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
present discourse is addressed to the learned. Plato, indeed, in most
places, calls all the knowledge (as I may say) of universals by the
name of science, opposing it in a division to sense which apprehends
only particulars, whether such a mode of cognition is accomplished
by art or experience. And in this sense, as it appears to me in
the _Civil_ Dialogue, and in the Sophista, he seems to use the
name of science; placing likewise the illustrious Sophistic science,
which Socrates in the Gorgias, says, is a certain experience: also,
the adulatory, and many others, which are experiences, but not true
sciences. But again, dividing this knowledge of universals into
that which knows causes, and into that which understands without a
cause, he thinks that the one should be called science, but the other
experience. And hence, to arts he sometimes attributes the name of
science, but to experience never. For how (says he in the Banquet)
can a thing which possesses no reason be science? All knowledge,
therefore, which contains the reason and cause of the things known,
is a certain science. Again, therefore, he divides this science which
is endued with a power from the cause of knowing, by the peculiarity
of its subjects, and he places one, conjectural of things divisible;
but the other of such as subsist by themselves, and are ever knowable
after the same manner. And according to this division he separates from
science, medicine, and every faculty which is conversant with material
concerns. But he calls mathematical knowledge, and whatever possesses
a power of contemplating eternal objects, by the name of science.
Lastly, dividing this science, which we distinguished from arts, he
considers one part as void of supposition; but the other as flowing
from supposition. And that the one which is void of supposition, has
a power of knowing universals: that it rises to good, and the supreme
cause of all; and that it considers good as the end of its elevation:
but that the other, which previously fabricates for itself definite
and determinate principles, from which it evinces things consequent to
such principles, does not tend to the principle, but to the conclusion.
And hence he asserts, that mathematical knowledge, because it makes
use of supposition, falls short of that science which is without
supposition, and is perfect. For there is one true science, by means
of which we are disposed to know all the things _which are_, and
from which also principles emerge to all sciences; to some, indeed,
constituted more proximately, but to others more remotely. We must
not say, therefore, that Plato expels mathematical knowledge from the
number of the sciences, but that he asserts it to be the second from
that one science, which possesses the supreme seat of all: nor must we
affirm, that he accuses it as ignorant of its own principles, but that
receiving these from the master science dialectic, and possessing them
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