Book,  Paragraph

 1   I,  2 |      limit and an end: nor of any finite line; for in every case
 2   I,  2 |    something beyond it, since any finite line can be extended. And
 3   I,  5 |          if the simple bodies are finite, the composite must also
 4   I,  5 |        the composite must also be finite, since that which is composed
 5   I,  5 |       which is composed of bodies finite both in number and in magnitude
 6   I,  5 |        and in magnitude is itself finite in respect of number and
 7   I,  5 |        circle must necessarily be finite in every respect, for the
 8   I,  5 |            because in the case of finite radii it is always finite;
 9   I,  5 |         finite radii it is always finite; and secondly, because in
10   I,  5 |     belongs.~(2) Again, if from a finite time a finite time be subtracted,
11   I,  5 |           if from a finite time a finite time be subtracted, what
12   I,  5 |  subtracted, what remains must be finite and have a beginning. And
13   I,  5 |      certain time. This will be a finite time, since the total time
14   I,  5 |           since the total time is finite in which the heavens complete
15   I,  5 |           cuts the other, is also finite. Therefore there will be
16   I,  5 |      shown as follows. Let A be a finite line moving past the finite
17   I,  5 |       finite line moving past the finite line, B. Of necessity A
18   I,  5 |    traverse an infinite line in a finite time. Infinite time, then,
19   I,  5 |           no difference whether a finite is passing by an infinite
20   I,  5 |      infinite or an infinite by a finite. For when A is passing B,
21   I,  5 |     therefore, the time which the finite moving line takes to pass
22   I,  5 |          of the infinite past the finite is also infinite. For the
23   I,  5 |         their circular orbit in a finite time; so that they pass
24   I,  5 |          their orbit, such as the finite line AB. The revolving body,
25   I,  5 |           have to admit that in a finite time it has traversed the
26   I,  5 |     infinite equal to itself in a finite time. But that we know to
27   I,  5 |         the time of revolution is finite, the area traversed must
28   I,  5 |       area traversed must also be finite; but the area traversed
29   I,  5 |           therefore, it is itself finite.~We have now shown that
30   I,  6 |         places are determined and finite, the corresponding bodies
31   I,  6 | corresponding bodies must also be finite. Further, if up and down
32   I,  6 |           Assume the weight to be finite, and take an infinite body,
33   I,  6 |          from the infinite body a finite mass, BD, the weight of
34   I,  6 |        weights, therefore, of the finite and of the infinite body
35   I,  6 |        and thus the weight of the finite body is greater than that
36   I,  6 |        since the infinite and the finite cannot be equal. It does
37   I,  6 |           infinite body cannot be finite. It must then be infinite.
38   I,  6 |        given movement. Further, a finite weight traverses any finite
39   I,  6 |       finite weight traverses any finite distance in a finite time.
40   I,  6 |          any finite distance in a finite time. It necessarily follows
41   I,  6 |         more than as great as the finite, will move accordingly,
42   I,  6 |      between the infinite and the finite: proportion can only hold
43   I,  6 |      between a less and a greater finite time. And though you may
44   I,  6 |        would it help us. For some finite body could have been found
45   I,  6 |      found greater than the given finite in the same proportion which
46   I,  6 |        the infinite and the given finite; so that an infinite and
47   I,  6 |         so that an infinite and a finite weight must have traversed
48   I,  6 |        the time, so long as it is finite, in which the infinite performs
49   I,  6 |   infinite performs the motion, a finite weight must necessarily
50   I,  6 |        necessarily move a certain finite distance in that same time.
51   I,  7 |        must necessarily be either finite or infinite, and if infinite,
52   I,  7 |           must represent either a finite or an infinite number of
53   I,  7 |           primary movements being finite in number, the kinds of
54   I,  7 |         body are necessarily also finite, since the movement of a
55   I,  7 |          the simple movements are finite, and every natural body
56   I,  7 |       body is to be composed of a finite number of kinds, then each
57   I,  7 |           to be acted upon by the finite or to act upon it may be
58   I,  7 |       cannot be acted upon by the finite.) Let A be an infinite,
59   I,  7 |         Let A be an infinite, B a finite, C the time of a given movement
60   I,  7 |          is to B, so is E to some finite quantum. We assume that
61   I,  7 |     caused in the infinite by any finite agent in any time whatever.
62   I,  7 |         of that patient will be a finite quantity, since no proportion
63   I,  7 |          proportion holds between finite and infinite.~(2. The infinite
64   I,  7 |      infinite cannot act upon the finite.) Nor, again, can the infinite
65   I,  7 |         produce a movement in the finite in any time whatever. Let
66   I,  7 |         Let A be an infinite, B a finite, C the time of action. In
67   I,  7 |           in the time C. Thus the finite and infinite effect the
68   I,  7 |         is to CD, so is E to some finite part of B. This part will
69   I,  7 | proportionately. There is thus no finite time in which infinites
70   I,  7 |         where it is shown that no finite thing possesses infinite
71   I,  7 |      power, and no infinite thing finite power.) If then that which
72   I,  8 |          form, and always it is a finite change. For instance, to
73   I,  8 |         in a sense an opposed and finite goal.) There must therefore
74   I,  12|      whether the supposed time is finite or infinite; for its capacity
75   I,  12|         of being must include the finite time since it covers infinite
76   I,  12|  direction is neither infinite or finite. (2) Further, why, after
77 III,  2 |          infinitely varied. For a finite number of causes would produce
78 III,  4 |          whether the elements are finite or infinite in number, and,
79 III,  4 |       infinite in number, and, if finite, what their number is. Let
80 III,  4 |         since the hypothesis of a finite number will give identical
81 III,  4 |       would be better to assume a finite number of principles. They
82 III,  4 |       assume as principles things finite either in kind or in number.
83 III,  4 |          sense, which are in fact finite in number, though this requires
84 III,  5 |          they must be several and finite in number.~
85 III,  7 |           come to a stop, since a finite quantum cannot contain an
86 III,  7 |     cannot contain an infinity of finite quanta. When earth produces
87 III,  7 |       only go on for ever, if the finite body contains an infinity,