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[18arg] Some interesting and instructive remarks about that part of Geometry which is called “Optics”; of another part called “Harmony,” and also of a third called “Metric.”

A PART of Geometry which relates to the sight is called ὀπτική or “Optics,” another part, relating to the ears, is known as κανονική or “Harmony,” which musicians make use of as the foundation of their art. These are concerned respectively with the spaces and the intervals between lines and with the theory of musical numbers.

Optics effect many surprising things, such as the appearance in one mirror of several images of the same thing; also that a mirror placed in a certain position shows no image, but when moved to another spot gives reflections; also that if you look straight into a mirror, your reflection is such that your head [p. 189] appears below and your feet uppermost. 1 This science also gives the reasons for optical illusions, such as the magnifying of objects seen in the water, and the small size of those that are remote from the eye.

Harmony, on the other hand, measures the length and pitch of sounds. The measure of the length of a tone is called ῥυθμός, or rhythm of its pitch, μέλος, or “melody.” There is also another variety of Harmony which is called μετρική, or “Metric,” by which the combination of long and short syllables, and those which are neither long nor short, and the verse measure according to the principles of geometry are examined with the aid of the ears. “But these things,” says Marcus Varro, 2 “we either do not learn at all, or we leave off before we know why they ought to be learned. But the pleasure,” he says, “and the advantage of such sciences appear in their later study, when they have been completely mastered; but in their mere elements they seem foolish and unattractive.” 3

1 The first effect is produced when the surface of a mirror is divided into numerous smaller mirrors. Pliny, N. H. xxxiii. 129, describes cups, the interior of which was so fashioned as to give numerous reflections. The second is described (e.g.) in Pausanias viii. 37. 7. The third is produced when one looks into a concave mirror from a certain distance. Magic mirrors of various kinds and properties were known in antiquity, as well as divination by means of mirrors. See Trans. Numais. and Ant. Soc. of Phila., 1910, pp. 187 ff.

2 p. 337, Bipont.

3 Cf. xvi. 8. 15 ff.

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