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
Lastly, they all subsist in
bodies, but in a corporeal manner; since all forms have their being
in these, according to the partible nature of bodies. Hence, all of
them appear every where, and each according to its proper order; and
diversity arises from pre-dominating power. The point, indeed, is every
where impartible, and when that which is divisible into parts, excels
according to the diminution of beings, it vindicates to itself, an
illustrious subsistence of partible natures. And sometimes the point is
entirely superior, according to the excellence of cause; but sometimes
it is connected with divisibles, and sometimes it is allotted in them
an adventitious existence; and, as if swallowed up by the partition of
the lowest natures, loses its own proper impartibility. As, therefore,
with respect to the monad, one[130] is the mother of number, but the
other is as matter spread under, and the receptacle of numbers; and
each of them a principle, (yet neither of them is number), but in a
different respect: in the same manner a point also, is partly the
parent and author of magnitudes; but is partly a principle in another
respect, and not according to a generative cause. But is a point, then,
the only impartible? Or may we affirm this of the now in time, and of
unity in numbers? Shall we not say, that to the philosopher, indeed,
discoursing concerning the universality of things, it is proper to
behold every thing, however falling under distribution; but that to
him who is endued with the science of particulars, who produces his
contemplation from certain definite principles, and runs back even to
these, but very little scrutinizes the progressions of beings, it is
requisite to attempt, consider, and treat concerning that impartible
nature alone, which regards his first principles; and to behold that
simplicity which presides over all the particular subjects of his
knowledge? In consequence of this reasoning, therefore, a point alone,
according to the geometric matter, is destitute of partition; but unity
according to that which is arithmetical. And the reason of a point,
however in some other respects it may be imperfect, yet is perfect in
the present science. For, indeed, the physician also says, that the
elements of bodies are fire and water, and things similar to these; and
as far as to these the resolution of bodies proceeds. But the natural
philosopher passes on to more simple elements; and the one defines an
element simple as to sense, but the other simple as to reason; and both
of them properly as to their peculiar science. We must not, therefore,
think that the definition of a point is faulty, nor determine it as
imperfect; for so far as pertains to the geometric matter, and its
principles, it is sufficiently delivered. This alone, indeed, is
wanting to its completion, that the definition does not clearly say,
_that which is impartible with me is a point; and my principle, and
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