Book,  Paragraph

  1   I,  2 |           the whole, whether it is infinite in size or limited in its
  2   I,  2 |           straight line:-not of an infinite line; for, if it were perfect,
  3   I,  4 |            the same two points are infinite in number. Even if we are
  4   I,  5 |         remain. First, is there an infinite body, as the majority of
  5   I,  5 |          Now the conception of the infinite possesses this power of
  6   I,  5 |        that the assumption that an infinite body exists should be of
  7   I,  5 |         moment to our inquiry. The infinite, then, we must now discuss,
  8   I,  5 |        simple or as composite; the infinite body, therefore, will be
  9   I,  5 |           the simple bodies can be infinite in magnitude, or whether
 10   I,  5 |           If the body so moving is infinite, the radii drawn from the
 11   I,  5 |            from the centre will be infinite. But the space between infinite
 12   I,  5 |    infinite. But the space between infinite radii is infinite: and by
 13   I,  5 |          between infinite radii is infinite: and by the space between
 14   I,  5 |      falling. This, I say, will be infinite: first, because in the case
 15   I,  5 |            forces us to believe in infinite number, because there is
 16   I,  5 |         between the radii. Now the infinite cannot be traversed, and
 17   I,  5 |      traversed, and if the body is infinite the interval between the
 18   I,  5 |           the radii is necessarily infinite: circular motion therefore
 19   I,  5 |     universally. Take a line, ACE, infinite in one direction, E, and
 20   I,  5 |           E, and another line, BB, infinite in both directions. Let
 21   I,  5 |        however, is impossible. The infinite, then, cannot revolve in
 22   I,  5 |        could the world, if it were infinite.~(3) That the infinite cannot
 23   I,  5 |        were infinite.~(3) That the infinite cannot move may also be
 24   I,  5 |          impossible to traverse an infinite line in a finite time. Infinite
 25   I,  5 |    infinite line in a finite time. Infinite time, then, would be required. (
 26   I,  5 |            finite is passing by an infinite or an infinite by a finite.
 27   I,  5 |       passing by an infinite or an infinite by a finite. For when A
 28   I,  5 |         takes to pass the other is infinite, then necessarily the time
 29   I,  5 |      occupied by the motion of the infinite past the finite is also
 30   I,  5 |            past the finite is also infinite. For the infinite to move
 31   I,  5 |          is also infinite. For the infinite to move at all is thus absolutely
 32   I,  5 |         body, therefore, cannot be infinite.~(4) Again, as a line which
 33   I,  5 |        which has a limit cannot be infinite, or, if it is infinite,
 34   I,  5 |          be infinite, or, if it is infinite, is so only in length, so
 35   I,  5 |             so a surface cannot be infinite in that respect in which
 36   I,  5 |          or a sphere, it cannot be infinite, any more than a foot-rule
 37   I,  5 |           then no such thing as an infinite sphere or square or circle,
 38   I,  5 |        similarly where there is no infinite at all there can be no infinite
 39   I,  5 |    infinite at all there can be no infinite movement; and from this
 40   I,  5 |           this it follows that, an infinite circle being itself an impossibility,
 41   I,  5 |           no circular motion of an infinite body.~(5) Again, take a
 42   I,  5 |         Again, take a centre C, an infinite line, AB, another infinite
 43   I,  5 |         infinite line, AB, another infinite line at right angles to
 44   I,  5 |             CD cutting E at F. The infinite line, therefore, refuses
 45   I,  5 |            Again, if the heaven is infinite and moves in a circle, we
 46   I,  5 |          time it has traversed the infinite. For suppose the fixed heaven
 47   I,  5 |           suppose the fixed heaven infinite, and that which moves within
 48   I,  5 |           It results that when the infinite body has completed its revolution,
 49   I,  5 |    revolution, it has traversed an infinite equal to itself in a finite
 50   I,  5 |           circle is not endless or infinite, but has its limit.~
 51   I,  6 |        away from the centre can be infinite. For the upward and downward
 52   I,  6 |         movement within it will be infinite; and that we have already
 53   I,  6 |          alone it is clear that an infinite body is an impossibility;
 54   I,  6 |          there is no such thing as infinite weight, then it follows
 55   I,  6 |        none of these bodies can be infinite. For the supposed infinite
 56   I,  6 |         infinite. For the supposed infinite body would have to be infinite
 57   I,  6 |     infinite body would have to be infinite in weight. (The same argument
 58   I,  6 |           one supposition involves infinite weight, so the infinity
 59   I,  6 |            to the surface involves infinite lightness.) This is proved
 60   I,  6 |          to be finite, and take an infinite body, AB, of the weight
 61   I,  6 |        weight C. Subtract from the infinite body a finite mass, BD,
 62   I,  6 |         much as you please from an infinite. If now the masses are proportionate
 63   I,  6 |           of the finite and of the infinite body are equal. Again, if
 64   I,  6 |           greater than that of the infinite. And, further, the weight
 65   I,  6 |        will be the same, since the infinite and the finite cannot be
 66   I,  6 |          with C, and take from the infinite mass a part BD of weight
 67   I,  6 |       another. (For the mass being infinite you may subtract from it
 68   I,  6 |          Possible to take from the infinite mass a body of equal weight
 69   I,  6 |       clear that the weight of the infinite body cannot be finite. It
 70   I,  6 |            finite. It must then be infinite. We have therefore only
 71   I,  6 |    impossible in order to prove an infinite body impossible. But the
 72   I,  6 |           But the impossibility of infinite weight can be shown in the
 73   I,  6 | necessarily follows from this that infinite weight, if there is such
 74   I,  6 |          no proportion between the infinite and the finite: proportion
 75   I,  6 |       supposed to hold between the infinite and the given finite; so
 76   I,  6 |           given finite; so that an infinite and a finite weight must
 77   I,  6 |            is finite, in which the infinite performs the motion, a finite
 78   I,  6 |        distance in that same time. Infinite weight is therefore impossible,
 79   I,  6 |          reasoning applies also to infinite lightness. Bodies then of
 80   I,  6 |          lightness. Bodies then of infinite weight and of infinite lightness
 81   I,  6 |          of infinite weight and of infinite lightness are equally impossible.~
 82   I,  6 |       impossible.~That there is no infinite body may be shown, as we
 83   I,  6 |          which the existence of an infinite is to be asserted or denied),
 84   I,  6 |           if the total mass is not infinite, it may yet be great enough
 85   I,  6 |       however, let us treat of the infinite universally.~
 86   I,  7 |    necessarily be either finite or infinite, and if infinite, either
 87   I,  7 |         finite or infinite, and if infinite, either of similar or of
 88   I,  7 |    represent either a finite or an infinite number of kinds. That the
 89   I,  7 |           That the kinds cannot be infinite is evident, if our original
 90   I,  7 |          proper motion. Now if the infinite body is to be composed of
 91   I,  7 |          parts must necessarily be infinite in quantity, that is to
 92   I,  7 |          as we have already shown, infinite weight and lightness do
 93   I,  7 |        that their places should be infinite in extent, so that the movements
 94   I,  7 |          all these bodies would be infinite. But this is not possible,
 95   I,  7 |        particles, say, of fire, is infinite. But body we saw to be that
 96   I,  7 |          dissimilar elements, each infinite? Each would have to be infinitely
 97   I,  7 |       conceivable, again, that the infinite should exist as a whole
 98   I,  7 |         shall have to admit either infinite weight or infinite lightness.
 99   I,  7 |          either infinite weight or infinite lightness. Nor, secondly,
100   I,  7 |            movement is circular be infinite, since it is impossible
101   I,  7 |           it is impossible for the infinite to move in a circle. This,
102   I,  7 |        saying that the heavens are infinite, which we have shown to
103   I,  7 |          it is impossible that the infinite should move at all. If it
104   I,  7 |            there is another place, infinite like itself, to which it
105   I,  7 |           it is impossible for the infinite to be acted upon by the
106   I,  7 |          shown as follows.~(1. The infinite cannot be acted upon by
107   I,  7 |           the finite.) Let A be an infinite, B a finite, C the time
108   I,  7 |      movement can be caused in the infinite by any finite agent in any
109   I,  7 |           holds between finite and infinite.~(2. The infinite cannot
110   I,  7 |       finite and infinite.~(2. The infinite cannot act upon the finite.)
111   I,  7 |       finite.) Nor, again, can the infinite produce a movement in the
112   I,  7 |         time whatever. Let A be an infinite, B a finite, C the time
113   I,  7 |        time C. Thus the finite and infinite effect the same alteration
114   I,  7 |          will no time in which the infinite can effect this movement.
115   I,  7 |          this movement. And, as to infinite time, in that nothing can
116   I,  7 |        between infinites.) Nor can infinite be acted upon in any way
117   I,  7 |           acted upon in any way by infinite. Let A and B be infinites,
118   I,  7 |         time, and the part of this infinite, E, cannot be so modified
119   I,  7 |        another. Is their time then infinite? No, for infinite time has
120   I,  7 |        time then infinite? No, for infinite time has no end, but the
121   I,  7 |           it is impossible that an infinite body should be perceptible.
122   I,  7 | perceptible. There is therefore no infinite body beyond the heaven.
123   I,  7 |     considerations as follows. The infinite, considered as a whole of
124   I,  7 |          there is no centre of the infinite, and that which moves in
125   I,  7 |          centre. Nor again can the infinite move in a straight line.
126   I,  7 |           have to be another place infinite like itself to be the goal
127   I,  7 |         its motion will have to be infinite. For infinite force is force
128   I,  7 |           have to be infinite. For infinite force is force of an infinite
129   I,  7 |      infinite force is force of an infinite body, and of an infinite
130   I,  7 |           infinite body, and of an infinite body the force is infinite.
131   I,  7 |         infinite body the force is infinite. So the motive body also
132   I,  7 |           motive body also will be infinite. (The proof of this is given
133   I,  7 |          no finite thing possesses infinite power, and no infinite thing
134   I,  7 |   possesses infinite power, and no infinite thing finite power.) If
135   I,  7 |          what is it that moves the infinite? If it moves itself, it
136   I,  7 |        possibly be conceived as an infinite animal? And if there is
137   I,  7 |          the world is conceived as infinite. And, generally, that which
138   I,  7 |        body of the universe is not infinite.~
139   I,  8 |        place. But if movement were infinite speed would be infinite
140   I,  8 |            infinite speed would be infinite also; and if speed then
141   I,  8 |        implies superior weight, so infinite increase of weight necessitates
142   I,  8 |    increase of weight necessitates infinite increase of speed.~Further,
143   I,  9 |           like form are several or infinite in number. Hence there either
144   I,  10|         other hand, the worlds are infinite in number the view is more
145   I,  12|            same thing to exist for infinite time and not to exist for
146   I,  12|             But if a thing has for infinite time more than one capacity,
147   I,  12|           a thing which exists for infinite time is destructible, it
148   I,  12|        being. Now if it exists for infinite time let this capacity be
149   I,  12|         supposed time is finite or infinite; for its capacity of being
150   I,  12|        finite time since it covers infinite time.~It is therefore impossible
151   I,  12|           not being, either for an infinite, or for a definitely limited
152   I,  12|     limited space of time; and the infinite time is only a possible
153   I,  12|           one direction is neither infinite or finite. (2) Further,
154   I,  12|          alike and the moments are infinite in number, it is clear that
155   I,  12|  destructible thing existed for an infinite time. It has therefore for
156   I,  12|            It has therefore for an infinite time the capacity of not
157   I,  12|         the thing will have for an infinite time the capacity both of
158   I,  12|       non-existent, throughout the infinite time in which it was capable
159   I,  12|            which exists for a time infinite either absolutely or in
160  II,  6 |       first show incapacity for an infinite time, and capacity afterwards
161  II,  6 |     necessarily be retarded for an infinite time. Equally impossible
162  II,  6 |         For such movement would be infinite and indefinite, but every
163  II,  6 |      additions of speed and for an infinite time. The remaining alternative
164  II,  13|         that the earth below us is infinite, saying, with Xenophanes
165  II,  13|          natural movements? In the infinite chaos there can have been
166  II,  14|           if they are thrown to an infinite distance. From these considerations
167 III,  2 |          it is or we shall have an infinite process, which is impossible.
168 III,  2 |     infinitely; for to traverse an infinite is impossible, and impossibilities
169 III,  2 |            movement in the void or infinite, may be asked to explain
170 III,  2 |       constraint, we shall have an infinite process. The same difficulty
171 III,  2 |            the view that there are infinite bodies moving in an infinite
172 III,  2 |       infinite bodies moving in an infinite is that, if the cause of
173 III,  2 |            hand, the causes are of infinite variety, their motions too
174 III,  4 |         the elements are finite or infinite in number, and, if finite,
175 III,  4 |       denying that their number is infinite, as some suppose. We begin
176 III,  4 |             according to them, are infinite in number and indivisible
177 III,  4 |      differences of bodies are not infinite, plainly the elements will
178 III,  4 |           if the clements would be infinite in number. The atoms differ
179 III,  4 |            simple movements is not infinite, because the simple motions
180 III,  4 |            number of places is not infinite, on these grounds also we
181 III,  4 |          the number of elements is infinite.~
182 III,  5 |            and denser than air, an infinite body-so they say-bracing
183 III,  6 |          somewhere. (1) Suppose it infinite. Then the time occupied
184 III,  6 |    occupied by the process will be infinite, and also that occupied
185 III,  6 |          follow that there are two infinite times which are mutually
186 III,  6 |            the synthesis, which is infinite, being preceded by the period