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
of possessing in their essences, intelligibles contractedly; and of
perfecting intellections in themselves. For every intellect, proposes
to itself that which is intelligible; and this is as a centre to
intellect, about which it continually revolves: for intellect folds
itself, and operates about this, and is united within itself on all
sides, by universal intellectual energies. But it extends to souls by
illumination, a self-vital, and self-motive power, and an ability of
turning, and leaping round intellect, and of returning according to
proper convolutions, unfolding the impartibility of intellect. Again,
the intellectual orders excel souls after the manner of centres, but
souls energize circularly about their nature. For every soul, according
to its intellectual part, and the supreme _one_, which is the
very flower of its essence, receives a centre: but, according to its
multitude, it has a circular revolution, desiring, by this means, to
embrace the intellect which it participates. But, to the celestial
bodies, the circle affords an assimilation to intellect, equality, a
comprehension of the universe, in proper limits, revolutions which
take place in determinate measures, a perpetual subsistence, a nature
without beginning and end, and every thing of this kind. And to the
elements under the concave of the moon’s orb, it is the cause of a
period, conversant with mutations; an assimilation to the heavens; that
which is without generation, in generated natures; that which abides in
things which are moved; and whatever is bounded in partible essences.
For all things are perpetual, through the circle of generation; and
equability is every where preserved on account of the reciprocation
of corruption. Since, if generation did not return, in a circular
revolution, in a short space of time, the order, and all the ornament
of the elements would vanish. But again, the circle procures to animals
and plants, that similitude which is found in generations; for these
are produced from seeds, and seeds from these. Hence, generation here,
and a circumvolution, alternately takes place, from the imperfect to
the perfect, and the contrary; so that corruption subsists together
with generation. But, besides this, to unnatural productions it
imposes order, and reduces their indeterminate variety to the
limitation of bound; and, through this, nature herself is gracefully
ornamented in the last vestiges of her powers. Hence, things contrary
to nature have a revolution according to determinate numbers, and not
only fertility, but also sterility, subsists according to the alternate
convolutions of circles (as the discourse of the Muses evinces), and
all evils though they are dismissed from the presence of the gods,
into the place of mortals, yet these roll round, says Socrates, and to
these there is present a circular revolution, and a circular order;
so that nothing immoderate and evil is deserted by the gods; but that
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