Book, Paragraph
1 I, 2 | than one, then either (i) a finite or (ii) an infinite plurality.
2 I, 2 | infinite plurality. If (i) finite (but more than one), then
3 I, 2 | and if many, whether a finite or an infinite plurality.
4 I, 4 | water. Hence, since every finite body is exhausted by the
5 I, 4 | repeated abstraction of a finite body, it seems obviously
6 I, 4 | an infinite multitude of finite equal particles in a finite
7 I, 4 | finite equal particles in a finite quantity-which is impossible.
8 I, 4 | to assume a smaller and finite number of principles, as
9 I, 6 | substance is one genus: also a finite number is sufficient, and
10 I, 6 | number is sufficient, and a finite number, such as the principles
11 III, 4 | necessarily infinite or finite, even if some things dealt
12 III, 5 | be, if the elements are finite in number. For they must
13 III, 5 | potency-suppose fire is finite in amount while air is infinite
14 III, 5 | over and annihilate the finite body. On the other hand,
15 III, 5 | the parts will be either finite or infinite in variety of
16 III, 5 | in variety of kind. (i) Finite they cannot be, for if the
17 III, 5 | impossible, and the places are finite, the whole too must be finite;
18 III, 5 | finite, the whole too must be finite; for the place and the body
19 III, 6 | that is taken is always finite, but always different. Again, "
20 III, 6 | infinite by division. In a finite magnitude, the infinite
21 III, 6 | a determinate part of a finite magnitude and add another
22 III, 6 | the magnitude, for every finite magnitude is exhausted by
23 III, 6 | independently as what is finite does.~By addition then,
24 III, 7 | postulate only that the finite straight line may be produced
25 IV, 8 | times, so long as both are finite), but there is no ratio
26 VI, 2 | with infinite things in a finite time. For there are two
27 VI, 2 | extremities. So while a thing in a finite time cannot come in contact
28 VI, 2 | over the infinite is not a finite but an infinite time, and
29 VI, 2 | by means of moments not finite but infinite in number.~
30 VI, 2 | infinite, then, cannot occupy a finite time, and the passage over
31 VI, 2 | and the passage over the finite cannot occupy an infinite
32 VI, 2 | as follows. Let AB be a finite magnitude, and let us suppose
33 VI, 2 | infinite time G, and let a finite period GD of the time be
34 VI, 2 | passing over AB will be finite: for it will be divisible
35 VI, 2 | magnitude, say BE, in a finite time, and if this BE measures
36 VI, 2 | time like the magnitude is finite. That infinite time will
37 VI, 2 | traversing this part must be finite, the limit in one direction
38 VI, 2 | length can be traversed in a finite time. It is evident, then,
39 VI, 4 | the matter of their being finite or infinite, they will all
40 VI, 7 | a thing should undergo a finite motion in an infinite time,
41 VI, 7 | is occupied by the whole finite motion. In all cases where
42 VI, 7 | velocity it is clear that the finite magnitude is traversed in
43 VI, 7 | magnitude is traversed in a finite time. For if we take a part
44 VI, 7 | Consequently, since these parts are finite, both in size individually
45 VI, 7 | whole time must also be finite: for it will be a multiple
46 VI, 7 | the line AB represents a finite stretch over which a thing
47 VI, 7 | that also must occupy a finite time in consequence of the
48 VI, 7 | infinite cannot be composed of finite parts whether equal or unequal,
49 VI, 7 | will be a measure of things finite in multitude or in magnitude,
50 VI, 7 | while on the other hand the finite stretch of motion AB is
51 VI, 7 | must be accomplished in a finite time. Moreover it is the
52 VI, 7 | he will prove that in a finite time there cannot be an
53 VI, 7 | or not, if only each is finite: for it is clear that while
54 VI, 7 | process of subtraction is finite both in respect of the quantity
55 VI, 7 | will not be traversed in finite time: and it makes no difference
56 VI, 7 | evident that neither can a finite magnitude traverse an infinite
57 VI, 7 | infinite magnitude in a finite time, the reason being the
58 VI, 7 | time it will traverse a finite magnitude and in each several
59 VI, 7 | time it will traverse a finite magnitude.~And since a finite
60 VI, 7 | finite magnitude.~And since a finite magnitude will not traverse
61 VI, 7 | traverse an infinite in a finite time, it is clear that neither
62 VI, 7 | will an infinite traverse a finite in a finite time. For if
63 VI, 7 | infinite traverse a finite in a finite time. For if the infinite
64 VI, 7 | infinite could traverse the finite, the finite could traverse
65 VI, 7 | traverse the finite, the finite could traverse the infinite;
66 VI, 7 | traversing of the infinite by the finite. For when the infinite magnitude
67 VI, 7 | say GD, will occupy the finite and then another, and then
68 VI, 7 | completed a motion over the finite and the finite will have
69 VI, 7 | over the finite and the finite will have traversed the
70 VI, 7 | of the infinite over the finite to occur in any way other
71 VI, 7 | any way other than by the finite traversing the infinite
72 VI, 7 | infinite cannot traverse the finite.~Nor again will the infinite
73 VI, 7 | traverse the infinite in a finite time. Otherwise it would
74 VI, 7 | would also traverse the finite, for the infinite includes
75 VI, 7 | the infinite includes the finite. We can further prove this
76 VI, 7 | is established that in a finite time neither will the finite
77 VI, 7 | finite time neither will the finite traverse the infinite, nor
78 VI, 7 | infinite, nor the infinite the finite, nor the infinite the infinite,
79 VI, 7 | is evident also that in a finite time there cannot be infinite
80 VI, 9 | granted that it traverses the finite distance prescribed. These
81 VI, 10 | true, we cannot show to be finite in this way, since it is
82 VII, 1 | since the motion of A is finite the time will also be finite.
83 VII, 1 | finite the time will also be finite. But since the movents and
84 VII, 1 | occupied by the motion of A is finite: consequently the motion
85 VII, 1 | motion will be infinite in a finite time, which is impossible.~
86 VII, 1 | contrary supposition: for in a finite time there may be an infinite
87 VII, 1 | unity: whether this unity is finite or infinite makes no difference
88 VII, 1 | through the motion EZHO in the finite time K, this involves the
89 VII, 1 | motion is passed through in a finite time: and whether the magnitude
90 VII, 1 | magnitude in question is finite or infinite this is in either
91 VIII, 6 | rather than many, and a finite rather than an infinite
92 VIII, 6 | always assume that things are finite rather than infinite in
93 VIII, 6 | by nature that which is finite and that which is better
94 VIII, 8 | thing is rectilinear and finite it is not continuous locomotion:
95 VIII, 8 | whether it is possible in a finite time to traverse or reckon
96 VIII, 8 | whether it is possible in a finite time to traverse an infinite
97 VIII, 9 | rectilinear motion on a finite straight line is if it turns
98 VIII, 10| premisses is that nothing finite can cause motion during
99 VIII, 10| either all infinite or all finite or partly-that is to say
100 VIII, 10| the whole of B, will be finite. Therefore a finite thing
101 VIII, 10| will be finite. Therefore a finite thing cannot impart to anything
102 VIII, 10| it is impossible for the finite to cause motion during an
103 VIII, 10| infinite force to reside in a finite magnitude. This can be shown
104 VIII, 10| some extent by our supposed finite magnitude possessing an
105 VIII, 10| is the time occupied by a finite power in the performance
106 VIII, 10| adding to the latter another finite power and continually increasing
107 VIII, 10| reach a point at which the finite power has completed the
108 VIII, 10| continual addition to a finite magnitude I must arrive
109 VIII, 10| get the result that the finite force will occupy the same
110 VIII, 10| impossible. Therefore nothing finite can possess an infinite
111 VIII, 10| is also impossible for a finite force to reside in an infinite
112 VIII, 10| infinite, since it exceeds any finite force. Moreover the time
113 VIII, 10| occupied by the action of any finite force must also be finite:
114 VIII, 10| finite force must also be finite: for if a given force moves
115 VIII, 10| another way-by taking a finite magnitude in which there
116 VIII, 10| will be a measure of the finite force residing in the infinite
117 VIII, 10| infinite force to reside in a finite magnitude or for a finite
118 VIII, 10| finite magnitude or for a finite force to reside in an infinite
119 VIII, 10| magnitude, this must be either a finite or an infinite magnitude.
120 VIII, 10| that it is impossible for a finite magnitude to have an infinite
121 VIII, 10| a thing to be moved by a finite magnitude during an infinite
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