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
But the cause of
this is, indeed, unknown to the vulgar, though, to those who understand
where number and figure subsist, the reason is manifest. Fifthly,
it is replete with that division of forms, which divides forms into
other similar forms, from another second totality, which is also
distributed into similar parts. And by this, a triangular reason is
divided into triangles, and a quadrangular reason into quadrangles.
And hence, exercising our inward powers, we effect what I have said
in images, since it pre-existed by far the first in its principles.
But by regarding these distributions, we may render many causes of
figures, reducing them to their first principles. And the more common,
or geometrical figure, is allotted an order of this kind, and from so
many causes, receives the perfection of its nature. But, from hence
it advances to the genera of the gods, and is variously attributed
according to its various forms, and energizes differently in different
gods. To some, indeed, affording more simple figures; but to others,
such as are more composite. And to some, again, assigning primary
figures, and those which are produced in superficies; but to others
(entering the tumor of solid bodies) such figures, as in solids are
convenient to themselves. For all figures, indeed, subsist in all,
since the forms of the gods are accumulated, and full of universal
powers: but, by their peculiarity, they produce one thing according
to another. For one possesses all things circularly, another in a
triangular manner, but another according to a quadrangular reason. And
in a similar manner in solids.
DEFINITION XV.
A CIRCLE is a Plane Figure, comprehended by one Line, which is
called the Circumference, to which all Right Lines falling from
a certain Point within the Figure, are equal to each other.
DEFINITION XVI.
And that Point is called the CENTRE of the CIRCLE.
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