• MATHEMATICAL ‘ARTS’ 
309 
(ardd/xr]) and ‘ a certain elaborate npoa-aydyiov ’ (1 approxi 
mator). The art of weighing, he says, 1 ‘ is concerned with 
the lieavier and lighter weight ’, as ‘ logistic ’ deals with odd 
and even in their relation to one another, and geometry with 
magnitudes greater and less or equal; in the Protagoras he 
speaks of the man skilled in weighing 
‘ who puts together first the pleasant, and second the painful 
things, and adjusts the near and the far on the balance ’ 2 ; 
the principle of the lever was therefore known to Plato, who 
was doubtless acquainted with the work of Archytas, the 
reputed founder of the science of mechanics, 3 
(a) Optics. 
In the physical portion of the Timaeus Plato gives his 
explanation of the working of the sense organs. The account 
of the process of vision and. the relation of vision to the 
light of day is interesting, 4 and at the end of it is a reference 
to the properties of mirrors, which is perhaps the first indica 
tion of a science of optics. When, says Plato, we see a thing 
in a mirror, the fire belonging to the face combines about the 
bright surface of the mirror with the fire in the visual current; 
the right portion of the face appears as the left in the image 
seen, and vice versa, because it is the mutually opposite parts 
of the visual current and of the object seen which come into 
contact, contrary to the usual mode of impact. (That is, if you 
imagine your reflection in the mirror to be another person 
looking at you, his left eye is the image of your right, and the 
left side of his left eye is the image of the right side of your 
right.) But, on the other hand, the right side really becomes 
the right side and the left the left when the light in com 
bination with that with which it combines is transferred from 
one side to the other; this happens when the smooth part 
of the mirror is higher at the sides than in the middle (i. e. the 
mirror is a hollow cylindrical mirror held with its axis 
vertical), and so diverts the right portion of the visual current 
to the left and vice versa. And if you turn the mirror so that 
its axis is horizontal, everything appears upside down. 
1 Charmides, 166 B, 2 Protagoras, 356 B. 
3 Diog. L. viii. 88, 4 Timaeus, 45 b-46 c.