Book, Paragraph
1 I, 2 | not infinite and has no magnitude; for to have that it will
2 I, 3 | then, Being will not have magnitude, if it is substance. For
3 I, 4 | not fall below a certain magnitude. If, therefore, the process
4 I, 4 | because there is no minimum magnitude, and of quality, because
5 II, 5 | result is of considerable magnitude. Thus one who comes within
6 III, 4 | whether there is a sensible magnitude which is infinite.~We must
7 III, 5 | the infinite is neither a magnitude nor an aggregate, but is
8 III, 5 | divisible must be either a magnitude or an aggregate. But if
9 III, 5 | unless both number and magnitude, of which it is an essential
10 III, 6 | beginning and an end of time, a magnitude will not be divisible into
11 III, 6 | division.~Now, as we have seen, magnitude is not actually infinite.
12 III, 6 | by division. In a finite magnitude, the infinite by addition
13 III, 6 | determinate part of a finite magnitude and add another part determined
14 III, 6 | shall not traverse the given magnitude. But if we increase the
15 III, 6 | amount, we shall traverse the magnitude, for every finite magnitude
16 III, 6 | magnitude, for every finite magnitude is exhausted by means of
17 III, 6 | exceed every determinate magnitude, just as in the direction
18 III, 6 | division every determinate magnitude is surpassed in smallness
19 III, 6 | exceeds every assignable magnitude, unless it has the attribute
20 III, 7 | such as to surpass every magnitude, but that there should be
21 III, 7 | number is surpassed. In magnitude, on the contrary, every
22 III, 7 | contrary, every assigned magnitude is surpassed in the direction
23 III, 7 | direction there is no infinite magnitude. The reason is that what
24 III, 7 | for the number of times a magnitude can be bisected is infinite.
25 III, 7 | Hence since no sensible magnitude is infinite, it is impossible
26 III, 7 | to exceed every assigned magnitude; for if it were possible
27 III, 7 | infinite is not the same in magnitude and movement and time, in
28 III, 7 | infinite in virtue of the magnitude covered by the movement (
29 III, 7 | means, and also why every magnitude is divisible into magnitudes.)~
30 III, 7 | largest quantity another magnitude of any size you like. Hence,
31 III, 8 | succession out of existence.~(b) Magnitude is not infinite either in
32 IV, 2 | of each body by which the magnitude or the matter of the magnitude
33 IV, 2 | magnitude or the matter of the magnitude is defined: for this is
34 IV, 2 | as the extension of the magnitude, it is the matter. For this
35 IV, 2 | this is different from the magnitude: it is what is contained
36 IV, 8 | let Z be void, equal in magnitude to B and to D. Then if A
37 IV, 8 | But the cube also has a magnitude equal to that occupied by
38 IV, 8 | occupied by the void; a magnitude which, if it is also hot
39 IV, 11 | something to something, and all magnitude is continuous. Therefore
40 IV, 11 | the movement goes with the magnitude. Because the magnitude is
41 IV, 11 | the magnitude. Because the magnitude is continuous, the movement
42 IV, 11 | before" and "after" hold in magnitude, they must hold also in
43 IV, 11 | as was said, goes with magnitude, and time, as we maintain,
44 V, 2 | the direction of complete magnitude is increase, motion in the
45 V, 4 | its path is an irregular magnitude, e.g. a broken line, a spiral,
46 V, 4 | a spiral, or any other magnitude that is not such that any
47 VI, 1 | reasoning applies equally to magnitude, to time, and to motion:
48 VI, 1 | made clear as follows. If a magnitude is composed of indivisibles,
49 VI, 1 | indivisibles, the motion over that magnitude must be composed of corresponding
50 VI, 1 | indivisible motions: e.g. if the magnitude ABG is composed of the indivisibles
51 VI, 2 | 2~And since every magnitude is divisible into magnitudes-for
52 VI, 2 | indivisible parts, and every magnitude is continuous-it necessarily
53 VI, 2 | things traverses a greater magnitude in an equal time, an equal
54 VI, 2 | an equal time, an equal magnitude in less time, and a greater
55 VI, 2 | less time, and a greater magnitude in less time, in conformity
56 VI, 2 | will pass over a greater magnitude. More than this, it will
57 VI, 2 | will pass over a greater magnitude in less time: for in the
58 VI, 2 | than this, say ZK. Now the magnitude GO that A has passed over
59 VI, 2 | over is greater than the magnitude GE, and the time ZK is less
60 VI, 2 | will pass over a greater magnitude in less time. And from this
61 VI, 2 | will pass over an equal magnitude in less time than the slower.
62 VI, 2 | passes over the greater magnitude in less time than the slower,
63 VI, 2 | quicker will traverse an equal magnitude in less time than the slower.
64 VI, 2 | will pass over an equal magnitude (as well as a greater) in
65 VI, 2 | will pass over an equal magnitude in less time than the slower,
66 VI, 2 | slower has traversed the magnitude GD in the time ZH. Now it
67 VI, 2 | quicker will traverse the same magnitude in less time than this:
68 VI, 2 | And if this is divided the magnitude GK will also be divided
69 VI, 2 | GD was: and again, if the magnitude is divided, the time will
70 VI, 2 | time it is clear that all magnitude is also continuous; for
71 VI, 2 | divisions of which time and magnitude respectively are susceptible
72 VI, 2 | if time is continuous, magnitude is continuous also, inasmuch
73 VI, 2 | asses over half a given magnitude in half the time taken to
74 VI, 2 | qualification it passes over a less magnitude in less time; for the divisions
75 VI, 2 | divisions of time and of magnitude will be the same. And if
76 VI, 2 | infinite in both respects, magnitude is also infinite in both
77 VI, 2 | the time is infinite the magnitude must be infinite also, and
78 VI, 2 | infinite also, and if the magnitude is infinite, so also is
79 VI, 2 | follows. Let AB be a finite magnitude, and let us suppose that
80 VI, 2 | a certain segment of the magnitude: let BE be the segment that
81 VI, 2 | which it is.) Then, since a magnitude equal to BE will always
82 VI, 2 | and BE measures the whole magnitude, the whole time occupied
83 VI, 2 | segments into which the magnitude is divisible. Moreover,
84 VI, 2 | occupied in passing over every magnitude, but it is possible to ass
85 VI, 2 | possible to ass over some magnitude, say BE, in a finite time,
86 VI, 2 | a part, and if an equal magnitude is passed over in an equal
87 VI, 2 | follows that the time like the magnitude is finite. That infinite
88 VI, 2 | that of the quicker, the magnitude ABGD, into three indivisibles,
89 VI, 2 | indivisibles, for an equal magnitude will be passed over in an
90 VI, 4 | the motion of the whole magnitude.~Again, since every motion
91 VI, 4 | will be the motion of the magnitude ABG.~Again, if there is
92 VI, 5 | magnitudes: let AB be a magnitude, and suppose that it has
93 VI, 5 | prior to G to which the magnitude has changed, and something
94 VI, 6 | more evident in the case of magnitude, because the magnitude over
95 VI, 6 | of magnitude, because the magnitude over which what is changing
96 VI, 6 | intermediate between them must be a magnitude and divisible into an infinite
97 VI, 7 | period of time, and a greater magnitude is traversed in a longer
98 VI, 7 | is clear that the finite magnitude is traversed in a finite
99 VI, 7 | finite in multitude or in magnitude, which, whether they are
100 VI, 7 | none the less limited in magnitude); while on the other hand
101 VI, 7 | fraction, not the whole, of the magnitude will be traversed, because
102 VI, 7 | time another part of the magnitude will be traversed: and similarly
103 VI, 7 | its parts, the infinite magnitude will not be thus exhausted,
104 VI, 7 | Consequently the infinite magnitude will not be traversed in
105 VI, 7 | no difference whether the magnitude is infinite in only one
106 VI, 7 | that neither can a finite magnitude traverse an infinite magnitude
107 VI, 7 | magnitude traverse an infinite magnitude in a finite time, the reason
108 VI, 7 | it will traverse a finite magnitude and in each several part
109 VI, 7 | it will traverse a finite magnitude.~And since a finite magnitude
110 VI, 7 | magnitude.~And since a finite magnitude will not traverse an infinite
111 VI, 7 | finite. For when the infinite magnitude A is in motion a part of
112 VI, 7 | we take the motion or the magnitude to be infinite? If either
113 VI, 8 | primary part any more than a magnitude or in fact anything continuous:
114 VI, 9 | any more than any other magnitude is composed of indivisibles.~
115 VI, 10 | so far as the body or the magnitude is in motion and the partless
116 VI, 10 | AB to BG-either from one magnitude to another, or from one
117 VI, 10 | be found in the complete magnitude proper to the peculiar nature
118 VI, 10 | the complete loss of such magnitude. Locomotion, it is true,
119 VII, 1 | B, G, D form an infinite magnitude that passes through the
120 VII, 1 | finite time: and whether the magnitude in question is finite or
121 VII, 4 | time they traverse the same magnitude: and when I call it "the
122 VIII, 6 | itself must as a whole have magnitude, though nothing that we
123 VIII, 7 | are-motion in respect of magnitude, motion in respect of affection,
124 VIII, 7 | increased or decreased its magnitude changes in respect of place.~
125 VIII, 7 | perfection and imperfection of magnitude: and changes to the respective
126 VIII, 8 | affection or essential form or magnitude): and contraries are specifically
127 VIII, 8 | the intervening degrees of magnitude: and in becoming and perishing
128 VIII, 10| without parts and without magnitude, beginning with the establishment
129 VIII, 10| force to reside in a finite magnitude. This can be shown as follows:
130 VIII, 10| extent by our supposed finite magnitude possessing an infinite force
131 VIII, 10| continually increasing the magnitude of the power so added I
132 VIII, 10| continual addition to a finite magnitude I must arrive at a magnitude
133 VIII, 10| magnitude I must arrive at a magnitude that exceeds any assigned
134 VIII, 10| to reside in an infinite magnitude. It is true that a greater
135 VIII, 10| force can reside in a lesser magnitude: but the superiority of
136 VIII, 10| be still greater if the magnitude in which it resides is greater.
137 VIII, 10| Now let AB be an infinite magnitude. Then BG possesses a certain
138 VIII, 10| moving D. Now if I take a magnitude twice as great at BG, the
139 VIII, 10| the time occupied by this magnitude in moving D will be half
140 VIII, 10| continually taking a greater magnitude in this way I shall never
141 VIII, 10| infinite-just as a number or a magnitude is-if it exceeds all definite
142 VIII, 10| another way-by taking a finite magnitude in which there resides a
143 VIII, 10| resides in the infinite magnitude, so that this force will
144 VIII, 10| residing in the infinite magnitude.~It is plain, then, from
145 VIII, 10| force to reside in a finite magnitude or for a finite force to
146 VIII, 10| to reside in an infinite magnitude. But before proceeding to
147 VIII, 10| motion must be a motion of a magnitude (for that which is without
148 VIII, 10| for that which is without magnitude cannot be in motion), and
149 VIII, 10| in motion), and that the magnitude must be a single magnitude
150 VIII, 10| magnitude must be a single magnitude moved by a single movent (
151 VIII, 10| unmoved movent cannot have any magnitude. For if it has magnitude,
152 VIII, 10| magnitude. For if it has magnitude, this must be either a finite
153 VIII, 10| a finite or an infinite magnitude. Now we have already’ proved
154 VIII, 10| there cannot be an infinite magnitude: and we have now proved
155 VIII, 10| impossible for a finite magnitude to have an infinite force,
156 VIII, 10| to be moved by a finite magnitude during an infinite time.
157 VIII, 10| without parts and without magnitude.~—THE END-~ ~
|