Book, Paragraph
1 III, 3 | other, that the two vectors AB and BA, are one and the
2 VI, 2 | be shown as follows. Let AB be a finite magnitude, and
3 VI, 2 | either an exact measure of AB or less or greater than
4 VI, 2 | occupied in passing over AB will be finite: for it will
5 VI, 3 | has traversed the distance AB. That being so, the slower
6 VI, 3 | traverse a distance less than AB, say AG. But since the slower
7 VI, 4 | there will be a motion of AB and a motion of BG. That
8 VI, 4 | be the motion of the part AB and EZ the motion of the
9 VI, 4 | motion of one of the parts AB, BG) or of anything else (
10 VI, 4 | of DZ are the motions of AB, BG and of nothing else:
11 VI, 5 | change has been effected in AB or again in BG, AG cannot
12 VI, 5 | has been changing in both AB and BG (for it must either
13 VI, 5 | case of magnitudes: let AB be a magnitude, and suppose
14 VI, 7 | us suppose that the line AB represents a finite stretch
15 VI, 7 | whole stretch of motion AB which shall be a measure
16 VI, 7 | which shall be a measure of AB. Now this part of the motion
17 VI, 7 | is occupied by the whole AB. And if again I take another
18 VI, 7 | finite stretch of motion AB is a certain multiple of
19 VI, 7 | consequently the motion AB must be accomplished in
20 VI, 8 | coming to a stand. For let AB be the primary time in which
21 VI, 8 | is coming to a stand. Now AB cannot be without parts:
22 VI, 8 | be in motion. But since AB is therefore divisible,
23 VI, 8 | every one of the parts of AB: for we have shown above
24 VI, 10 | that it is changing from AB to BG-either from one magnitude
25 VI, 10 | changing it must be either in AB or in BG or partly in one
26 VI, 10 | it is changing, it is in AB. That being so, it will
27 VII, 1 | its motion in itself, let AB be taken to represent that
28 VII, 1 | first place to assume that AB, because it is in motion
29 VII, 1 | moved by something. For AB, which has been taken to
30 VII, 1 | GB is not in motion, then AB will not be in motion: for
31 VII, 1 | BG is at rest, and thus AB cannot be in motion essentially
32 VII, 1 | primarily. But ex hypothesi AB is in motion essentially
33 VII, 1 | Therefore if GB is not in motion AB will be at rest. But we
34 VIII, 5 | moved: so while we say that AB is moved by itself, we may
35 VIII, 5 | itself. But if I take away G, AB will move itself, A imparting
36 VIII, 5 | part of itself. So only AB moves itself. That which
37 VIII, 5 | moved? If so, it will not be AB primarily that is moved
38 VIII, 5 | something is taken away from AB, the remainder of AB will
39 VIII, 5 | from AB, the remainder of AB will still continue to move
40 VIII, 10| heating or pushing, and that AB is the time occupied by
41 VIII, 10| resides is greater. Now let AB be an infinite magnitude.
42 VIII, 10| never arrive at the full AB, whereas I shall always
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