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date: 01 December 2022



  • Wilbur R. Knorr
  •  and Alexander Jones


Catoptrics, a special field of *optics, is properly the geometric theory of the visual appearances of objects seen under reflection (anaklasis), but among the ancients also includes studies of refraction (diaklasis) and of burning mirrors (pyria). The basic principle that rays are reflected at equal angles is already understood in the 4th cent. bce (cf. Pl. Ti. 46ac; Arist. [Pr.] 16. 13). The earliest extant compilation of catoptrical theorems is *Euclid's Catoptrica (early 3rd cent. bce), a text whose authenticity is sometimes doubted. Euclid proves theorems on the location, size, and orientation of images in plane, convex, and concave mirrors, and proposes a false theorem on the convergence of rays in concave spherical mirrors. A version of some of the Euclidean results, with additional descriptions of deployments of trick mirrors, is in a work, extant only in a medieval Latin translation and misattributed to Ptolemy (4), but usually (though doubtfully) now ascribed to *Heron of Alexandria (mid-1st cent.


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