion to that Radius as the lesser of the Sines of Incidence and Refraction hath to the difference of those Sines. And then if in the same Line you find any two Points Q and q, so that TQ be to ET as Et to tq, taking tq the contrary way from t which TQ lieth from T, and if the Point Q be the Focus of any incident Rays, the Point q shall be the Focus of the refracted ones.
And by the same means the Focus of the Rays after two or more Reflexions or Refractions may be found.
Cas. 4. Let ACBD [in Fig. 7.] be any refracting Lens, spherically Convex or Concave or Plane on either side, and let