Euclid,

Catoptrics (Mirrors)19©

translated by Henry Mendell (Cal. State U., L.A.)

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Prop. 19: In plane mirrors the right parts appear left and the left parts right and the image is equal to the thing seen, and the distance from the mirror is equal.

(diagram 1) Let there be a plane mirror, AG, and eye, B, and sight-lines, BA, BG reflected to E, D, and let there be a thing-seen, ED, (diagram 2) and from E, D to the mirror let perpendiculars be drawn, EZ, DQ, and let them be extended, (diagram 3 = gen. diag.) and let sight-lines BG, BZ also be extended and let them fall-together with perpendiculars at K, L, and let AK be joined. Accordingly, E appears on K and D on L. For this was shown earlier. Therefore, the left parts appear right and the right parts left. (diagram 4) And since the angle by KGZ is equal to that by ZGE, and those at Z are right, (diagram 5) ZK would then also be equal to ZE. (diagram 6) For the same reasons, also DQ to QL. (diagram 7) Therefore, the distance which ED is apart from mirror ED is equal to that which image KL is apart. And thing-seen ED is equal to image KL due to EZ being equal to ZK and DQ to QL, while a common, QZ, is also at right angles.