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 — Plato — John Shaqi
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
Plato · en
13. It is likewise evident, that if the propositions be universal,
from which the demonstrative syllogism consists, the conclusion must
necessarily be eternal. For necessary propositions are eternal; but
from things necessary and eternal, necessary and eternal truth must
arise. There is no demonstration, therefore, of corruptible natures,
nor any science absolutely, but only by accident; because it is not
founded on that which is universal. For what confirmation can there
be of a conclusion, whose subject is dissoluble, and whose predicate
is neither always, nor simply, but only partially inherent? But as
there can be no demonstration, so likewise there can be no definition
of corruptible natures; because definition is either the principle of
demonstration, or demonstration differing in the position of terms, or
it is a certain conclusion of demonstration. It is the beginning of
demonstration, when it is either assumed for an immediate proposition,
or for a term in the proposition; as if any one should prove that man
is risible, because he is a rational animal. And it alone differs
in position from demonstration, as often as the definition is such
as contains the cause of its subjects existence. As the following:
an eclipse of the sun is a concealment of its light, through the
interposition of the moon between that luminary and the earth. For
the order of this definition being a little changed, passes into a
demonstration; thus,
The moon is subjected and opposed to the sun:
That which is subjected and opposed, conceals:
The moon, therefore, being subjected and opposed, conceals the
sun.
But _that_ definition is the conclusion of demonstration, which
extends to the material cause; as in the preceding instance, the
conclusion affirming that the subjection and opposition of the moon
conceals the sun, is a definition of an eclipse including the material
cause.