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
For among the Pythagoreans we shall find various angles dedicated to
various gods. Thus, Philolaus, consecrates to some a triangular, but to
others a quadrangular angle; and to others, again, different angles.
Likewise, he permits the same to many gods, and many to the same god,
according to the different powers which they contain. And with a view
to this, and to the demiurgic triangle, which is the primary cause of
all the ornament of the elements, it appears to me, that Theodorus
Asinæus the philosopher, constitutes some of the gods, according to
sides; but others, according to angles. The first, indeed, supplying
progression and power; but the second, the conjunction of the universe,
and the collection of progressive natures again into one. But these,
indeed, direct us to the knowledge of the things which are. And we must
not wonder that lines are here said to contain an angle. For the one
and impartible nature which is found in these, is adventitious: but
in the gods themselves, and in true beings, the whole, and impartible
good, precedes things many, and divided.
DEFINITION X.
When a Right Line standing on a Right Line, makes the successive
Angles on each side equal to one another, each of the equal
Angles, is a Right Angle; and the insisting Right Line, is called
a PERPENDICULAR to that upon which it stands.
DEFINITION XI.
An OBTUSE ANGLE is that which is greater than a RIGHT
ANGLE.
DEFINITION XII.
But an ACUTE ANGLE, is that which is less than a
RIGHT ANGLE.
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