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
That geometry, according to the transition which takes place from
things more composite to such as are more simple, runs from body, which
is diffused into distance by three dimensions, to a superficies by
which it is bounded; but from superficies to a line, the boundary of
superficies; and from a line to a point destitute of all dimension,
has been often said, and is perfectly manifest. But because these
terms, in many places, on account of their simplicity, appear to be
more excellent than the nature of composites; but in many, as when they
subsist in things which they terminate, they are similar to accidents,
it is necessary to determine in what genera of beings each of these
may be beheld[125]. I say then, that such things as are destitute of
matter, which subsist in separate reasons, and in those forms which
are placed under themselves, are always allotted a subsistence of
more simple essences, superior to the subsistence of such as are more
composite. On this account, both in intellect, and in the ornaments,
as well of the middle kind as among those peculiar to the soul, and
in natures themselves, the terms which proximately vivify bodies,
excel according to essence the things which are terminated; and are
more impartible, more uniform, and more primary than these. For in
immaterial forms, unity is more perfect than multitude; that which is
impartible, than that which is endued with unbounded progression; and
that which terminates, than that which receives bound from another.
But such things as are indigent of matter, and abide in others, and
degenerate from the perfection of their essence, which are scattered
about subjects, and have an unnatural union, are allotted more
composite reasons, prior to such as are more simple. Hence, things
which appear in the phantasy invested with form, and the matter of
the figures which the phantasy contains, and whatever in sensibles is
generated by nature, have, in a preceding order, the reasons of the
things terminated; but the reasons which terminate, in a following
and adventitious rank[126].] For lest that which is distributed into
three dimensions, should be extended into infinite magnitude, either
according to intelligence or sense, it was every way terminated by
superficies. And lest a plane superficies should conceal itself in an
infinite progression, a line approaching opposed its diffusion, and
gave bound to its indefinite extension. And, in like manner, a point
limited the progressions of a line; composite natures deriving their
subsistence from such as are simple. For this also is again manifest,
that in separate forms the reasons of terms subsist in themselves,
but not in those which are terminated; and abiding such as they are
in reality, possess a power of constituting secondary natures. But,
in inseparable forms they give themselves up to things which are
terminated, reside in them, become, as it were, their parts, and
are replenished with baser natures. On which account, that which is
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