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 stable disposition, of pure and uncontaminated order, and of
indeclinable power, are deservedly manifested as from an image, by a
quadrangular figure. But, besides these, Philolaus also, according to
another apprehension, calls a quadrangular angle, the angle of Rhea,
Ceres and Vesta. For, since a quadrangle constitutes the earth, and is
its proximate element, as we learn from Timæus, but the earth herself
receives from all these divinities, genital seeds, and prolific powers,
he does not unjustly consecrate the angle of a quadrangle to these
goddesses, the bestowers of life. For some call both the earth and
Ceres, Vesta[183], and they say that Rhea totally participates her
nature, and that all generative causes are contained in her essence.
Philolaus, therefore, says that a quadrangular angle comprehends, by
a certain terrestrial power, one union of the divine genera. But some
assimilate a quadrangle to universal virtue, so far as every quadrangle
from its perfection has four right angles. Just as we say that each of
the virtues is perfect, content with itself, the measure and bound of
life, and the middle of every thing which, in morals, corresponds to
the obtuse and acute. But it is by no means proper to conceal, that
Philolaus attributes a triangular angle to four, but a quadrangular
angle to three gods, exhibiting their alternate transition, and the
community of all things in all, of odd natures in the even, and of even
in the odd. Hence, the tetradic ternary, and the triadic quaternary,
participating of prolific and efficacious goods, contain the whole
ornament of generable natures, and preserve them in their proper
state. From which the duodenary, or the number twelve, is excited
to a singular unity, viz. the government of Jupiter. For Philolaus
says, that the angle of a dodecagon (or twelve-sided figure) belongs
to Jove, so far as Jupiter contains and preserves, by his singular
union, the whole number of the duodenary. For also, according to Plato,
Jupiter presides over the duodenary[184], and governs and moderates
the universe with absolute sway. And thus much we have thought proper
to discourse concerning quadrilateral figures, as well declaring the
sense of our author, as likewise affording an occasion of more profound
inspections to such as desire the knowledge of intelligible and occult
essences.
DEFINITION XXXV.
PARALLEL RIGHT LINES are such as being in the same Plane, and
produced both ways infinitely, will in no part mutually coincide.
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