Book, Paragraph
1 I, 2 | whole and its parts. On this point, indeed, they were already
2 I, 3 | substances? Some thinkers did, in point of fact, give way to both
3 I, 4 | from what is not (on this point all the physicists agree),
4 I, 5 | of contraries.~Up to this point we have practically had
5 I, 9 | being, accepting on this point the statement of Parmenides.
6 II, 2 | nature" is used.~The next point to consider is how the mathematician
7 II, 2 | form and the matter up to a point (e.g. the doctor has a knowledge
8 II, 2 | form or essence? Up to a point, perhaps, as the doctor
9 II, 8 | cause difficulty on this point. Yet it is impossible that
10 III, 4 | indestructible. For there must be a point at which what has come to
11 III, 5 | because it is infinite on that point a general proof can be given
12 III, 7 | of the untraversable. In point of fact they do not need
13 IV, 1 | air. But when we come to a point we cannot make a distinction
14 IV, 1 | Hence if the place of a point is not different from the
15 IV, 1 | is not different from the point, no more will that of any
16 IV, 5 | body in it,~(2) Nor that a point should have a place,~(3)
17 IV, 7 | absurd to suppose that the point is void; for the void must
18 IV, 8 | is no void.~Further, in point of fact things that are
19 IV, 8 | a line does not exceed a point unless it is composed of
20 IV, 10 | to another, any more than point to point. If then it did
21 IV, 10 | any more than point to point. If then it did not cease-to-be
22 IV, 11 | there corresponds to the point the body which is carried
23 IV, 11 | identical substratum (whether a point or a stone or something
24 IV, 11 | correspondence with the point; for the point also both
25 IV, 11 | with the point; for the point also both connects and terminates
26 IV, 11 | this way, using the one point as two, a pause is necessary,
27 IV, 11 | is necessary, if the same point is to be the beginning and
28 IV, 11 | is "number" of the same point because it is beginning
29 IV, 11 | for we can use the middle point as two, so that on that
30 IV, 12 | minimum is one (or two); in point of extent there is no minimum.~
31 IV, 13 | obvious as it is with the point, which is fixed. It divides
32 IV, 13 | always one and the same point, since it is other and other
33 V, 3 | Hence, if as some say "point" and "unit" have an independent
34 V, 4 | the same, e.g. when one point changes again and again
35 V, 4 | activities must also in point of number be two (for only
36 VI, 1 | being continuous and the point indivisible. For the extremities
37 VI, 1 | separate.~Nor, again, can a point be in succession to a point
38 VI, 1 | point be in succession to a point or a moment to a moment
39 VI, 2 | demonstrated at each stage as a new point of departure: for the quicker
40 VI, 3 | future time at the actual point of division. Also the present
41 VI, 6 | finds an extreme in the point of division. Therefore motion
42 VI, 8 | still unaltered, not one point only but two at least being
43 VI, 9 | pursuer must first reach the point whence the pursued started,
44 VI, 9 | the goal and the middle point of the course and the other
45 VI, 9 | that between the middle point and the starting-post. This,
46 VI, 9 | orbit as described from a point A on a circumference, it
47 VI, 9 | from B or G or any other point on the same circumference
48 VI, 10 | 10~Our next point is that that which is without
49 VI, 10 | there can be no motion of a point or of any other indivisible.
50 VI, 10 | it is evident that the point also must first traverse
51 VI, 10 | composed of points, for the point, as it continually traverses
52 VI, 10 | divisible. Therefore, if a point is in motion, there must
53 VI, 10 | principle is involved.~Our next point is that no process of change
54 VIII, 1 | since time contains no point of contact for us except
55 VIII, 2 | later that will make this point clearer.~As regards the
56 VIII, 2 | But we will leave this point also to be elucidated at
57 VIII, 3 | objections involving the point that we have just raised
58 VIII, 3 | reply to them: thus we may point out that there cannot be
59 VIII, 3 | same things. We may further point out that the defender of
60 VIII, 3 | repeat that assertion. We may point out that, even if it is
61 VIII, 5 | things must up to a certain point be in contact): and the
62 VIII, 6 | has served to clear up the point about which we raised a
63 VIII, 7 | start afresh from another point. We must consider whether
64 VIII, 7 | Again, there is another point of view from which it will
65 VIII, 7 | thing at the same time: the point is of no importance to the
66 VIII, 8 | it has reached the same point from which it started).
67 VIII, 8 | coming to a stand at that point and beginning its motion
68 VIII, 8 | have ceased to be at the point B: it can only have been
69 VIII, 8 | in thought. However, the point A is the real starting-point
70 VIII, 8 | locomotion from the extreme point of E to G, and that, at
71 VIII, 8 | moment when A is at the point B, D is proceeding in uniform
72 VIII, 8 | A is at B at a sectional point of time and does not occupy
73 VIII, 8 | again: then the extreme point D has served as finishing-point
74 VIII, 8 | starting-point for it, one point thus serving as two: therefore
75 VIII, 8 | H is at D at a sectional point of time and has not come
76 VIII, 8 | potentially, existent. Now the point in the middle is potential:
77 VIII, 8 | distance into two halves one point is treated as two, since
78 VIII, 8 | result follows: for then one point must be reckoned as two:
79 VIII, 8 | unless we hold that the point of time that divides earlier
80 VIII, 8 | become. It is true that the point is common to both times,
81 VIII, 8 | so is white at the last point of the actual time in which
82 VIII, 8 | becoming white: and this point has no other point consecutive
83 VIII, 8 | this point has no other point consecutive with or in succession
84 VIII, 8 | a special bearing on the point at issue. If we look at
85 VIII, 8 | at the question from the point of view of general theory,
86 VIII, 8 | must, on arriving at any point in the course of its locomotion,
87 VIII, 8 | process of locomotion to that point, if it is not forced out
88 VIII, 8 | serve better to make this point clear universally in respect
89 VIII, 8 | than the foregoing on the point at issue. We will suppose
90 VIII, 8 | meet in the same extreme point?~On the other hand, in motion
91 VIII, 8 | since it is in motion to the point at which it will finally
92 VIII, 8 | motions: for a motion to a point and a motion from that point
93 VIII, 8 | point and a motion from that point are not always contraries
94 VIII, 9 | such a way that there is a point from which that which is
95 VIII, 9 | can be said to start and a point at which it can be said
96 VIII, 9 | for why should any one point on the line be a limit rather
97 VIII, 9 | than any other? Any one point as much as any other is
98 VIII, 9 | consequently since this point is not a point on the circular
99 VIII, 9 | since this point is not a point on the circular line, there
100 VIII, 9 | circular line, there is no point at which that which is in
101 VIII, 9 | proceeding always about a central point and not to an extreme point:
102 VIII, 9 | point and not to an extreme point: therefore it remains still,
103 VIII, 9 | continuously in motion. Our next point gives a convertible result:
104 VIII, 10| some time or other reach a point at which the finite power
105 VIII, 10| all definite limits. This point may also be proved in another
106 VIII, 10| must come to an end, and a point will be reached at which
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