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The Improvement of Human Reason - Exhibited in the Life of Hai Ebn Yokdhan by Ibn Tufail
page 64 of 141 (45%)
terminated on this side which is next to me, is evident to my sight: And
that it cannot be infinitely extended on that opposite side, which
rais'd this Scruple in me; I prove thus: Suppose two Lines drawn from
the Extremity of this Heavenly Body, on that terminated Side which is
next to me, which Lines should be produc'd quite through this Body_, in
infinitum, _according to the Extension of the Body; then suppose a long
part of one of these Lines, cut off at this End which is next to me;
then take the Remainder of what was cut off, and draw down that end of
it where it was cut off; And lay it even with the end of the other Line
from which there was nothing cut off; and let that Line which was
shortned, lye parallel with the other; then suppose them through this
Body, till you come to that side which we suppos'd to be infinite:
Either you will find both these Lines infinitely extended, and then one
of them cannot be shorter than the other, but that which had a part of
it cut off, will be as long as that which was not, which is absurd: Or
else the Line which was cut will not be so long as that other, and
consequently finite: Therefore if you add that part to it which was cut
off from it at first, which was finite, the whole will be finite; and
then it will be no longer or shorter than that Line which had nothing
cut off from it, therefore equal to it; But this is finite, therefore
the other is finite. Therefore the Body in which such Lines are drawn is
finite; And all Bodies in which such Lines may be drawn, are finite: But
such Lines may be drawn in all Bodies. Therefore if we suppose an
infinite Body, we suppose an Absurdity and Impossibility._

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[Illustration 6]

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