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
Previous to the acquisition of all learning and ratiocinative
discipline, it is necessary we should possess certain natural
principles of knowledge, as subservient to our future progress and
attainments. Thus, in every science there are some things which require
an immediate assent as soon as proposed; whose certainty is too evident
and illustrious to stand in need of any demonstrative proof deduced
from that particular science which, like stately pillars, they equally
support and adorn. Hence we are informed by the geometrician, that a
point is that which is destitute of all parts whatever; but we must
previously understand the meaning of the word _part_. Thus the
arithmetician defines an odd number, that which is divided according
to unequal parts; but it is necessary we should antecedently know
the meaning of the word _unequal_. Thus, too, art as well as
science operates by antecedent knowledge; and hence the architect,
the statuary, and the shipwright, learn the names and the use of their
respective implements, previous to the exercise of the materials
themselves. This is particularly evident in the discursive arts of
rhetoric and logic; thus the logician reasons by syllogism, the
rhetorician by induction, and the sophist by digressions and examples;
while each proceeds in an orderly progression from principles simple
and evident, to the most remote and complicated conclusions.
2. The antecedent knowledge of things may be divided into two parts:
the one a knowledge of their existence, or that they exist; the other
a knowledge of the terms expressive of their existence. Thus, previous
to the enquiry why iron is attracted by the magnet, it is necessary
we should learn the reality of this attraction, and the general mode
of its operation: thus too, in an enquiry concerning the nature of
motion and time, we must be previously convinced of their existence
in the nature of things. The second division of antecedent knowledge
takes place in subjects whose very existence admits of a dispute: thus
previous to a solution of the questions, Whether there are any gods
or not? Whether there is a providence or not? and the like, it is
necessary we should first understand the meaning of the terms; since
we in vain investigate the nature of any thing while we are ignorant
of the meaning of its name; although, on the contrary, we may have a
perfect conception of the meaning of some words, and yet be totally
ignorant whether the things they express have a real, or only an
imaginary existence. Thus, the meaning of the word _centaur_ is
well understood by every one; but its existence is questioned by most.