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
which many participate, which exists in many, and fills particular
natures according to its subject matter. Besides this, establishing
a twofold order of participants, one subsisting in sensible objects,
but the other in the phantasy, (since matter is twofold; one indeed,
of things united with sense, but the other of such as fall under the
inspection of phantasy, as Aristotle asserts, in a certain place[96])
we must allow that the universal, which is distributed in the many,
is likewise twofold. The one, indeed, sensible, as being that which
sensible objects participate; but the other imaginative, as that
which subsists in the _many_ of the phantasy. For the phantasy,
on account of its forming motion, and because it subsists with, and
in body, always receives impressions which are both divided and
figured. So that whatever is known by it, is allotted a correspondent
existence: on which account, Aristotle[97] does not hesitate to call
it passive intellect. But if it is intellect, why is it not impassive,
and destitute of matter? And if it operates with passion, how can it
with propriety be called intellect? For impassivity, indeed, properly
belongs to intellect and an intelligent nature: but passivity is very
remote from such an essence. But (unless I am deceived) Aristotle
being willing to explain its middle nature between cognitions the most
primary, and such as are the last, calls it at the same time intellect,
because similar to primary cognitions, and passive from that alliance
which it possesses with such as are posterior. For first cognitions are
indeed destitute of figures and forms; comprehending in themselves,
intelligible natures, energizing about themselves, united with the
objects of knowledge, and free from all extrinsical impression and
passion. But last cognitions exercise themselves through the medium
of instruments, are rather passions than energies, admit extrinsical
knowledge, and move themselves together with their various subjects.
For such (says Plato) are the sensations which arise from violent
passions. But the phantasy, obtaining a middle centre in the order of
cognitions, is excited, indeed, by itself, and produces that which
falls under cogitation: but because it is not separate from body,
it deduces into partition, interval, and figure, the objects of its
knowledge, from the indivisibility of an intellectual life. Hence,
whatever it knows, is a certain impression and form of intelligence.
For it understands the circle, together with its interval, void,
indeed, of external matter, but possessing intelligible matter. On
this account, like sensible matter, it does not contain one circle
only: for we behold in its receptacle, distance, together with the
more and the less, and a multitude of circles and triangles. If then
an universal nature is distributed in sensible circles, since each of
these completes a circular figure, and they are all mutually similar,
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