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
A Circle is the first, most simple, and most perfect of figures. For
it excels all solids, because it exists in a more simple place; but
it is superior to the figures subsisting in planes, on account of
its similitude and identity. And it has a corresponding proportion
to bound, and unity, and a better co-ordination of being. Hence, in
a distribution of mundane and super-mundane figures, you will always
find that the circle is of a diviner nature. For if you make a division
into the heavens, and the universal regions of generation, you must
assign to the heavens a circular form; but to generation, that of a
right line, For whatever among generable natures is circular, descends
from the heavens; since generation revolves into itself, through
their circumvolutions, and reduces its unstable mutation to a regular
and orderly continuance. But if you distribute incorporeal natures
into soul and intellect, you will say, that the circle belongs to
intellect, and the right line to the soul. And on this account, the
soul, by its conversion to intellect, is said to be circularly moved;
and it possesses the same proportion to intellect, as generation to
the heavens. For it is circularly moved, (says Socrates[167],) because
it imitates intellect. But the generation and progression of soul is
made according to a right-line. For it is the property, of the soul
to apply herself at different times to different forms. But if you
wish to divide into body and soul, you must constitute every thing
corporeal, according to the right line; but you must assign to every
animal a participation of the identity and similitude of the circle.
For body is a composite, and is endued with various powers, similar to
right-lined figures: but soul is simple and intelligent; self-motive,
and self-operative; converted into, and energizing in herself. From
whence, indeed, Timæus also, when he had composed the elements of
the universe from right-lined figures, assigned to them a circular
motion and formation, from that divine soul which is seated in the
bosom of the world. And thus, that the circle every where holds the
first rank, in respect of other figures, is sufficiently evident from
the preceding observations. But it is requisite to survey its whole
series, beginning supernally, ending in inferiors, and perfecting all
things, according to the aptitude of the natures which receive its
alliance. To the gods, therefore, it affords a conversion to their
causes, and ineffable union: it occasions their abiding in themselves,
prevents their departing from their own beatitude, strengthens their
highest unions, as centres desirable to inferior natures; and stably
places about these the multitude of the powers which the gods possess,
containing them in the simplicity of their essences. But the circle
affords to intellectual natures, a perpetual energy in themselves, is
the cause of their being filled with knowledge from themselves, and
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