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| Paragraph 1 |
For just as the universal propositions of mathematics deal not with
objects which exist separately, apart from extended magnitudes and
from numbers, but with magnitudes and numbers, not however qua such
as to have magnitude or to be divisible, clearly it is possible that
there should also be both propositions and demonstrations about sensible
magnitudes, not however qua sensible but qua possessed of certain
definite qualities. |
| Paragraph 2 |
The same account may be given of harmonics and optics; |
| Paragraph 3 |
Each question will be best investigated in this way - by setting up
by an act of separation what is not separate, as the arithmetician
and the geometer do. |
| Paragraph 4 |
Now since the good and the beautiful are different (for the former
always implies conduct as its subject, while the beautiful is found
also in motionless things), those who assert that the mathematical
sciences say nothing of the beautiful or the good are in error. |
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created 1996/11/25 modified 2009/04/26