It is very singular to notice how small a matter makes the difference between the intelligibility and unintelligibility of a demonstration to an audience as a whole not mathematical. In no part of Physics have I found this so marked as in the most elementary portions of geometrical optics. Such a formula as

when interpreted directly as signifying that “the sum of the reciprocals of the distances of the object and image from the surface of a concave spherical mirror, is equal to double the reciprocal of the radius of the mirror,”. if understood at all, is understood as a sort of memoria technica which enables the student to make calculations; but unless he have some knowledge of mathematics it suggests absolutely no higher meaning.