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
subsisting in one reason, but differing in magnitudes or subjects:
in like manner, there is a common something in the circles, which
subsist in the receptacle of the phantasy, of which all its circles
participate, and according to which they all possess the same form;
but in the phantasy they possess but one difference only, that of
magnitude. For when you imagine many circles about the same centre,
they all of them exist in one immaterial subject and life, which is
inseparable from a simple body, which, by the possession of interval,
exceeds an essence destitute of parts; but they differ in magnitude
and parvitude, and because they are contained and contain. Hence,
that universal is twofold, which is understood as subsisting in the
many: one, indeed, in sensible forms; but the other in such as are
imaginative. And the reason of a circular and triangular figure, and of
figure universal, is twofold. The one subsisting in intelligible, but
the other in sensible matter. But prior to these is the reason which
resides in cogitation, and that which is seated in nature herself.
The former being the author of imaginative circles, and of the one
form which they contain; but the other, of such as are sensible.
For there are circles existing in the heavens, and universally
those produced by nature, the reason of which does not fall under a
cogitative distribution. For in incorporeal causes, things possessing
interval, are distinguished by no intervals: such as are endued with
parts, subsist without parts: and magnitudes without the diffusion of
magnitude, as on the contrary in corporeal causes, things without parts
subsist divisibly, and such as are void of magnitude with the extension
of magnitude. Hence, the circle resident in cogitation, is one, simple
and free from interval: and magnitude itself is there destitute of
magnitude; and figure expressed by no figure: for such are reasons
separate from matter. But the circle subsisting in the phantasy, is
divisible, figured, endued with interval, not one only, but one and
many, nor form alone, but distributed with form. And the circle, in
sensible objects, is composite, distant with magnitude, diminished by
a certain reason, full of ineptitude, and very remote from the purity
of immaterial natures. We must therefore say, that geometry, when it
asserts any thing of circle and diameter, and of the passions and
affections which regard the circle; as of contacts, divisions, and the
like: neither teaches nor discourses concerning sensible forms, (since
it endeavours to separate us from these), nor yet concerning the form
resident in cogitation, (for here the circle is one, but geometry
discourses of many, proposing something of each, and contemplating the
same of all: and here it is indivisible, but the geometric circle is
divisible); but we must confess, that it considers universal itself;
yet as distributed in imaginative circles. And that it beholds, indeed,
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