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
from an impartible nature, dyadic. And that a point is posterior to
unity, a line to the duad, and a superficies to the triad, Parmenides
himself shews, by first of all taking away multitude from one by
negation, and afterwards the whole. Because, if multitude is before
that which is a whole, number also will be prior to that which is
continuous, and the duad to the line, and unity to the point: since the
epithet _not many_, belongs to unity which generates multitude,
but to the point, the term _not a whole_, is proper, because it
produces a whole; for this is said to have no part. And these things
are affirmed of a line, while we more accurately contemplate its
nature. But we should also admit the followers of Apollonius, who say,
that we obtain a notion of a line, when we are ordered to measure the
lengths alone, either of ways or walls; for we do not then subjoin
either breadth or bulk, but only make one distance the object of our
consideration. In the same manner we perceive superficies, when we
measure fields; and a solid, when we take the dimensions of wells. For
then, collecting all the distances together, we say, that the space of
the well is so much, according to length, breadth, and depth. But a
line may become the object of our sensation, if we behold the divisions
of lucid places from those which are dark, and survey the moon when
dichotomized: for this medium has no distance with respect to latitude;
but is endued with longitude, which is extended together with the light
and shadow.
DEFINITION III.
But the Extremities of a Line are Points.
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Elsewhere in the archive
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account