Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

XVI
INTRODUCTION
indissoluble permanency of unperverted manners, and of the
mutation of the best polities, into such as are irrational and
full of perturbation. Again, the mathematical science perfects
us in ethical philosophy, inserting in our manners, order, and
an elegant life, and delivering those figures, melodies, and
motions, which are adapted to virtue, and by which the Athenian
guest in Plato wishes those to be perfected who are designed
to possess ethical virtue from their youth. It likewise places
before our view the principles of the virtues, in one way indeed
in numbers, but in another in figures, and in another in
musical symphonies, and exhibits the excesses and deficiencies
of the vices, through which we are enabled to moderate and
adorn our manners. On this account also Socrates, in the
Gorgias, accusing Callicles of an inordinate and intemperate
life, says to him, "You neglect geometry, and geometric equality."
But in the Republic, he discovers the interval between
tyrannic and kingly pleasure, according to a plane and solid
* The passage alluded to by Proclus is in the 9th book of the Republic, and is
as follows: "What then, said I, shall we boldly say concerning all the pleasures,
both respecting the avaricious and the ambitious part of the soul, that such of them
as are obedient to science and reason, and, in conjunction with these, pursue and
obtain the pleasures of which the prudent part is the leader, shall obtain the
truest pleasures, as far as it is possible for them to attain true pleasure, and in
as much as they follow truth, pleasures which are properly their own; if indeed
what is best for every one, be most properly his own? But surely, it is most
properly, said he, his own. When then the whole soul is obedient to the philosophic
part, and there is no sedition in it, then every part in other respects performs
its proper business, and is just, and also reaps its own pleasures, and such
as are the best, and as far as is possible, the most true. Certainly, indeed. But
when any of the othcrs govern, it happcns that it ncithcr attains its own plcasurcs,
and it compels the other parts to pursue a pleasure foreign to them, and not at all
tnre. It does so, said he. Do not then the parts which are most remote from
philosophy and reason, most especially effectuate such things? Very much so.
And is not that which is most remote from law and order, likewise most remote
fm reamn? It plainly is. And have not the amorous, and the tyrannical desk
appeared to be most remw from law and order? Extremely so. And the royal
and the moderate ones, thc least remote? Yes. The tyrant, then, I think, shall
be tht mw moat from true pleasure, and such as is most properly his own, and