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 elementsProclus
Philosophy
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
Proclus
Euclid. Elements; Platonists
the right line is the more simple; for in this, dissimilitude cannot
be conceived, even in opinion. But in the circular line, the concave
and the convex, indicate dissimilitude. And a right line, indeed, does
not infer a circumference according to thought; but a circumference
brings with it a right line, though not according to its generation,
yet with respect to its centre. But what if it should be said that a
circumference requires a right line to its construction! For if either
extreme of a right line remains fixt, but the other is moved, it will
doubtless describe a circle, whose centre will be the abiding extreme
of the right line. Shall we say that the generator of the circle is
the point which is carried about the abiding point, but not the right
line itself? For the line only determines the distance, but the point
composes the circular line, while it is moved in a circular manner:
but of this enough. Again, a circumference appears to be proximate to
bound, and to have the same proportion to other lines, as bound to the
universality of things. For it is finite, and is alone among simple
lines perfective of figure. But a right line is proximate to infinity;
for its capacity of infinite extension never fails: and as all the
rest are produced from bound and infinite, in the same manner from the
circular and right line, every mixt genus of lines is composed, as
well of planes as of those which consist in solid bodies. And on this
account, the soul also[143] previously assumed into herself the right
and circular according to her essence, that she might moderate all
the co-ordination of infinite, and all the nature of bound, which the
world contains. By a right line, indeed, constituting the progression
of these principles into the universe; but by a circular line, their
return to their original source: and by the one, producing all things
into multitude; but by the other, collecting them into one. And not
only the soul, but he also who produced the soul, and endued her
with these powers, contains in himself both these primary causes.
For when he previously assumed the beginning, middle, and end of all
things, he terminated right lines (says Plato[144]), by a circular
progression according to nature. And proceeding to all things by
provident energies, and returning to himself, he established himself,
says Timæus, after his own peculiar manner. But a right line is the
mark or symbol of a providence, indeclinable, incapable of perversion,
immaculate, never-failing, omnipotent, and present to all beings, and
to every part of the universe. But a circumference, and that which
environs, is the symbol of an energy retiring into union with itself,
and which rules over all things according to one intellectual bound.
When, therefore, the demiurgus of the universe had established in
himself these two principles, the right and the circular line, and had
given them dominion, he produced from himself two unities; the one,
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