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
without interval; and lastly, by ascending into an union with herself,
of surveying every object which is subject to the power of cognition.
The figure, therefore, which is self-motive, precedes that which is
moved by another; and the impartible that which is self-motive: but
that which is the same with _one_, precedes the impartible itself.
For all things are bounded, when they return to the unities of their
nature; since all things pass through these as a divine entrance into
being. And thus much for this long digression, which we have delivered
according to the sentiments of the Pythagoreans. But the geometrician,
contemplating that figure which is seated in the phantasy, and defining
this, in the first place, (since this definition agrees with sensibles,
in the second place) says, that figure is that which is comprehended by
one or more boundaries. For, since he receives it together with matter,
and conceives of it as distant with intervals, he does not improperly
call it finite and terminated[164]. [Since every thing which contains
either intelligible or feasible matter, is allotted an adventitious
bound; and is not itself bound, but that which is bounded.] Nor is it
the bound of itself; but one of its powers is terminating, and the
other terminated. Nor does it subsist in bound itself, but is contained
by bound. For figure is joined to quantity, and subsists together
with it; and, at the same time, quantity is subjected to figure; but
the reason and aspect of that quantity is nothing else than figure
and form. Since, indeed, reason terminates quantity, and adds to it
a particular character and bound, either simple or composite. For,
since this also exhibits the twofold progression of _bound_ and
_infinite_ in its proper forms, (in the same manner as the reason
of an angle,) it invests the objects of its comprehension with one
boundary and simple form, according to _bound_, but with many,
according to infinity[165]. Hence, every thing figured, vindicates to
itself either one boundary, or a many. Euclid, therefore, denominating
that which is figured and material, and annexed to quantity figure,
does not improperly say, that it is contained by one or more terms.
But Possidonius defines figure to be concluding bound, separating
the reason of figure from quantity; and considering it as the cause
of terminating, defining, and comprehending quantity. For that which
encloses, is different from that which is enclosed; and bound from that
which is bounded. And Possidonius, indeed, seems to regard the external
surrounding bound; but Euclid, the whole subject. Hence, the one calls
a circle a figure, with relation to its whole plane, and exterior
ambit; but the other with relation to its circumference only. And the
one defines that which is figured, and which is beheld together with
its subject: but the other desires to define the reason of the circle;
I mean that which terminates and concludes its quantity. But if any
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