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
infinity in intelligibles is the primary cause and prolific power of
the universe; but in material natures it is imperfect, and is alone
all things in dormant capacity. And in short, those forms which, on
account of their simplicity and impartibility, hold a superior rank
among principles, preserve, indeed, (in conformity to their nature,)
their own property in their participations, but become worse than
more composite reasons. For matter is able to participate these more
clearly, and to be prepared for their reception, rather than that of
the most simple causes of beings. On which account, the vestigies of
separate principles descend into matter; but the participations of
those in a second and third order, become more conspicuous. Hence,
matter participates more of the cause of body, than of a plane; and of
this more than the form of a line; and of this still more than that of
a point, which contains all these, and is the boundary of them all.
For the reason of a point presides over this whole series, unites
and contains all partible natures, terminates their progressions,
produces them all by its infinite power, and comprehends them in its
indivisible bound. On which account also, in the images of immaterial
forms, some are the boundaries of others; but a point is the limit
of them all. But that we must not think with the Stoics, that these
boundaries of bodies alone subsist from cogitation; but that there are
certain natures of this kind among beings, which previously contain
the demiurgical reasons of things, we shall be enabled to remember, if
we regard the whole world, the convolutions of its parts, the centres
of those convolutions, and the axes which penetrate through the whole
of these revolving circles. For the centres subsist in energy, since
they contain the spheres, preserve them in their proper state, unite
their intervals, and bind and establish to themselves the powers which
they possess. But the axes themselves being in an immoveable position,
evolve the spheres, give them a circular motion, and a revolution round
their own abiding nature. And the poles of the spheres, which both
terminate the axes, and bind in themselves the other convolutions, do
they not perspicuously evince, that points are endued with demiurgical
and capacious powers, that they are perfective of every thing distant
by intervals, and are the sources of union, and an unceasing motion?
From whence, indeed, Plato[127] also says, that they have an adamantine
subsistence; shewing by this, the immutable, eternal, and stable
power of their essence, ever preserving itself in the same uniform
mode of existence. He adds too, that the whole spindle of the Fates,
is turned about these, and leaps round their coercive union. But other
more recondite and abstruse discourses affirm, that the demiurgus
presides over the world, seated in the poles, and, by his divine love,
converting the universe to himself. But the Pythagoreans thought
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