Book, Paragraph
1 I, 4 | infinite multitude of finite equal particles in a finite quantity-which
2 II, 9 | angles of a triangle should equal two right angles. But not
3 II, 9 | though if the angles are not equal to two right angles, then
4 II, 9 | of the triangle are not equal to two right angles.~The
5 IV, 4 | of a thing would not be equal to the thing-which it is
6 IV, 4 | than its extension, but equal to it; for the extremities
7 IV, 6 | a mickle": thus if many equal bodies can be together,
8 IV, 8 | because, other things being equal, the moving body differs
9 IV, 8 | ratio. For let Z be void, equal in magnitude to B and to
10 IV, 8 | the full. But in a time equal to H, A will traverse the
11 IV, 8 | movement, i.e. in a time equal to H. If, then, there is
12 IV, 8 | it will traverse Z in an equal time whether Z be full or
13 IV, 8 | this be full or void, in an equal time; for there will be
14 IV, 8 | respects, move faster over an equal space, and in the ratio
15 IV, 8 | Therefore all will possess equal velocity. But this is impossible.~
16 IV, 8 | water, an amount of water equal to the cube will be displaced;
17 IV, 8 | penetrated the cube to a distance equal to that which this portion
18 IV, 8 | cube also has a magnitude equal to that occupied by the
19 IV, 8 | light, it will occupy an equal amount of void, and fill
20 IV, 8 | of place or of the void equal to itself. How then will
21 IV, 8 | the void or place that is equal to it? And if there can
22 IV, 8 | situation if there is an equal interval attached to it
23 IV, 9 | must always change into equal amounts (e.g. if air has
24 IV, 9 | the same time out of an equal amount of air a cupful of
25 IV, 9 | always be balanced by an equal transformation of air into
26 IV, 9 | somewhere else there must be an equal amount of water produced
27 IV, 9 | bulk of the whole may be equal, or that nothing moves.
28 IV, 14 | then, and will there be two equal times at once? Surely not.
29 IV, 14 | For a time that is both equal and simultaneous is one
30 IV, 14 | if their number also is equal and simultaneous; and for
31 IV, 14 | same, because the number of equal and simultaneous movements
32 IV, 14 | number if the two numbers are equal, but not the same decad
33 VI, 1 | distance is divisible and an equal velocity will cause a thing
34 VI, 2 | greater magnitude in an equal time, an equal magnitude
35 VI, 2 | magnitude in an equal time, an equal magnitude in less time,
36 VI, 2 | short of it: so that in an equal time the quicker will pass
37 VI, 2 | quicker will pass over an equal magnitude in less time than
38 VI, 2 | quicker will traverse an equal magnitude in less time than
39 VI, 2 | always occupy either an equal time or less or more time
40 VI, 2 | occupies more time and of equal velocity if its motion occupies
41 VI, 2 | if its motion occupies an equal time, the quicker is neither
42 VI, 2 | the quicker is neither of equal velocity nor slower, it
43 VI, 2 | quicker can occupy neither an equal time nor more time. It can
44 VI, 2 | quicker will pass over an equal magnitude (as well as a
45 VI, 2 | quicker will pass over an equal magnitude in less time than
46 VI, 2 | susceptible are the same and equal.~Moreover, the current popular
47 VI, 2 | Then, since a magnitude equal to BE will always be passed
48 VI, 2 | always be passed over in an equal time, and BE measures the
49 VI, 2 | be divisible into periods equal in number to the segments
50 VI, 2 | it is a part, and if an equal magnitude is passed over
51 VI, 2 | magnitude is passed over in an equal time, then it follows that
52 VI, 2 | period of time and in an equal time the quicker passes
53 VI, 2 | three indivisibles, for an equal magnitude will be passed
54 VI, 2 | will be passed over in an equal time. Suppose then that
55 VI, 4 | and these motions will be equal to DE, EZ respectively:
56 VI, 4 | of the parts, OI will be equal to DZ: if on the other hand
57 VI, 4 | must be the same as and equal to DZ.~This then is what
58 VI, 6 | thing that is in motion with equal velocity and began its motion
59 VI, 6 | thing whose velocity is equal has traversed a certain
60 VI, 7 | is completed in as many equal periods of the time as there
61 VI, 7 | multiple of the portion, equal to the time occupied in
62 VI, 7 | again I take another part equal to AE, that also must occupy
63 VI, 7 | of finite parts whether equal or unequal, because there
64 VI, 7 | which, whether they are equal or unequal, are none the
65 VI, 7 | time. Again, in another equal part of the time another
66 VI, 7 | time that we take, whether equal or unequal to the part originally
67 VI, 7 | difference whether the parts are equal or not, if only each is
68 VI, 9 | everything when it occupies an equal space is at rest, and if
69 VI, 9 | row being composed of an equal number of bodies of equal
70 VI, 9 | equal number of bodies of equal size, passing each other
71 VI, 9 | race-course as they proceed with equal velocity in opposite directions,
72 VI, 9 | that half a given time is equal to double that time. The
73 VI, 9 | that a body occupies an equal time in passing with equal
74 VI, 9 | equal time in passing with equal velocity a body that is
75 VI, 9 | in motion and a body of equal size that is at rest; which
76 VI, 9 | the stationary bodies of equal size, B, B...the bodies,
77 VI, 9 | size, B, B...the bodies, equal in number and in size to
78 VI, 9 | to the middle of the A’s, equal in number, size, and velocity
79 VI, 9 | each of the two occupies an equal time in passing each A.
80 VI, 9 | passing each of the B’s is equal to that occupied by it in
81 VI, 9 | each of the A’s, because an equal time is occupied by both
82 VI, 10 | first traversing a space equal to or less than itself.
83 VI, 10 | must first traverse a space equal to or less than itself.
84 VI, 10 | have to traverse a distance equal to itself. Thus the line
85 VI, 10 | continually traverses a distance equal to itself, will be a measure
86 VII, 1 | B, and the others may be equal, or the motions of the others
87 VII, 1 | find that whether they are equal or some are greater, in
88 VII, 1 | possible, each motion is either equal to or greater than that
89 VII, 4 | velocity must accomplish an equal motion in an equal time,
90 VII, 4 | accomplish an equal motion in an equal time, then we may have a
91 VII, 4 | may have a circumference equal to a straight line, or,
92 VII, 4 | accomplishes a locomotion in an equal time, we may have an alteration
93 VII, 4 | alteration and a locomotion equal to one another: thus an
94 VII, 4 | thus an affection will be equal to a length, which is impossible.
95 VII, 4 | But is it not only when an equal motion is accomplished by
96 VII, 4 | accomplished by two things in an equal time that the velocities
97 VII, 4 | velocities of the two are equal? Now an affection cannot
98 VII, 4 | Now an affection cannot be equal to a length. Therefore there
99 VII, 4 | cannot be an alteration equal to or less than a locomotion:
100 VII, 4 | possible for the two to be equal. For if in the time A the
101 VII, 4 | that one thing traverses an equal distance in less time than
102 VII, 4 | over a part of the circle equal to G’, while G will occupy
103 VII, 4 | there may be a straight line equal to a circle. But these are
104 VII, 4 | different in different cases: "equal" is similarly equivocal;
105 VII, 4 | velocity if they occupy an equal time in accomplishing a
106 VII, 4 | accomplishing a certain equal amount of motion. Suppose,
107 VII, 4 | this case the alteration is equal to the locomotion and of
108 VII, 4 | say that two things are of equal velocity if they accomplish
109 VII, 4 | accomplish locomotion over an equal distance in an equal time,
110 VII, 4 | an equal distance in an equal time, we have to admit the
111 VII, 4 | therefore, that things are of equal velocity in an equal time
112 VII, 4 | of equal velocity in an equal time they traverse the same
113 VII, 4 | one alteration to be of equal velocity with another? One
114 VII, 4 | have here alterations of equal velocity, since each alteration
115 VII, 4 | each alteration occupies an equal time. But what alteration?
116 VII, 4 | cannot here speak of an "equal" alteration: what corresponds
117 VII, 4 | let us say that there is equal velocity where the same
118 VII, 4 | change is accomplished in an equal time. Are we, then, to find
119 VII, 4 | that two alterations are of equal velocity, we ought to look
120 VII, 4 | different, while they are equal or unequal according as
121 VII, 4 | as the things altered are equal or unequal.~And now we must
122 VII, 4 | how is one becoming of equal velocity with another? They
123 VII, 4 | with another? They are of equal velocity if in an equal
124 VII, 4 | equal velocity if in an equal time there are produced
125 VII, 4 | than the other if in an equal time the product is different
126 VII, 5 | the combined weights an equal distance in an equal time:
127 VII, 5 | an equal distance in an equal time: for in this case the
128 VIII, 1 | two forces lasts for an equal period of time. But it is
129 VIII, 1 | triangle always has its angles equal to two right angles, but
130 VIII, 7 | way as that which is of equal or standard measure is the
131 VIII, 8 | follows. Suppose the line E is equal to the line Z, that A proceeds
132 VIII, 10| by this motion cannot be equal to G: for the greater the
133 VIII, 10| time than another does an equal amount of work when engaged
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