Of this I now design to give a notable Instance in the Doctrine of Dioptricks.
This Dioptrick Problem is that of finding the Focus of any sort of Lens , exposed either to converging, diverging, or parallel Rays of Light, proceeding from, or tending to a given Point in the Axis of the Lens , be the Ratio of Refraction what it will, according to the Nature of the transparent Material whereof the Lens is formed, and also with allowance for the thickness of the Lens between the Vertices of the two Spherical Segments. This Problem being solved in one Case, mutatis mutandis , will exhibit Theorems for all the possible Cases, whether the Lens be Double-Convex or Double-Concave , Plano-Convex , or Plano-Concave , or Convexo-Concave , which sort are usually call'd Menisci . But this only to be understood of those Beams which are nearest to the Axis of the Lens , so as to occasion no sensible difference by their Inclination thereto; and the Focus