Book, Paragraph
1 V, 3 | continuous": and we have shown in what circumstances each
2 VI, 2 | into magnitudes-for we have shown that it is impossible for
3 VI, 2 | continuous. For since it has been shown that the quicker will pass
4 VI, 2 | is the time. This may be shown as follows. Let AB be a
5 VI, 3 | both. And if it is once shown that it is essentially of
6 VI, 3 | divisible: for all time has been shown to be divisible. Thus on
7 VI, 4 | does so we have already shown: that infinity does so will
8 VI, 5 | change, which we have in fact shown to be indivisible because
9 VI, 5 | that changes having been shown to be divisible): and let
10 VI, 6 | B at once): for we have shown above that that that which
11 VI, 8 | coming to a stand has been shown to be in motion: consequently
12 VI, 8 | coming to a stand has been shown to be in motion. But since
13 VI, 8 | parts of AB: for we have shown above that it is coming
14 VI, 8 | of its parts, as may be shown by the same method as that
15 VI, 10 | But this we have already shown above to be impossible:
16 VI, 10 | points.~Again, it may be shown in the following way that
17 VI, 10 | time; and all time has been shown above to be divisible. Therefore,
18 VII, 1 | out to prove has thus been shown, but our argument so far
19 VII, 2 | If, therefore, it can be shown that that which is pushing
20 VIII, 5 | impossibility: for we have shown above that there must always
21 VIII, 5 | divisible, for it has been shown already in our general course
22 VIII, 6 | one and eternal. We have shown that there must always be
23 VIII, 7 | be primary. This may be shown as follows. It is impossible
24 VIII, 9 | 9~It can now be shown plainly that rotation is
25 VIII, 9 | and complete, which may be shown as follows. The straight
26 VIII, 10| infinite time.~It has now to be shown that in no case is it possible
27 VIII, 10| finite magnitude. This can be shown as follows: we take it for
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