What do you think? Should not philosophers make all these problems subjects of research and inquiry and in solitary study look into mirrors of every kind, liquid and solid? There is also over and above these questions further matter for discussion. For instance, why is it that in flat mirrors all images and objects reflected are shown in almost precisely their original dimensions, whereas in convex and spherical mirrors everything is seen smaller, in concave mirrors on the other hand larger than nature? Why again and under what circumstances are left and right reversed? When does one and the same mirror seem now to withdraw the image into its depths, now to extrude it forth to view? Why do concave mirrors when held at right angles to the rays of the sun kindle tinder set opposite them? What is the cause of the prismatic colours of the rainbow, or of the appearance in heaven of two rival images of the sun, with sundry other phenomena treated in a monumental volume by Archimedes of Syracuse, a man who showed extraordinary and unique subtlety in all branches of geometry, but was perhaps particularly remarkable for his frequent and attentive inspection of mirrors.

If you had only read this book, Aemilianus, and, instead of devoting yourself to the study of your fields and their dull clods, had studied the mathematician’s slate and blackboard, believe me, although your face is hideous enough for a tragic mask of Thyestes, you wo............