Book, Paragraph
1 II, 2 | and likewise "number", "line", and "figure", do not involve
2 II, 7 | definition of "straight line" or "commensurable", &c.),
3 II, 9 | nature. Since a straight line is what it is, it is necessary
4 II, 9 | angles, then the straight line is not what it is either.
5 III, 7 | that the finite straight line may be produced as far as
6 IV, 5 | body contains it. On the line on which it is moved, its
7 IV, 6 | is impossible to draw a line of division beyond which
8 IV, 8 | For this reason, too, a line does not exceed a point
9 IV, 9 | sometimes in a straight line.~These then are the reasons
10 IV, 11| as the extremities of a line form a number, and not as
11 IV, 11| not as the parts of the line do so, both for the reason
12 IV, 11| lines that are parts of one line.~In so far then as the "
13 IV, 12| sometimes not: e.g. of a "line", the smallest in respect
14 IV, 12| is no minimum; for every line is divided ad infinitum.
15 IV, 13| other when one divides the line; but in so far as it is
16 IV, 14| or both along a straight line; and similarly in all other
17 V, 3 | most distant in a straight line: for the shortest line is
18 V, 3 | straight line: for the shortest line is definitely limited, and
19 V, 3 | is in succession, e.g. a line or lines if it is a line,
20 V, 3 | line or lines if it is a line, a unit or units if it is
21 V, 4 | should e.g. the "end" of a line and the "end" of walking
22 V, 4 | is regular, as a straight line is regular, the irregular
23 V, 4 | circle or on a straight line, and it is the same with
24 V, 4 | magnitude, e.g. a broken line, a spiral, or any other
25 V, 4 | with locomotion in a broken line: and a lesser degree of
26 VI, 1 | of indivisibles": e.g. a line cannot be composed of points,
27 VI, 1 | composed of points, the line being continuous and the
28 VI, 1 | between points is always a line and that which is intermediate
29 VI, 2 | been said that neither a line nor a surface nor in fact
30 VI, 7 | let us suppose that the line AB represents a finite stretch
31 VI, 10| composed of moments, just as a line is not composed of points,
32 VI, 10| equal to itself. Thus the line will be composed of points,
33 VI, 10| be a measure of the whole line. But since this is impossible,
34 VII, 4 | circumference equal to a straight line, or, of course, the one
35 VII, 4 | circle and the straight line? It would be absurd to suppose
36 VII, 4 | of another in a straight line cannot be similar, but that
37 VII, 4 | or less than the straight line; and if so it is possible
38 VII, 4 | there may be a straight line equal to a circle. But these
39 VII, 4 | the equality of a straight line and a circumference. What,
40 VII, 4 | locomotion is a genus or that line is a genus? (We may leave
41 VIII, 8| turns back in a straight line undergoes two contrary locomotions,
42 VIII, 8| only when it is a straight line that is traversed, but also
43 VIII, 8| actual. So in the straight line in question any one of the
44 VIII, 8| is in motion divides the line by coming to a stand at
45 VIII, 8| as follows. Suppose the line E is equal to the line Z,
46 VIII, 8| the line E is equal to the line Z, that A proceeds in continuous
47 VIII, 8| follow the same straight line are contrary to each other.
48 VIII, 8| follow the same straight line are contrary motions, and
49 VIII, 8| in motion on a circular line we shall find singleness
50 VIII, 8| are on the same straight line (for then they are contrary
51 VIII, 8| they are along the same line. Therefore in the case we
52 VIII, 9| as follows. The straight line traversed in rectilinear
53 VIII, 9| as an infinite straight line; and even if there were,
54 VIII, 9| motion on a finite straight line is if it turns back a composite
55 VIII, 9| should any one point on the line be a limit rather than any
56 VIII, 9| a point on the circular line, there is no point at which
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