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
them erect, and others fitting; and some similar to a heart, but others
spherical, and others expressed by different figures. And again, some
it fabricates of a simple form; but others it composes from a multitude
of forms; and some are sacred and venerable; but others are domestic,
exhibiting the peculiar gentleness of the gods. And some it constructs
of a severe aspect; and lastly, attributes to others, different
symbols, according to the similitude and sympathy pertaining to the
gods[163]. Since, therefore, figure derives its origin from the gods
themselves, it arrives, by a gradual progression, even to inferiors,
in these also appearing from primary causes. Since it is requisite to
suppose the perfect before the imperfect, and things situated in the
stability of their own essence, prior to those which subsist in others,
and previous to things full of their own privation, such as preserve
their proper nature sincere. Such figures, therefore, as are material,
participate of material inelegance, and do not possess a purity
convenient to their nature. But the celestial figures are divisible,
and subsist in others. And the figures of souls are endued with
division, and variety, and involution of every kind; but the figures
of intellects, together with immaterial union, possess a progression
into multitude. And lastly, the figures of the gods are free, uniform,
simple, and generative; they subsist before all things, containing all
perfection in themselves, and extending from themselves to all things,
the completion of forms. We must not, therefore, listen to, and endure
the opinions of many, who affirm, that certain additions, ablations,
and alterations, produce sensible figures, (for motions, since they are
imperfect, cannot possess the principle and primary cause of effects;
nor could the same figures often be produced from contrary motions; for
the same form is sometimes generated from addition and detraction,)
but we must consider operations of this kind as subservient to other
purposes in generation, and derive the perfection of figure from other
primogenial causes. Nor must we subscribe to their opinion, who assert
that figures destitute of matter can have no subsistence; but those
only which appear in matter. Nor to theirs, who acknowledge, indeed,
that they are external to matter, but consider them as subsisting
alone, according to thought and abstraction. For where shall we
preserve in safety, the certainty, beauty, and order of figures, among
things which subsist by abstraction? For, since they are of the same
kind with sensibles, they are far distant from indubitable and pure
certainty. But from whence do they derive the certainty, order, and
perfection which they receive? For they either derive it from sensibles
(but they have no subsistence in these), or from intelligibles (but in
these they are more perfect), since, to say from that which is not, is
the most absurd of all. For nature does not produce imperfect figures,
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