[The Banquet (Il Convito) by Dante Alighieri]@TWC D-Link book
The Banquet (Il Convito)

CHAPTER XIV
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Geometry moves between two things antagonistic to it; as between the point and the circle, and I term circle freely anything that is round, either a body or superfices; for, as Euclid says, the point is the beginning of Geometry, and, according to what he says, the circle is the most perfect figure in it, which must therefore have reason for its end; so that between the point and the circle, as between the beginning and the end, Geometry moves.

And these two are antagonistic to its certainty; for the point by its indivisibility is immeasurable, and the circle, on account of its arc, it is impossible to square perfectly, and therefore it is impossible to measure precisely.

And again, Geometry is most white, inasmuch as it is without spot of error, and it is most certain in itself, and by its handmaid, called Perspective.
And the Heaven of Saturn has two properties because of which it can be compared to Astrology.

One is the slowness of its movement through the twelve signs; for twenty-nine years and more, according to the writings of the Astrologers, is the time that it requires in its orbit.

The other is, that above all the other planets it is highest.
And these two properties are in Astrology, for in completing its circle, as in the acquirement of this Science, the greatest space of time is revolved, because its demonstrations are more than any other of the aforementioned Sciences, and long experience is requisite to those who would acquire good judgment in it.


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