**Euclid, Optics, Prop. 47**©- translated by Henry Mendell

Vignettes of Ancient Mathematics |

There are certain locations, such that when the eye is placed at them unequal magnitudes put together at the same point will appear equal to each of the unequal lines.

For let BG be larger than GD, and about BG, GD let there be inscribed semicircles and about the whole BD. And so the angle in semicircle BAD is equal to the angle in BKG. For each of them is right. Therefore BG appears equal to BD. In the same way, BD also to GD when the equals are placed on each of semicircles BAD, GZD. Therefore there are certain locations, such that when the eye is placed at them unequal magnitudes put together at the same point will appear equal to each of the unequal lines.