Book,  Paragraph

  1   I,  1 |      itself for the most part with bodies and magnitudes and their
  2   I,  1 |     constituted by nature some are bodies and magnitudes, some possess
  3   I,  1 |        being in every respect. Now bodies which are classed as parts
  4   I,  1 |            them is in a sense many bodies. But the whole of which
  5   I,  2 |        starting-point. All natural bodies and magnitudes we hold to
  6   I,  2 |   completes itself in three forms.~Bodies are either simple or compounded
  7   I,  2 |  compounded of such; and by simple bodies I mean those which possess
  8   I,  2 |          in the case of the simple bodies, compound in that of the
  9   I,  2 |      natural to each of the simple bodies. Again, if the unnatural
 10   I,  2 |         straight upward and earthy bodies straight downward towards
 11   I,  2 |          the movement of composite bodies is, as we said, determined
 12   I,  2 |           being unnatural to these bodies, is the natural movement
 13   I,  2 |           movement of the rotating bodies about the centre is unnatural,
 14   I,  2 |            is something beyond the bodies that are about us on this
 15   I,  3 |        identify it with one of the bodies which move in this way.
 16   I,  3 |        properties. But all natural bodies which change their properties
 17   I,  3 |             for instance, with the bodies of animals and their parts
 18   I,  3 |           parts and with vegetable bodies, and similarly also with
 19   I,  3 |      number of what we call simple bodies cannot be greater than it
 20   I,  4 |       inoperative. So that if both bodies were there, one of them,
 21   I,  5 |        further, that if the simple bodies are finite, the composite
 22   I,  5 |          that which is composed of bodies finite both in number and
 23   I,  5 |            the same as that of the bodies which compose it. What remains
 24   I,  5 |          whether any of the simple bodies can be infinite in magnitude,
 25   I,  6 |          finite, the corresponding bodies must also be finite. Further,
 26   I,  6 |            is determinate. But the bodies which move up and down may
 27   I,  6 |         follows that none of these bodies can be infinite. For the
 28   I,  6 |         you please.) These assumed bodies will be commensurate in
 29   I,  6 |        also to infinite lightness. Bodies then of infinite weight
 30   I,  7 |         movements too of all these bodies would be infinite. But this
 31   I,  7 |         should be perceptible. All bodies, however, that occupy place
 32   I,  7 |           no up or down, gives the bodies no place for their motion;
 33   I,  8 |            not proved universal of bodies that none whatever can exist
 34   I,  8 |            be composed of the same bodies as it. Moreover each of
 35   I,  8 |           it. Moreover each of the bodies, fire, I mean, and earth
 36   I,  8 |          Clearly, then, one of the bodies will move naturally away
 37   I,  8 |     identical nature of the simple bodies in the various universes,
 38   I,  8 |            of nature in the simple bodies according as they are more
 39   I,  8 |            the same. Moreover, the bodies must have some movement,
 40   I,  8 |            constraint. If then the bodies have a natural movement,
 41   I,  8 |            that makes one of these bodies move up and the other down;
 42   I,  8 |         elsewhere: for we have two bodies, one weightless, one endowed
 43   I,  9 |        cannot be any of the simple bodies. For, first, it has been
 44  II,  1 |         conceived of all the upper bodies as earthy and endowed with
 45  II,  2 |           right and left, in these bodies relatively to ourselves.
 46  II,  3 |         attributes of the heavenly bodies. But let not that deter
 47  II,  3 |            exist, the intermediate bodies must exist also: each element
 48  II,  3 |       naturally eternal: and these bodies we know to possess movement.
 49  II,  3 |        relation of the elements of bodies to one another. This matter
 50  II,  3 |             with that of the other bodies, follows on that of earth;
 51  II,  4 |          Further, those who divide bodies into planes and generate
 52  II,  4 |            same again holds of the bodies between these and the centre.
 53  II,  4 |      between these and the centre. Bodies which are bounded by the
 54  II,  4 |         wholes, spherical; and the bodies below the sphere of the
 55  II,  4 |     evidence may be drawn from the bodies whose position is about
 56  II,  7 |          their movement, the upper bodies are carried on a moving
 57  II,  8 |          the same centre. Whenever bodies are moving with their proper
 58  II,  8 |            here with the revolving bodies: for the are intercepted
 59  II,  8 |           in shape from ambulatory bodies. Since, therefore, the heavens
 60  II,  9 |         suppose that the motion of bodies of that size must produce
 61  II,  9 |            our earth the motion of bodies far inferior in size and
 62  II,  9 |            know, shatter the solid bodies even of inanimate things:
 63  II,  9 |         rocks and the strongest of bodies. But if the moving bodies
 64  II,  9 |          bodies. But if the moving bodies are so great, and the sound
 65  II,  9 |          not hear, and show in our bodies none of the effects of violent
 66  II,  9 |     concord corroborates our view. Bodies which are themselves in
 67  II,  9 |        matter that if the heavenly bodies moved in a generally diffused
 68  II,  10|          the movement of all other bodies is composite and relatively
 69  II,  10|      influence on the intermediate bodies varying, as the mathematicians
 70  II,  11|         One, then, of the heavenly bodies being spherical, clearly
 71  II,  12|      movements in the intermediate bodies, and not, rather, in each
 72  II,  12|      thinking of the stars as mere bodies, and as units with a serial
 73  II,  12|        actions, just as with men’s bodies one is in good condition
 74  II,  12|           moves not at all and the bodies near to it with few movements.
 75  II,  12|           single movement, and the bodies intermediate between the
 76  II,  12|            move many of the divine bodies, while the numerous other
 77  II,  12|          to the single motion many bodies and to the single body many
 78  II,  12|        star, is really moving many bodies. For this last sphere moves
 79  II,  13|    possible that there are several bodies so moving, which are invisible
 80  II,  13|         earth each of these moving bodies can obstruct it. Indeed,
 81  II,  13|          be the way of flat-shaped bodies: for even the wind can scarcely
 82  II,  13|       decide at the outset whether bodies have a natural movement
 83  II,  13|      results as representing fact. Bodies, we say, which have no natural
 84  II,  13|       which the larger and heavier bodies always move to the centre
 85  II,  13|      remains, why now do all heavy bodies move to the earth. For the
 86  II,  14|   indicated by the fact that heavy bodies moving towards the earth
 87  II,  14|             but also because heavy bodies forcibly thrown quite straight
 88  II,  14|          that the motions of heavy bodies always make equal angles,
 89 III,  1 |       inquiry into nature concerns bodies: for a natural substance
 90 III,  1 |       others. And some subject all bodies whatever to generation,
 91 III,  1 |            with respect to natural bodies there are impossibilities
 92 III,  1 |          it is applied to physical bodies, but there will be difficulties
 93 III,  1 |    necessarily present in physical bodies which are necessarily excluded
 94 III,  1 |       thing, but the attributes of bodies are all divisible in one
 95 III,  1 |         But either all perceptible bodies or some, such as earth and
 96 III,  1 |         that method will give them bodies which are not any element
 97 III,  1 |            of numbers. For natural bodies are manifestly endowed with
 98 III,  2 |            that each of the simple bodies should have a natural movement
 99 III,  2 |           who say that the primary bodies are in perpetual movement
100 III,  2 |            movement, and the other bodies, moving without constraint,
101 III,  2 |          they now stand, the heavy bodies moving towards the centre
102 III,  2 |           the centre and the light bodies away from it. But that is
103 III,  2 |        possible or impossible that bodies in unordered movement should
104 III,  2 |   combinations like those of which bodies of nature’s composing are
105 III,  2 |            that there are infinite bodies moving in an infinite is
106 III,  2 |         the world we know, not all bodies, but only bodies of the
107 III,  2 |           not all bodies, but only bodies of the same kind, have a
108 III,  2 |            original state in which bodies are separated and in movement.
109 III,  2 |           by building it up out of bodies in separation, making them
110 III,  2 |        show that there are certain bodies whose necessary impetus
111 III,  2 |         relative speeds of the two bodies will be in inverse ratio
112 III,  2 |      suffices to show (1) that all bodies are either light or heavy,
113 III,  3 |           3~It remains to say what bodies are subject to generation,
114 III,  3 |            primary constituents of bodies, we must ask which of such
115 III,  3 |          we must ask which of such bodies are elements, and why; and
116 III,  3 |            a body into which other bodies may be analysed, present
117 III,  3 |          not itself divisible into bodies different in form. That,
118 III,  3 |         clearly there must be such bodies. For flesh and wood and
119 III,  3 |         wood and all other similar bodies contain potentially fire
120 III,  3 |          and earth and the related bodies are elementary bodies of
121 III,  3 |      related bodies are elementary bodies of which all things are
122 III,  3 |            of all the homoeomerous bodies, separately invisible; and
123 III,  3 |        explains why from these two bodies all others are generated. (
124 III,  3 |           or mixed, mixed in mixed bodies and simple in simple, there
125 III,  3 |           must obviously be simple bodies; for there are simple movements.
126 III,  4 |          that all the homoeomerous bodies are elements. Any one who
127 III,  4 |  Observation shows that even mixed bodies are often divisible into
128 III,  4 |        which is not divisible into bodies different in form. But even
129 III,  4 |      Indeed even two or three such bodies serve the purpose as well,
130 III,  4 |           composed of homocomerous bodies. They do not pretend that
131 III,  4 |          say that since the atomic bodies differ in shape, and there
132 III,  4 |           is an infinity of simple bodies. But they have never explained
133 III,  4 |     Further, if the differences of bodies are not infinite, plainly
134 III,  4 |          view which asserts atomic bodies must needs come into conflict
135 III,  4 |            two or more, the simple bodies must be the same in number
136 III,  5 |            say that fire is of all bodies the finest. Hence fire will
137 III,  5 |           must be one of the other bodies that is primary and not
138 III,  5 |   principle of distinction between bodies being quantity, the various
139 III,  5 |       definite ratio, and whatever bodies are in this ratio to one
140 III,  5 |          For the ratios of smaller bodies may be repeated among greater
141 III,  5 |          be repeated among greater bodies.~Those who start from fire
142 III,  5 |           of figures as fire is of bodies, or-more ingeniously-the
143 III,  5 |         following argument. As all bodies are composed of that which
144 III,  5 |        combination will form other bodies, as the fusing of gold-dust
145 III,  5 |        facts of nature. For if all bodies are quantitatively commensurable,
146 III,  5 |           shown of fire and of all bodies whose parts are relatively
147 III,  5 |           of movement. If then all bodies are one, all will have one
148 III,  6 |          in resolving into smaller bodies, a body of some size, cannot
149 III,  6 |     smaller it is. The elements of bodies must therefore be subject
150 III,  6 |            body, there will be two bodies in the same place at the
151 III,  7 |            or as those who resolve bodies into planes say, or is there
152 III,  7 |           there is no expansion of bodies, the impossibility of this
153 III,  7 |            the assertion of atomic bodies. For if the particles were
154 III,  7 |           also assert that not all bodies are divisible, coming thus
155 III,  8 |        shape to each of the simple bodies is unsound, for the reason,
156 III,  8 |           manifest that the simple bodies are often given a shape
157 III,  8 |           elements themselves, not bodies made up of them. Any one
158 III,  8 |           to be in accord with the bodies. Because fire is mobile
159 III,  8 |             and fire and the other bodies do the same. The obvious
160 III,  8 |       supposed to cut and break up bodies as fire does; still it remains
161 III,  8 |            For though it separates bodies different in kind, it combines
162  IV,  1 |       light". We must ask what the bodies so called are, how they
163  IV,  1 |           we mean that one, of two bodies endowed with weight and
164  IV,  2 |         heavier than wood. For all bodies, in spite of the general
165  IV,  2 |           in their view, all these bodies are composed) which disposes
166  IV,  2 |            and heavy between these bodies, it follows that there must
167  IV,  2 |            apparent that there are bodies which, when smaller in bulk
168  IV,  2 |           insufficient to say that bodies of equal weight are composed
169  IV,  2 |          or atomic parts, of which bodies endowed with weight are
170  IV,  2 |    position to assert that of such bodies the larger is the heavier.
171  IV,  2 |             But since in composite bodies the weight obviously does
172  IV,  2 |             which is imprisoned in bodies, lightens them and sometimes
173  IV,  2 |           to explain why there are bodies which are absolutely heavy
174  IV,  2 |     sometimes lighter than smaller bodies is one which they have passed
175  IV,  2 |       light is always lighter than bodies which have weight and move
176  IV,  2 |             water and earth) among bodies endowed with weight. Again,
177  IV,  2 | attributing the upward movement of bodies to a void which does not
178  IV,  2 |         the question why composite bodies are some light and some
179  IV,  2 |         lightness and heaviness of bodies by distinctions of size,
180  IV,  2 |     lightness and heaviness of the bodies intermediate between the
181  IV,  2 |             it imagines that these bodies which differ in size are
182  IV,  3 |   difficulty-the question why some bodies move always and naturally
183  IV,  3 |       similar and undifferentiated bodies are moved with the same
184  IV,  3 |           heavy and the light, the bodies are thought to have a spring
185  IV,  3 |         that locomotion belongs to bodies only when isolated from
186  IV,  3 |           when isolated from other bodies, and is generated last of
187  IV,  3 |     various motions of the various bodies, and the meaning of the
188  IV,  4 |    distinctive properties of these bodies and of the various phenomena
189  IV,  4 |         confine the application to bodies which do not combine lightness
190  IV,  4 |         heaviness and lightness of bodies which combine these qualities
191  IV,  4 |        rise to the surface of some bodies they sink to the bottom
192  IV,  4 |           bottom of air. Now other bodies are severally light and
193  IV,  4 |        happens to preponderate the bodies will be heavy and light
194  IV,  4 |       properties of the elementary bodies that a body which is regarded
195  IV,  4 |        lightness. Earth, then, and bodies in which earth preponderates,
196  IV,  4 |            own place each of these bodies has weight except fire,
197  IV,  4 |            some maintain, that all bodies have weight. Different views
198  IV,  4 |        which the movement of these bodies takes place. For the centre
199  IV,  5 |         and always moves downward. Bodies composed of kinds of matter
200  IV,  5 |            must needs be two other bodies which sink in some bodies
201  IV,  5 |          bodies which sink in some bodies and rise to the surface
202  IV,  5 |            be as numerous as these bodies, i.e. four, but though they
203  IV,  5 |          only have lightness among bodies to whose surface they rise.
204  IV,  5 |     species of matter as there are bodies. For if, first, there is
205  IV,  5 |          number of the constituent bodies or to the fullness of the
206  IV,  5 |       follow that the intermediate bodies move downward in some cases
207  IV,  5 |           to make the intermediate bodies behave as air and water
208  IV,  5 |            of body. But if the two bodies are one matter, or two matters
209  IV,  6 |                     6~The shape of bodies will not account for their
210  IV,  6 |  Democritus. He says that the warm bodies moving up out of the water
211  IV,  6 |            the water hold up heavy bodies which are broad, while the
212  IV,  6 |          fall through, because the bodies which offer this resistance
213  IV,  6 |      movement of the upward moving bodies) is not uniform in direction.
214  IV,  6 |          is less easily disrupted. Bodies of the opposite shape sink