Book, Paragraph
1 I, 2 | many, for the continuous is divisible ad infinitum.~There is,
2 I, 3 | 2) Substance is plainly divisible into other substances, if
3 III, 1 | continuous ("what is infinitely divisible is continuous"). Besides
4 III, 5 | be indivisible; for the divisible must be either a magnitude
5 III, 5 | be either indivisible or divisible into infinites. But the
6 III, 6 | a magnitude will not be divisible into magnitudes, number
7 III, 6 | in the full sense. It is divisible both in the direction of
8 III, 7 | also why every magnitude is divisible into magnitudes.)~Our account
9 IV, 8 | that which exceeds must be divisible into the excess + that which
10 IV, 10 | in reality.~Further, if a divisible thing is to exist, it is
11 IV, 10 | part of it is though it is divisible. For what is "now" is not
12 IV, 10 | the same. No determinate divisible thing has a single termination,
13 IV, 12 | quanta and continuous and divisible. The movement has these
14 V, 4 | must (since every motion is divisible) be continuous, and a continuous
15 V, 4 | irregular being as such divisible. But the difference would
16 VI, 1 | these parts into which it is divisible are different in this way,
17 VI, 1 | indivisibles, since each is divisible into the parts of which
18 VI, 1 | no continuous thing is divisible into things without parts.
19 VI, 1 | be either indivisible or divisible, and if it is divisible,
20 VI, 1 | divisible, and if it is divisible, it must be divisible either
21 VI, 1 | is divisible, it must be divisible either into indivisibles
22 VI, 1 | divisibles that are infinitely divisible, in which case it is continuous.~
23 VI, 1 | everything continuous is divisible into divisibles that are
24 VI, 1 | divisibles that are infinitely divisible: for if it were divisible
25 VI, 1 | divisible: for if it were divisible into indivisibles, we should
26 VI, 1 | of indivisibles and are divisible into indivisibles, or none.
27 VI, 1 | through, the motion must be divisible: for at the time when O
28 VI, 1 | if the whole distance is divisible and an equal velocity will
29 VI, 1 | time, the time must also be divisible, and conversely, if the
30 VI, 1 | carried over the section A is divisible, this section A must also
31 VI, 1 | this section A must also be divisible.~
32 VI, 2 | since every magnitude is divisible into magnitudes-for we have
33 VI, 2 | continuous I mean that which is divisible into divisibles that are
34 VI, 2 | divisibles that are infinitely divisible: and if we take this as
35 VI, 2 | be finite: for it will be divisible into periods equal in number
36 VI, 2 | into which the magnitude is divisible. Moreover, if it is the
37 VI, 2 | the indivisible will be divisible, and that which has no parts
38 VI, 3 | thing is time, it will be divisible: for all time has been shown
39 VI, 3 | time has been shown to be divisible. Thus on this assumption
40 VI, 3 | assumption the present is divisible. But if the present is divisible,
41 VI, 3 | divisible. But if the present is divisible, there will be part of the
42 VI, 3 | indivisible: for if it is divisible it will be involved in the
43 VI, 4 | everything that changes must be divisible. For since every change
44 VI, 4 | everything that changes must be divisible.~Now motion is divisible
45 VI, 4 | divisible.~Now motion is divisible in two senses. In the first
46 VI, 4 | In the first place it is divisible in virtue of the time that
47 VI, 4 | In the second place it is divisible according to the motions
48 VI, 4 | applicable to everything that is divisible into parts.~Motion is also
49 VI, 4 | in time and all time is divisible, and in less time the motion
50 VI, 4 | that every motion must be divisible according to time. And since
51 VI, 4 | spheres of motion are not all divisible in a like manner: thus quantity
52 VI, 4 | essentially, quality accidentally divisible). For suppose that A is
53 VI, 4 | Again, the time will be divisible similarly to the motion:
54 VI, 4 | being-in-motion will also be divisible. For let G be the whole
55 VI, 4 | the motion of a thing is divisible into the motions of the
56 VI, 4 | these are only accidentally divisible because that which changes
57 VI, 4 | fact that all the terms are divisible or infinite is a direct
58 VI, 4 | the thing that changes is divisible or infinite: for the attributes "
59 VI, 4 | infinite: for the attributes "divisible" and "infinite" belong in
60 VI, 5 | belonging to it. For let AG be divisible, and let it be divided at
61 VI, 5 | without parts, it must be divisible, and the changing thing
62 VI, 5 | having been shown to be divisible): and let OI be the time
63 VI, 5 | the man and the time are divisible: but with the fair complexion
64 VI, 5 | otherwise (though they are all divisible accidentally, for that in
65 VI, 5 | quality is an accident is divisible). For of actual subjects
66 VI, 5 | essentially, not accidentally, divisible have no primary part. Take
67 VI, 5 | other hand it is taken to be divisible, there will be something
68 VI, 6 | motion: and (as all time is divisible) let it be divided at K.
69 VI, 6 | moments. If, then, all time is divisible, and that which is intermediate
70 VI, 6 | of time, and all time is divisible, in half the time it will
71 VI, 6 | must be a magnitude and divisible into an infinite number
72 VI, 6 | everything (that is) that is divisible and continuous: though it
73 VI, 6 | periods of time are infinitely divisible.~Consequently no absolutely
74 VI, 8 | But since AB is therefore divisible, the thing is coming to
75 VI, 8 | since all time is infinitely divisible, there cannot be anything
76 VI, 8 | parts. Since, then it is divisible, it must be a period of
77 VI, 8 | everything continuous is divisible into an infinite number
78 VI, 8 | whole period of time is divisible), so that in one part of
79 VI, 10 | two: for then it would be divisible into parts. Nor again can
80 VI, 10 | moment, and all time is divisible, for everything that is
81 VI, 10 | has been shown above to be divisible. Therefore, if a point is
82 VI, 10 | the indivisible will be divisible into something less than
83 VI, 10 | just as the time is so divisible: the fact being that the
84 VII, 1 | which is in motion, must be divisible since everything that is
85 VII, 1 | everything that is in motion is divisible. Let it be divided, then,
86 VII, 1 | in motion will always be divisible, and if a part of it is
87 VII, 4 | these, I mean, must not be divisible in the way in which colour
88 VII, 5 | the ship to traverse are divisible into as many parts as there
89 VIII, 3 | removed is, it is true, divisible into a number of parts,
90 VIII, 3 | fact that the decrease is divisible into an infinite number
91 VIII, 3 | alteration is infinitely divisible it does not follow from
92 VIII, 5 | motion must be infinitely divisible, for it has been shown already
93 VIII, 5 | that which is moved, being divisible though actually undivided,
94 VIII, 5 | things that are potentially divisible.~From what has been said,
95 VIII, 8 | becoming, time cannot be divisible into time-atoms. For suppose
96 VIII, 10| air or the water, being divisible, is a movent only in virtue
|