Book,  Paragraph

  1   I,  6 |        no such thing as infinite weight, then it follows that none
  2   I,  6 |     would have to be infinite in weight. (The same argument applies
  3   I,  6 |    supposition involves infinite weight, so the infinity of the
  4   I,  6 |    proved as follows. Assume the weight to be finite, and take an
  5   I,  6 |        infinite body, AB, of the weight C. Subtract from the infinite
  6   I,  6 |      body a finite mass, BD, the weight of which shall be E. E then
  7   I,  6 |          than C, since it is the weight of a lesser mass. Suppose
  8   I,  6 |          to BD which the greater weight bears to the smaller. For
  9   I,  6 |          weights, and the lesser weight is that of the lesser mass,
 10   I,  6 |         are equal. Again, if the weight of a greater body is greater
 11   I,  6 |         than that of a less, the weight of GB will be greater than
 12   I,  6 |         that of FB; and thus the weight of the finite body is greater
 13   I,  6 |      infinite. And, further, the weight of unequal masses will be
 14   I,  6 |          rather more than C: the weight of three masses of the full
 15   I,  6 |        whether we begin with the weight or with the mass. For example,
 16   I,  6 |          For example, assume the weight E to be commensurate with
 17   I,  6 |       infinite mass a part BD of weight E. Then let a mass BF be
 18   I,  6 |      commensurate in mass and in weight alike. Nor again does it
 19   I,  6 |   whether the total mass has its weight equally or unequally distributed.
 20   I,  6 |    infinite mass a body of equal weight to BD by diminishing or
 21   I,  6 |       then, it is clear that the weight of the infinite body cannot
 22   I,  6 |        impossibility of infinite weight can be shown in the following
 23   I,  6 |       the following way. A given weight moves a given distance in
 24   I,  6 |      distance in a given time; a weight which is as great and more
 25   I,  6 |    weights. For instance, if one weight is twice another, it will
 26   I,  6 |      movement. Further, a finite weight traverses any finite distance
 27   I,  6 |          from this that infinite weight, if there is such a thing,
 28   I,  6 |        less in proportion as the weight is greater. But there is
 29   I,  6 |         an infinite and a finite weight must have traversed an equal
 30   I,  6 |    performs the motion, a finite weight must necessarily move a
 31   I,  6 |         that same time. Infinite weight is therefore impossible,
 32   I,  6 |          Bodies then of infinite weight and of infinite lightness
 33   I,  7 |          already shown, infinite weight and lightness do not exist.
 34   I,  7 |         to admit either infinite weight or infinite lightness. Nor,
 35   I,  7 |        of fire. So that if it be weight that all possess, no body
 36   I,  7 |     Moreover, whatever possesses weight or lightness will have its
 37   I,  7 |         not everything possesses weight or lightness, but some things
 38   I,  8 |          also; and if speed then weight and lightness. For as superior
 39   I,  8 |        movement implies superior weight, so infinite increase of
 40   I,  8 |          so infinite increase of weight necessitates infinite increase
 41   I,  8 |     weightless, one endowed with weight, and below is place of the
 42   I,  8 |         of the body endowed with weight, since the region about
 43  II,  1 |        this fact will have great weight in convincing us of the
 44  II,  1 |          earthy and endowed with weight, and therefore supported
 45  II,  13|           Yet here is this great weight of earth, and it is at rest.
 46  II,  13|          can bear a considerable weight.~Now, first, if the shape
 47  II,  14|       every portion of earth has weight until it reaches the centre,
 48  II,  14|          a thing which possesses weight is naturally endowed with
 49  II,  14|          centre, and the greater weight driving the lesser forward
 50  II,  14|  spherical in shape: if, then, a weight many times that of the earth
 51  II,  14|       that any body endowed with weight, of whatever size, moves
 52 III,  1 |         parts of a thing have no weight, that the two together should
 53 III,  1 |         two together should have weight. But either all perceptible
 54 III,  1 |         as earth and water, have weight, as these thinkers would
 55 III,  1 |          Now if the point has no weight, clearly the lines have
 56 III,  1 |    planes. Therefore no body has weight. It is, further, manifest
 57 III,  1 |          their point cannot have weight. For while a heavy thing
 58 III,  1 |    suppose that what is heavy or weight is a dense body, and what
 59 III,  1 |          divisible.~Moreover, no weight can consist of parts not
 60 III,  1 |          of parts not possessing weight. For how, except by the
 61 III,  1 |         parts which will produce weight? And, further, when one
 62 III,  1 |           And, further, when one weight is greater than another,
 63 III,  1 |        the difference is a third weight; from which it will follow
 64 III,  1 |       indivisible part possesses weight. For suppose that a body
 65 III,  1 |         of four points possesses weight. A body composed of more
 66 III,  1 |          points will superior in weight to it, a thing which has
 67 III,  1 |         to it, a thing which has weight. But the difference between
 68 III,  1 |       But the difference between weight and weight must be a weight,
 69 III,  1 |    difference between weight and weight must be a weight, as the
 70 III,  1 |      weight and weight must be a weight, as the difference between
 71 III,  1 |         which makes the superior weight heavier is the single point
 72 III,  1 |     single point, therefore, has weight.~Further, to assume, on
 73 III,  1 |          and the point will have weight. For the three cases are,
 74 III,  1 |         reason of differences of weight is not this, but rather
 75 III,  1 |          manifestly endowed with weight and lightness, but an assemblage
 76 III,  1 |          form a body nor possess weight.~
 77 III,  2 |     necessary impetus is that of weight and lightness. Of necessity,
 78 III,  2 |         Suppose a body A without weight, and a body B endowed with
 79 III,  2 |        and a body B endowed with weight. Suppose the weightless
 80 III,  2 |     therefore, and one which has weight will move the same distance,
 81 III,  2 |        in motion but has neither weight nor lightness, must be moved
 82 III,  2 |    distance CE, and B, which has weight, be moved in the same time
 83 III,  2 |        body must have a definite weight or lightness. But since "
 84 III,  6 |       But if this body possesses weight or lightness, it will be
 85  IV,  1 |   lightness of things possessing weight. This can be made clearer
 86  IV,  1 |          two bodies endowed with weight and equal in bulk, which
 87  IV,  2 |         things both endowed with weight is said to be the lighter.
 88  IV,  2 | homogeneous masses, the superior weight always depending upon a
 89  IV,  2 |         owing to the increase of weight due to the increased number
 90  IV,  2 |       others, yet exceed them in weight. It is therefore obviously
 91  IV,  2 |         say that bodies of equal weight are composed of an equal
 92  IV,  2 |        which bodies endowed with weight are composed, are planes,
 93  IV,  2 |          in composite bodies the weight obviously does not correspond
 94  IV,  2 |          being often superior in weight (as, for instance, if one
 95  IV,  2 |   lighter than bodies which have weight and move downward, while,
 96  IV,  2 |        among bodies endowed with weight. Again, the suggestion of
 97  IV,  2 |          other body endowed with weight, is quicker in proportion
 98  IV,  3 |  movement is that which produces weight and lightness, and that
 99  IV,  4 |    however, the one has absolute weight, the other absolute lightness,
100  IV,  4 |         for instance, a talent’s weight of wood is heavier than
101  IV,  4 |        elements except fire have weight and all but earth lightness.
102  IV,  4 |   preponderates, must needs have weight everywhere, while water
103  IV,  4 |         each of these bodies has weight except fire, even air. Of
104  IV,  4 |   maintain, that all bodies have weight. Different views are in
105  IV,  4 |          It cannot then have any weight. If it had, there would
106  IV,  4 |         it sank: and if that had weight, there would be yet another
107  IV,  4 |         body. Fire, then, has no weight. Neither has earth any lightness,
108  IV,  5 |          have both lightness and weight, and water sinks to the
109  IV,  5 |     every body endowed with both weight and lightness has weightwhereas
110  IV,  5 |          weightwhereas earth has weight everywhere-but they only
111  IV,  5 |      beneath it: for fire has no weight even in its own place, as
112  IV,  5 |          body, if superiority of weight is due to superior size