Book,  Paragraph

  1   I,  1 |            magnitudes, some possess body and magnitude, and some
  2   I,  1 |       capable of subdivision, and a body is that which is every way
  3   I,  1 |             surface, and if three a body. Beyond these there is no
  4   I,  1 |             which they are applied, body alone among magnitudes can
  5   I,  1 |        clear. We cannot pass beyond body to a further kind, as we
  6   I,  1 |        surface, and from surface to body. For if we could, it would
  7   I,  1 |         would cease to be true that body is complete magnitude. We
  8   I,  2 |         with what we said above: as body found its completion in
  9   I,  2 |          will be that of the simple body which prevails in the composition.
 10   I,  2 |           both movement of a simple body is simple and simple movement
 11   I,  2 |             movement is of a simple body (for if it is movement of
 12   I,  2 |          necessarily be some simple body which revolves naturally
 13   I,  2 |           it is not natural, to the body moved. If then (1) the body,
 14   I,  2 |         body moved. If then (1) the body, whose movement is circular,
 15   I,  2 |             the other hand, (2) the body moving with this circular
 16   I,  2 |             movement belongs to the body which naturally prior, and
 17   I,  2 |             movement of some simple body. For the movement of composite
 18   I,  2 |           determined by that simple body which preponderates in the
 19   I,  2 |           which is unnatural to one body is natural to another-as,
 20   I,  2 |             some simple and primary body which is ordained to move
 21   I,  2 |            so, if, as some say, the body so moved is fire, this movement
 22   I,  3 |             is clear that not every body either possesses lightness
 23   I,  3 |            relatively to earth. The body, then, which moves in a
 24   I,  3 |          appropriate to each simple body, and so we should be compelled
 25   I,  3 |          the first place, that this body can possess no lightness
 26   I,  3 |      reasonable to assume that this body will be ungenerated and
 27   I,  3 |          are contrary. If then this body can have no contrary, because
 28   I,  3 |        exempted from contraries the body which was to be ungenerated
 29   I,  3 |         upon contact with a kindred body, which is resolved into
 30   I,  3 |           nothing out of which this body can have been generated.
 31   I,  3 |            elements. And so, if the body which moves with a circular
 32   I,  3 |             reasons why the primary body is eternal and not subject
 33   I,  3 |           implying that the primary body is something else beyond
 34   I,  3 |              The motion of a simple body must itself be simple, and
 35   I,  5 |         First, is there an infinite body, as the majority of the
 36   I,  5 |         assumption that an infinite body exists should be of peculiar
 37   I,  5 |           from the beginning.~Every body is necessarily to be classed
 38   I,  5 |             composite; the infinite body, therefore, will be either
 39   I,  5 |              Let us try the primary body first, and then go on to
 40   I,  5 |            consider the others.~The body which moves in a circle
 41   I,  5 |       following reasons. (1) If the body so moving is infinite, the
 42   I,  5 |            be traversed, and if the body is infinite the interval
 43   I,  5 |       finite line AB. The revolving body, therefore, cannot be infinite.~(
 44   I,  5 |      circular motion of an infinite body.~(5) Again, take a centre
 45   I,  5 |      results that when the infinite body has completed its revolution,
 46   I,  5 |             have now shown that the body which moves in a circle
 47   I,  6 |             from whatever point the body which sinks to the bottom
 48   I,  6 |   determinate, and consequently any body which either is in it, or
 49   I,  6 |           is clear that an infinite body is an impossibility; but
 50   I,  6 |           For the supposed infinite body would have to be infinite
 51   I,  6 |              so the infinity of the body which rises to the surface
 52   I,  6 |        finite, and take an infinite body, AB, of the weight C. Subtract
 53   I,  6 |          Subtract from the infinite body a finite mass, BD, the weight
 54   I,  6 |          finite and of the infinite body are equal. Again, if the
 55   I,  6 |             the weight of a greater body is greater than that of
 56   I,  6 |            the weight of the finite body is greater than that of
 57   I,  6 |            from the infinite mass a body of equal weight to BD by
 58   I,  6 |          the weight of the infinite body cannot be finite. It must
 59   I,  6 |          order to prove an infinite body impossible. But the impossibility
 60   I,  6 |            help us. For some finite body could have been found greater
 61   I,  6 |           That there is no infinite body may be shown, as we have
 62   I,  7 |                             7~Every body must necessarily be either
 63   I,  7 |         number, the kinds of simple body are necessarily also finite,
 64   I,  7 |            the movement of a simple body is simple, and the simple
 65   I,  7 |           finite, and every natural body must always have its proper
 66   I,  7 |         motion. Now if the infinite body is to be composed of a finite
 67   I,  7 |          arrive. Again, suppose the body to exist in dispersion,
 68   I,  7 |           of fire, is infinite. But body we saw to be that which
 69   I,  7 |            Nor, secondly, could the body whose movement is circular
 70   I,  7 |         therefore every perceptible body possesses the power of acting
 71   I,  7 |         impossible that an infinite body should be perceptible. All
 72   I,  7 |            is therefore no infinite body beyond the heaven. Nor again
 73   I,  7 |       beyond the heaven there is no body at all. For if you suppose
 74   I,  7 |             is force of an infinite body, and of an infinite body
 75   I,  7 |            body, and of an infinite body the force is infinite. So
 76   I,  7 |             infinite. So the motive body also will be infinite. (
 77   I,  7 |         weight that all possess, no body is, strictly speaking, light:
 78   I,  7 |        natural place for some other body, as experience shows. Necessarily,
 79   I,  7 |           then it is clear that the body of the universe is not infinite.~
 80   I,  8 |            to constraint? No, for a body which has no natural movement
 81   I,  8 |           not the action of another body that makes one of these
 82   I,  8 |         becomes more distant, and a body moves without constraint
 83   I,  8 |            the place, first, of the body which sinks to the bottom,
 84   I,  8 |          secondly, of the revolving body, namely the outermost place,
 85   I,  8 |       belonging to the intermediate body. Here in this third place
 86   I,  8 |             third place will be the body which rises to the surface;
 87   I,  8 |           and below is place of the body endowed with weight, since
 88   I,  8 |             been given to the heavy body. And its position cannot
 89   I,  9 |             all natural perceptible body.~First, however, we must
 90   I,  9 |          the whole, or that natural body whose place is at the extreme
 91   I,  9 |            we use this name for the body continuous with the extreme
 92   I,  9 |             we give the name to all body included within extreme
 93   I,  9 |           all physical and sensible body, because there neither is,
 94   I,  9 |            can come into being, any body outside the heaven. For
 95   I,  9 |           For if there is a natural body outside the extreme circumference
 96   I,  9 |             a simple or a composite body, and its position must be
 97   I,  9 |            be natural to some other body, since a place which is
 98   I,  9 |           which is unnatural to one body must be natural to another:
 99   I,  9 |          saw that there is no other body besides these. Then it is
100   I,  9 |            possible that any simple body should be outside the heaven.
101   I,  9 |           heaven. But, if no simple body, neither can any mixed body
102   I,  9 |         body, neither can any mixed body be there: for the presence
103   I,  9 |          the presence of the simple body is involved in the presence
104   I,  9 |             Further neither can any body come into that place: for
105   I,  9 |            saw, natural perceptible body. So that neither are there
106   I,  9 |          heaven. For in every place body can be present; and void
107   I,  9 |            in which the presence of body, though not actual, is possible;
108   I,  9 |           in the absence of natural body there is no movement, and
109   I,  9 |           heaven, as we have shown, body neither exists nor can come
110   I,  9 |           its proper place, but the body whose path is the circle
111   I,  10|             that if the totality of body, which is a continuum, is
112   I,  11|             is sight of the smaller body, but superior speed is that
113   I,  11|        speed is that of the greater body.~
114   I,  12|           which compose the natural body are the very same that destroy
115  II,  1 |          being imposed on the first body, whose natural motion is
116  II,  2 |             these principles to the body of the universe, we should
117  II,  2 |          and back, in every kind of body, but only in those which,
118  II,  3 |           the heaven, viz. a divine body, and for that reason to
119  II,  3 |            it is given the circular body whose nature it is to move
120  II,  3 |              then, is not the whole body of the heaven of the same
121  II,  3 |             centre of the revolving body; and of that body no part
122  II,  3 |         revolving body; and of that body no part can be at rest,
123  II,  3 |             could do so only if the body’s natural movement were
124  II,  3 |        inconceivable that a movable body should be eternal, if its
125  II,  3 |           is more than one circular body is the necessity of generation,
126  II,  3 |             eternal movement in one body necessitates eternal rest
127  II,  4 |         figure belongs to the first body, and the first body is that
128  II,  4 |           first body, and the first body is that at the farthest
129  II,  4 |  circumference. It follows that the body which revolves with a circular
130  II,  4 |            then will be true of the body continuous with it: for
131  II,  4 |     spherical throughout; for every body within it is contiguous
132  II,  4 |             that there is place and body and void without it. For
133  II,  4 |              but where formerly was body, is now none, and where
134  II,  4 |              and where now is none, body will be in a moment because
135  II,  4 |             void outside the moving body, because the whole body
136  II,  4 |             body, because the whole body would not always occupy
137  II,  4 |         substance of the enveloping body; since with each step away
138  II,  6 |             which is moved, being a body, is nevertheless unchanging,
139  II,  7 |      because they believe the upper body to be fire, the presumption
140  II,  7 |             sphere of the revolving body is necessarily heated by
141  II,  8 |           them out of the spherical body, and since the spherical
142  II,  8 |             and since the spherical body has two movements proper
143  II,  9 |       attached or fixed to a moving body, as the parts to a ship,
144  II,  9 |             is caused when a moving body is enclosed in an unmoved
145  II,  9 |           is enclosed in an unmoved body, and cannot be caused by
146  II,  9 |           continuous with, a moving body which creates no friction.
147  II,  10|         leads us to expect that the body which is nearest to that
148  II,  10|          are. For it is the nearest body which is most strongly influenced,
149  II,  12|          rather, in each successive body a variety of movement proportionate
150  II,  12|           expect, since the primary body shows one motion only, that
151  II,  12|           one motion only, that the body which is nearest to it should
152  II,  12|          thus nearer to the primary body than they, as observation
153  II,  12|            bodies and to the single body many motions. And there
154  II,  12|          motions have each only one body, in that each of them except
155  II,  12|             sphere being actually a body; so that its movement will
156  II,  12|            the force of any limited body is only adequate to moving
157  II,  12|        adequate to moving a limited body.~The characteristics of
158  II,  13|          the animal and that of the body are different. For this
159  II,  13|            amount great because the body which isolates it, the earth,
160  II,  13|             this would apply to any body, whereas movement to the
161  II,  13|         circumference. For since no body is a point, it will have
162  II,  13|             The expansion, when the body increased the place occupied,
163  II,  14|           to our postulate that any body endowed with weight, of
164  II,  14|     quantity must prevail until the body’s centre occupies the centre.
165 III,  1 |       natural substance is either a body or a thing which cannot
166 III,  1 |         come into existence without body and magnitude. This appears
167 III,  1 |         theory which composes every body of planes is, as the most
168 III,  1 |            the planes. Therefore no body has weight. It is, further,
169 III,  1 |          heavy or weight is a dense body, and what is light rare.
170 III,  1 |          weight. For suppose that a body of four points possesses
171 III,  1 |          points possesses weight. A body composed of more than four
172 III,  1 |           the number of planes in a body that makes one heavier than
173 III,  1 |        plane and as a plane is to a body. Now the various forms in
174 III,  1 |       points, and that there was no body at all. A further consideration
175 III,  1 |       neither be composed to form a body nor possess weight.~
176 III,  2 |           Now manifestly there is a body which is at rest at the
177 III,  2 |            make it plain that every body has its natural movement,
178 III,  2 |          from the centre. Suppose a body A without weight, and a
179 III,  2 |             A without weight, and a body B endowed with weight. Suppose
180 III,  2 |              Suppose the weightless body to move the distance CD,
181 III,  2 |         move further. Let the heavy body then be divided in the proportion
182 III,  2 |           distance CD. A weightless body, therefore, and one which
183 III,  2 |         case of lightness. Again, a body which is in motion but has
184 III,  2 |           the smaller and lighter a body is the further will a given
185 III,  2 |           Now let A, the weightless body, be moved the distance CE,
186 III,  2 |     distance CD. Dividing the heavy body in the proportion CE:CD,
187 III,  2 |             subtract from the heavy body a part which will in the
188 III,  2 |          sizes. Thus the weightless body will move the same distance
189 III,  2 |            motion of the weightless body will cover a greater distance
190 III,  2 |        therefore obvious that every body must have a definite weight
191 III,  2 |       transmits the movement to the body by first, as it were, impregnating
192 III,  2 | impregnating the air. That is why a body moved by constraint continues
193 III,  2 |           the natural movement of a body may be helped on in the
194 III,  2 |        occupied by void in which no body was. Now it is quite possible
195 III,  2 |           is quite possible for one body to be generated out of another,
196 III,  2 |       potentially a certain kind of body may, it is true, become
197 III,  2 |     actuality, But if the potential body was not already in actuality
198 III,  2 |        actuality some other kind of body, the existence of an extra-corporeal
199 III,  3 |           element, we take it, is a body into which other bodies
200 III,  3 |            were only one elementary body, it would not contain them.
201 III,  3 |             But since every natural body has it proper movement,
202 III,  4 |              not every homoeomerous body can be an element; only,
203 III,  4 |             or in number. Again, if body is distinguished from body
204 III,  4 |          body is distinguished from body by the appropriate qualitative
205 III,  4 |       proper movement, and a simple body has a simple movement, and
206 III,  5 |            either water or air or a body finer than water and denser
207 III,  5 |            is analysis, so that the body with the finer parts must
208 III,  5 |              And whether the finest body is fire or not makes no
209 III,  5 |           air, but one and the same body will be relatively to this
210 III,  5 |            pryamids: but the finest body is fire, while among figures
211 III,  5 |     smallest parts; and the primary body must have the primary figure:
212 III,  5 |         hand, they make the primary body an atom, the view will be
213 III,  5 |        generally, more of the finer body than of the coarser, obviously
214 III,  5 |             other hand, the primary body is divisible, then (a) those
215 III,  5 |             and also that not every body is either an element or
216 III,  5 |             infinitely, since every body is divisible and that which
217 III,  5 |           have to say that the same body is relatively to this fire
218 III,  5 |         which is the same for every body. For it is a matter of observation
219 III,  5 |          observation that a natural body possesses a principle of
220 III,  6 |             water, and every simple body undergo a process of analysis,
221 III,  6 |           stops somewhere. Then the body at which it stops will be
222 III,  6 |          have intended, a divisible body which will yet never be
223 III,  6 |       neither can it be a divisible body which analysis will never
224 III,  6 |          never reach. For a smaller body is more easily destroyed
225 III,  6 |    resolving into smaller bodies, a body of some size, cannot reasonably
226 III,  6 |            to fail with the smaller body. Now in fire we observe
227 III,  6 |     something incorporeal or from a body, and if from a body, either
228 III,  6 |          from a body, and if from a body, either from one another
229 III,  6 |           be incorporeal or possess body; and if it has body, there
230 III,  6 |         possess body; and if it has body, there will be two bodies
231 III,  6 |         generated from some kind of body. That would involve a body
232 III,  6 |          body. That would involve a body distinct from the elements
233 III,  6 |          prior to them. But if this body possesses weight or lightness,
234 III,  6 |    something incorporeal nor from a body which is not an element,
235 III,  7 |         process of excretion from a body of what was in it all the
236 III,  7 |            they say that water is a body present in air and excreted
237 III,  7 |        water. Again, when the mixed body is divided, they can show
238 III,  7 |          take up more room than the body did: but when water turns
239 III,  7 |          The fact is that the finer body takes up more room, as is
240 III,  7 |    accounting for the fact that the body which results from division
241 III,  7 |             for ever, if the finite body contains an infinity, which
242 III,  7 |        cannot be dissolved into any body but itself. Again, in the
243 III,  7 |    generation does not start from a body. For what is generated out
244 III,  7 |          have been generated from a body. And they must also assert
245 III,  7 |            fire, so that there is a body prior to the element-for
246 III,  7 |            to the element-for every body is either an element or
247 III,  7 |            of elements-or not every body is divisible.~
248 III,  8 |         contact with the containing body; while, if its shape is
249 III,  8 |             or any other continuous body? The elements alone cannot
250 III,  8 |        possession of angles makes a body produce heat and combustion,
251 III,  8 |              Again, combustion of a body produces fire, and fire
252 III,  8 |            sphere or a pyramid. The body, then, is turned into spheres
253 III,  8 |            expulsion of the foreign body is an incident in the compacting
254 III,  8 |            contradict themselves. A body of large particles, they
255 III,  8 |            power; for every natural body has, we maintain, its own
256  IV,  2 |            in the Timaeus, that the body which is composed of the
257  IV,  2 |          sometimes makes the larger body the lighter. The reason
258  IV,  2 |         account for the fact that a body composed of a number of
259  IV,  2 |       generally and in every case a body is relatively light when
260  IV,  2 |           The fact, again, that the body of greater bulk is sometimes
261  IV,  2 |           less solid than any other body, as well as more void, yet
262  IV,  2 |            of void, there will be a body, lighter than the absolutely
263  IV,  2 |             void and the solid in a body is no more equal to solving
264  IV,  2 |            or lead, or of any other body endowed with weight, is
265  IV,  3 |          The local movement of each body into its own place must
266  IV,  3 |            and the movement of each body to its own place is motion
267  IV,  3 |            it is to its like that a body moves when it moves to its
268  IV,  3 |          the relation of each outer body to that which is next within
269  IV,  3 |          meaning of the motion of a body to its own place, have now
270  IV,  4 |            elementary bodies that a body which is regarded as light
271  IV,  4 |             more than when empty. A body, then, in which air preponderates
272  IV,  4 |             it in air, since such a body does not rise in air but
273  IV,  4 |             and an absolutely heavy body. And by absolutely light
274  IV,  4 |             say, these two kinds of body, and it is not the case,
275  IV,  4 |        agreed that there is a heavy body, which moves uniformly towards
276  IV,  4 |           is also similarly a light body. For we see with our eyes,
277  IV,  4 |             therefore there is some body which rises to the surface
278  IV,  4 |        remains at rest-clearly this body is moving towards the extremity.
279  IV,  4 |              there would be another body in which it sank: and if
280  IV,  4 |          have no evidence of such a body. Fire, then, has no weight.
281  IV,  5 |              But since there is one body only which rises to the
282  IV,  5 |          Now in its own place every body endowed with both weight
283  IV,  5 |         support is withdrawn such a body moves downward until it
284  IV,  5 |       downward until it reaches the body next below it, air to the
285  IV,  5 |          two move downward when the body beneath is withdrawn because,
286  IV,  5 |            or to the surface of the body in which it rises, since
287  IV,  5 |         will be no absolutely light body, if superiority of weight
288  IV,  5 |           or to the fullness of the body: but the contrary is a matter
289  IV,  5 |             of some special kind of body. But if the two bodies are
290  IV,  6 |        downward motion of the heavy body and the disruption-resisting