Dr. Gregory's Elements of catoptrics and dioptrics / Translated from the Latin original, with a large supplement, by William Browne.

  • Gregory, David, 1659-1708. Catoptricae et dioptricae sphaericae elementa. English
Date:
1735
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Licence: Public Domain Mark

Credit: Dr. Gregory's Elements of catoptrics and dioptrics / Translated from the Latin original, with a large supplement, by William Browne. Source: Wellcome Collection.

    55/330 page 27
    Through A, the Centre of the Sphere, and the given Focus E, draw a right Line, meeting the Spherical Surface in B. In this take the Point C fuch, that B C may be to C A, as B E to E A. I fay C is the Focus required. Let E D be any one of the incident Rays, draw AD, CD, and produce them; draw likewife the right Line, E R, pa¬ rallel to the right Line CD. Since the Arch B D is extremely final], ED, E B, and CD, CB will be equal. Wherefore E D is to E A, as C D to C A ; that is, becaufe(DC, ER are parallel) as ER toEAj therefore the right Lines, ER, ED, and confequently the Angles, E R D, E D R are equal. But E D R is the Angle of Incidence of the Ray ED, and ERD is equal to its alternate ND A, wherefore (by Corol. 3. Fheor. 1.) DN is the reflected Ray belonging to the inci¬ dent one E D. And fince El) is taken at pleafure, it is plain that all the Rays pro¬ ceeding from E, after they are reflected from the Concave Spherical Surface, will, if they be produced backwards, meet in C, or will have their Focus in C. Q. E. 2). Corol.
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