The philosophical and mathematical commentaries of Proclus on the first book of Euclid's elements (Vol. 1 of 2) : $b To which are added, A history of the restoration of Platonic theology, by the latter Platonists: And a translation from the Greek of Proclus's Theological elements — Plato — John Shaqi
The philosophical and mathematical commentaries of Proclus on the first book of Euclid's elements (Vol. 1 of 2) : $b To which are added, A history of the restoration of Platonic theology, by the latter Platonists: And a translation from the Greek of Proclus's Theological elements
Plato · en
things.” He then subjoins the following instance of the difficulty
attending such an undertaking: “There are three things (says he),
from which science must necessarily be produced; but the fourth is
science itself. And it is requisite to establish the fifth as that
which is the object of knowledge, and has a true existence. One of
these is the name of a thing; the second its definition; the third
the resemblance; the fourth science. Now take each of these, desiring
to learn what we have lately asserted, and think concerning them all,
in a similar manner. A circle is called something, whose _name_
we have just expressed. After this follows its definition, composed
from nouns and verbs. For that which every where is equally distant
from the extremes to the middle, is the definition of that which we
signify by the name of a round, and a circumference, and a circle. But
the third is the circle which may be painted, or blotted out, which
may be made by a wheel, or destroyed. None of which affections, the
circle itself, which each of these respects, suffers, as being of a
different nature. But the fourth is science, and intellect, and true
opinion about these. And this again must be established as one whole,
which neither subsists in voice, nor in corporeal figures, but in
intellect and intelligence. It is therefore manifest, that this fourth
is different from the nature itself of the circle, and again different
from the three we have previously mentioned. But among the number of
these, intellect, by its relation and similitude, proximately adheres
to the fifth, while the rest are more remote from its nature. The same
may likewise be affirmed of a straight and crooked figure, of colour,
and of the good, the beautiful, and the just. And again, of every
body, whether fashioned by the hand, or the work of nature, whether
fire or water, and the rest of this kind; likewise of every animal,
and the manners of animals; and of all actions and passions. For
unless, among these, some one, after a manner, receives that fourth,
he will never perfectly participate the science about the fifth.” He
then proceeds to shew in what respect each of the preceding four are
different from the fifth. “Every circle (says he) which by the hands
of men is either painted, or fashioned by a wheel, is plainly contrary
to our fifth. For it every where participates of the right-line. But
we must affirm, that the circle itself has neither more nor less of
any thing whatever; that is, it possesses in itself, nothing of a
contrary nature. Besides, none of these are endued with any stability
of name. For nothing hinders our applying the appellation of straight
to that which we now denominate round, and calling the straight by
the denomination of the round; nor will there be any less stability
in these, when their names are changed into the contrary. The same
reasoning is likewise true of definition, since it is composed from
nouns and verbs, which possess no stability.