Reflection geometry: incident line and reflected ray
Fold-and-reverse constructions proving the angle of incidence equals reflection
Two related constructions work out the law of reflection by folding and reversing triangles. In the first, a b and b c face each other; a is carried reversed onto c while b stays as a pole, so the angle of incidence t is cut below S and shown equal to the reflected angle S, and so on successively with b onto d, c onto e, d onto f. In the second, a b c is the first cut, d c the incident line and c a the reflected ray, and an angle at o equal to n is built by reversing a b c onto the site c a d e. Curved reflectors met by fans of converging rays are drawn above, and further untranscribed text on other topics fills the sheet.
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Incidence equals reflection by reversal
a b and b c face one another; a passes reversed into c while b remains as a pole, so a n b rests upon a c g b. The angle t is then cut below S, whence the angle of incidence t equals the reflected angle S, and b rests upon d, c upon e, d upon f successively.
Constructing the reflected ray
a b c is the first cut, from which d c is the incident line and c a the reflected ray. One must make an angle at o equal to n by reversing a b c and setting it in the site c a d e, keeping the line a n over d o, then drawing a c and a e on the base c d.
Curved reflectors and converging rays
Above the text are curved reflecting arcs met by fans of straight rays, with smaller squared and triangular constructions worked out at the left margin.