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
From these also, as images, we may understand, that things more simple
procure bound and an end to every one of their proximate natures: for
soul perfects and determines the operations of nature; and nature
the motion of bodies. And prior to these, intellect measures the
convolutions of soul; and unity the life of intellect; for that is
the measure of all. Just as in these also, a solid is terminated by a
superficies; but a superficies by a line; and a line by a point; for
that is the boundary of them all. Hence, the line existing uniformly
in immaterial forms and impartible reasons, terminates and restrains
the various motion of a superficies in its progression, and proximately
unites its infinity. But in the images of these, when that which
bounds supervenes that which is bounded, it causes, by this means,
its limitation and bound. But if it should be enquired how lines are
the extremities of every superficies, since they are not the extremes
of every finite figure; for the superficies of a sphere is terminated
indeed, yet not by lines, but by itself? In answer to this, we must
say, that by receiving a superficies so far as it is distant by a
twofold interval, we shall find it terminated by lines according to
length and breadth. But if we behold a spherical superficies, we
must receive it as that which is endued with figure; which possesses
another quality, and conjoins the end with the beginning; and loses
its two extremities in the comprehensive embraces of one: and this one
extremity subsists in capacity only, and not in energy.
DEFINITION VII.
A Plane SUPERFICIES is that which is equally situated between
its bounding Lines.
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