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
15. We now propose to consider the mode in which the two preceding
demonstrations are distributed in different sciences. When sciences
then are so related, that the one is dependent on the other, as optics
on geometry, navigation on astronomy, and music composed by the
arbitration of the ear, on that which consists in the knowledge of
mathematical proportions: in this case, the demonstration of simple
existence, or _that_ they _exist_, pertains to the science of
sensibles; but the demonstration _why_ they _exist_ to the
science which is speculative and mathematical.
Thus the mathematician speculates the causes of a certain sensible
effect, without considering its actual existence; for the contemplation
of universals excludes the knowledge of particulars; and he whose
intellectual eye is fixed on that which is general and comprehensive,
will think but little of that which is sensible and singular. Thus,
by mathematics we may learn the responsive harmony of the _last
chord_, and its consonance with the _mean_; but we cannot
perceive this concord, if unaccustomed to the practice of the musical
art. In fine, those sciences which are more of a mathematical nature,
I mean such as are more amply conversant with the inspection of
things, considering their forms abstracted from every material subject,
always demonstrate the _why_; and such is geometry in respect
of optics. Thus geometry considers only such things as are peculiar
to right-lines, independent of every sensible connection. For the
geometrician does not investigate a right-line as contained in stone or
brass; but considers it as entirely detached and unconnected with any
object of sense.
On the contrary, optics receives a right-line just as it is perceived
in a rule, or engraved in brass. And, indeed, in treating of some
particulars, natural science has the same relation to optics, as optics
to geometry. Thus, in considering the reason of the appearance of
the rainbow, the natural philosopher defines the bow to be an image
refracted from a certain cloud against the sun; but why it is endued
with such a form, and seen with such a colour, must be assigned by him
who is skilled in optics. There are, again, sciences, one of which is
not subordinate to the other, because founded on principles totally
different; yet, in some particulars they agree with the preceding.
Thus, to know that an orbicular wound is the most difficult of cure,
belongs to the physician; but to know _why_, to the geometrician.