Book, Paragraph
1 III, 5 | a particular quantity, e,g, two or three cubits; quantity
2 IV, 8 | will move through B in time G, and through D, which is
3 IV, 8 | it does D, and the time G will be twice the time E.
4 VI, 1 | of the indivisibles A, B, G, each corresponding part
5 VI, 1 | when its motion was E, and G similarly when its motion
6 VI, 1 | of the sections A, B, and G, it follows that a thing
7 VI, 2 | which A has changed from G to D, B will not yet have
8 VI, 2 | traversed in infinite time G, and let a finite period
9 VI, 4 | also be divisible. For let G be the whole being-in-motion.
10 VI, 5 | something other than B, say G, it must again be changing
11 VI, 5 | must again be changing from G to B: for it cannot be assumed
12 VI, 5 | there is no interval between G and B, since change is continuous.
13 VI, 5 | from B to a primary "where" G. Then if BG is taken to
14 VI, 5 | will be something prior to G to which the magnitude has
15 VI, 6 | a thing has changed from G to D. Then if GD is indivisible,
16 VI, 9 | the middle of the A’s, and G, G...those originally occupying
17 VI, 9 | middle of the A’s, and G, G...those originally occupying
18 VI, 9 | First, as the B’s and the G’s pass one another, the
19 VI, 9 | first B reaches the last G at the same moment as the
20 VI, 9 | same moment as the first G reaches the last B. Secondly
21 VI, 9 | at this moment the first G has passed all the A’s,
22 VI, 9 | time occupied by the first G, since each of the two occupies
23 VI, 9 | B’s have passed all the G’s: for the first G and the
24 VI, 9 | all the G’s: for the first G and the first B will simultaneously
25 VI, 9 | time occupied by the first G in passing each of the B’
26 VI, 9 | the first B and the first G in passing all the A’s.
27 VI, 9 | orbit as described from B or G or any other point on the
28 VII, 1 | it be divided, then, at G. Now if GB is not in motion,
29 VII, 1 | then be moved by B, B by G, G by D, and so on, each
30 VII, 1 | then be moved by B, B by G, G by D, and so on, each member
31 VII, 1 | respective motions of A, B, G, and each of the other moved
32 VII, 1 | respectively the motions of G and D: for though they are
33 VII, 1 | possible. If, then, A, B, G, D form an infinite magnitude
34 VII, 4 | distance B’ and the slower (G) passes over the distance
35 VII, 4 | passes over the distance G’, B’ will be greater than
36 VII, 4 | B’ will be greater than G’: for this is what we took "
37 VII, 4 | part of the circle equal to G’, while G will occupy the
38 VII, 4 | circle equal to G’, while G will occupy the whole of
39 VII, 4 | whole of A in passing over G’. None the less, if the
40 VII, 5 | have moved B a distance G in a time D, then in the
41 VII, 5 | 1/2B twice the distance G, and in 1/2D it will move
42 VII, 5 | 2B the whole distance for G: thus the rules of proportion
43 VII, 5 | But if E move Z a distance G in a time D, it does not
44 VII, 5 | twice Z half the distance G in the same time. If, then,
45 VII, 5 | then, A move B a distance G in a time D, it does not
46 VII, 5 | B to traverse a part of G the ratio between which
47 VII, 5 | between which and the whole of G is proportionate to that
48 VIII, 1 | time cease to be movable-e.g. the cessation of the process
49 VIII, 4 | derived from themselves-e.g. animals-make this fact
50 VIII, 5 | is moved by A and moves G, G something that is moved
51 VIII, 5 | moved by A and moves G, G something that is moved
52 VIII, 5 | we eventually arrive at G we may take it that there
53 VIII, 5 | itself. But if I take away G, AB will move itself, A
54 VIII, 5 | and B being moved, whereas G will not move itself or
55 VIII, 5 | not true, further, that G is moved by A, which is
56 VIII, 8 | the motion from A towards G: for even if they are continuous
57 VIII, 8 | and starts again towards G: but when its motion is
58 VIII, 8 | ceased to be, and it is at G that it has really come
59 VIII, 8 | the extreme point of E to G, and that, at the moment
60 VIII, 8 | reached H before A has reached G for that which makes an
61 VIII, 8 | Then D is at the moment G white and not-white: for
62 VIII, 8 | and not-white in B, and G is in both A and B. We must
63 VIII, 8 | it except the last moment G. G belongs already to the
64 VIII, 8 | except the last moment G. G belongs already to the later
65 VIII, 8 | and white of perishing, at G the process is complete.
66 VIII, 8 | process is complete. And so G is the first moment at which
67 VIII, 8 | in locomotion from A to G and that at the moment of
68 VIII, 8 | moment of its arrival at G the continuity of its motion
69 VIII, 8 | undergoing locomotion from A to G it is at the same time undergoing
70 VIII, 8 | its locomotion to A from G: consequently it is simultaneously
71 VIII, 8 | must come to a stand at G. Therefore the motion is
72 VIII, 8 | undergoing locomotion from A to G cannot also simultaneously
73 VIII, 8 | undergoing locomotion from G to A: and since the latter
74 VIII, 8 | occur a state of rest at G: for this, as we found,
75 VIII, 8 | opposite of the motion from G. The foregoing argument,
76 VIII, 10| movement, B the moved, and G the infinite time. Now let
77 VIII, 10| motion cannot be equal to G: for the greater the amount
78 VIII, 10| duration of the part of G which is occupied by all
|