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
impartible is there endued with a partible essence, and that which is
void of latitude is diffused into breadth. And terms are no longer
able to preserve their simplicity and purity. For since they abide in
another, they necessarily change their own nature into the matter of
their containing subject. Matter, indeed, disturbs the perfection of
these, and causes the reason of a plane to become a profound plane;
but obscuring the one dimension of a line, causes it to be every way
partible; and gives corporeity to the indivisibility of a point, and
separates it together with the natures which it terminates. For all
these reasons falling into matter, the one kind from cogitation into
intelligible matter, but the other from nature into that which is
sensible, are replenished with their containing subjects; and depart
from their own simplicity, into foreign compositions and intervals. But
here a doubt arises how all these, existing in intellect and soul in
an impartible manner, and without any dimension, are distributed into
matter, some indeed, principally, but others on account of its nature?
Shall we say that there is a certain order in immaterial forms, so
that some are allotted the first, some the middle, and others the last
place; and that of forms some are more uniform, but that others are
more multiplied; and that some have their powers collected together,
but others tending into interval; and that some, again, border upon
bound, but that others are proximate to infinity? For though all
participate of these two principles, yet some originate from bound,
but others from infinity, of which they more largely participate.
Hence, a point is entirely impartible, since it subsists according
to bound, yet it occultly contains an infinite power, by which it
produces every interval, and the progression of all intervals, unfolds
its infinite power. But body, and the reason of body, participates
more of an infinite nature; on which account it is among the number of
things terminated by another, and divisible in infinitum, according
to all dimensions. But the mediums between these, according to the
distance of the extremes, are either among the number of things which
have an abundance of bound; or among such as have an affluence of
infinity: on which account they both terminate and are terminated.
For, indeed, so far as they consist from bound, they are able to
terminate others; but so far as they participate of infinity, they are
indigent of termination from others, Hence, since a point is also a
bound, it preserves its proper power in participation: but since it
likewise contains infinity occultly, and is compelled to be every where
present with the natures which it terminates, it resides with them
infinitely. And, because among immaterial forms there was a certain
infinite power capable of producing things distant from each other by
intervals, a point is present with its participants in capacity. For
Public-domain text, read in full here on John Shaqi.
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