Book, Paragraph

  1 III, 1 |       difficulty. Further (14), are numbers and lines and figures and
  2 III, 3 |         e.g. if two is the first of numbers, there will not be a Number
  3 III, 3 |             apart from the kinds of numbers; and similarly there will
  4 III, 5 |     connected with these is whether numbers and bodies and planes and
  5 III, 5 |            held to be wiser thought numbers were the first principles.
  6  IV, 2 |            being qua being, not qua numbers or lines or fire, it is
  7  IV, 2 |         defect, and these belong to numbers either in themselves or
  8  IV, 7 |          instance, in the sphere of numbers there will be number which
  9   V, 14|              the sense in which the numbers have a certain quality,
 10   V, 14|         quality, e.g. the composite numbers which are not in one dimension
 11   V, 14|            exists in the essence of numbers besides quantity is quality;
 12   V, 14|          and of this the quality in numbers is a part; for it is a differentia
 13   V, 15|      indefinitely or definitely, to numbers themselves or to 1. E.g.
 14 VII, 2 |          kind of substance, one for numbers, another for spatial magnitudes,
 15 VII, 2 |              And some say Forms and numbers have the same nature, and
 16 VII, 11|           they reduce all things to numbers, and they say the formula
 17 VII, 11|    substance other than these, e.g. numbers or something of the sort,
 18 VIII, 3|           substances are in a sense numbers, they are so in this sense
 19 VIII, 3|            and not, as some say, as numbers of units. For a definition
 20 VIII, 6|          both to definitions and to numbers, what is the cause of their
 21   X, 1 |             say that the measure of numbers is a number; we ought indeed
 22   X, 2 |          therefore, while there are numbers and a one both in affections
 23   X, 6 |         opposed then to the many in numbers as measure to thing measurable;
 24  XI, 2 |               and each of the other numbers composed of units, as one?
 25  XI, 4 |             e.g. lines or angles or numbers or some other kind of quantity-not,
 26 XII, 8 |             Ideas say the Ideas are numbers, and they speak of numbers
 27 XII, 8 |          numbers, and they speak of numbers now as unlimited, now as
 28 XII, 8 |        there should be just so many numbers, nothing is said with any
 29 XII, 10|             But if the Forms or the numbers are to exist, they will
 30 XII, 10|      Further, in virtue of what the numbers, or the soul and the body,
 31 XIII, 1|         objects of mathematics-i.e. numbers and lines and the like-are
 32 XIII, 1|          Ideas and the mathematical numbers, and (2) some recognize
 33 XIII, 1|   principles of existing things are numbers and Ideas; for after the
 34 XIII, 2|          account will apply also to numbers; for there will be a different
 35 XIII, 2|             classes of mathematical numbers.~Again, how is it possible
 36 XIII, 3|        extended magnitudes and from numbers, but with magnitudes and
 37 XIII, 3|             but with magnitudes and numbers, not however qua such as
 38 XIII, 3|            voice, but qua lines and numbers; but the latter are attributes
 39 XIII, 4|          any way with the nature of numbers, but treating it in the
 40 XIII, 4|        marriage-they connected with numbers; but it was natural that
 41 XIII, 6|         again the results regarding numbers which confront those who
 42 XIII, 6|         confront those who say that numbers are separable substances
 43 XIII, 6|      another, and so with the other numbers; but the units in the "2-
 44 XIII, 6|             of the other successive numbers. And so while mathematical
 45 XIII, 6|           these two), and the other numbers similarly, ideal number
 46 XIII, 6|         kind.~Again, these kinds of numbers must either be separable
 47 XIII, 6|           of perception consists of numbers which are present in them)-
 48 XIII, 6|          the only ways in which the numbers can exist. And of those
 49 XIII, 6|             out of numbers-only not numbers consisting of abstract units;
 50 XIII, 6|           who do not make the Ideas numbers nor say that Ideas exist;
 51 XIII, 6|         principle of things suppose numbers to consist of abstract units,
 52 XIII, 6|  Pythagoreans; but they suppose the numbers to have magnitude, as has
 53 XIII, 6|              then, in how many ways numbers may be described, and that
 54 XIII, 7|           with those in other ideal numbers. Now (1) all units are associable
 55 XIII, 7|             the Ideas cannot be the numbers. For what sort of number
 56 XIII, 7|        similar and undifferentiated numbers are infinitely many, so
 57 XIII, 7|            But if the Ideas are not numbers, neither can they exist
 58 XIII, 7|           prior or posterior to the numbers.~But (2) if the units are
 59 XIII, 7|          followed by the successive numbers, as they say "2,3,4" for
 60 XIII, 7|          units must be prior to the numbers after which they are named
 61 XIII, 7|             a fifth in 3 before the numbers 4 and 5 exist.-Now none
 62 XIII, 7|       itself; and so with the other numbers. For whether the units are
 63 XIII, 7|           similarly. This being so, numbers cannot be generated as they
 64 XIII, 7|          the case of the succeeding numbers, but they say 4 came from
 65 XIII, 7|            3) if those in different numbers are differentiated, but
 66 XIII, 7|            similarly with the other numbers. For let the 2’s in the
 67 XIII, 7|             when we are speaking of numbers. If not, not even the 2
 68 XIII, 7|       number.~Nor will the Ideas be numbers. For in this particular
 69 XIII, 7|             we do, neither will the numbers be generated from the indefinite
 70 XIII, 8|         attach to them; for even to numbers quality is said to belong
 71 XIII, 8|    Evidently then, if the Ideas are numbers, the units cannot all be
 72 XIII, 8|             some others speak about numbers correct. These are those
 73 XIII, 8|             identified with certain numbers, but think the objects of
 74 XIII, 8|           mathematics exist and the numbers are the first of existing
 75 XIII, 8|           with the other successive numbers). But if the 1 is the starting-point,
 76 XIII, 8| starting-point, the truth about the numbers must rather be what Plato
 77 XIII, 8|         must be a first 2 and 3 and numbers must not be associable with
 78 XIII, 8|        bodies should be composed of numbers, and that this should be
 79 XIII, 8|             they consisted of those numbers.~If, then, it is necessary,
 80 XIII, 8|             the middle place in odd numbers. (b) But if each of the
 81 XIII, 8|         even, but the generation of numbers is always the generation
 82 XIII, 8|           way, when 2 operates, the numbers got from 1 by doubling are
 83 XIII, 8|           another way, when the odd numbers operate, the other even
 84 XIII, 8|             operate, the other even numbers are produced. Again, if
 85 XIII, 8|          Idea of something, and the numbers are Ideas, infinite number
 86 XIII, 8|     horse-itself? The series of the numbers which are the several things-themselves
 87 XIII, 8|           must, then, be one of the numbers within these limits; for
 88 XIII, 8|              for those in identical numbers are similar), so that there
 89 XIII, 8|             is an Idea, each of the numbers will be man-himself, and
 90 XIII, 8|           11, nor of the succeeding numbers. Again, there both are and
 91 XIII, 8|       assumption that the series of numbers up to 10 is a complete series.
 92 XIII, 8|   principles, and the others to the numbers. This is why they identify
 93 XIII, 8|             heap, i.e. if different numbers consist of differentiated
 94 XIII, 8|          unit becomes the matter of numbers and at the same time prior
 95 XIII, 9|             there is not contact in numbers, but succession, viz. between
 96 XIII, 9|    difficulty; but if the 1 and the numbers are separable, as those
 97 XIII, 9|            Again, the discord about numbers between the various versions
 98 XIII, 9|         Forms at the same time also numbers, but did not see, if one
 99 XIII, 9|        exist and that the Forms are numbers and that the objects of
100 XIII, 9|            be wrong."~But regarding numbers the questions we have raised
101 XIII, 9|          say that the Ideas and the numbers are such substances, and
102 XIII, 9|             say it.~Those who posit numbers only, and these mathematical,
103 XIV, 1 |           One. (The former generate numbers out of the dyad of the unequal,
104 XIV, 1 |          these three as elements of numbers, two being matter, one the
105 XIV, 1 |           rather than substrata, of numbers and magnitudes-the many
106 XIV, 2 |       things that are generated are numbers and lines and bodies. Now
107 XIV, 2 |            then these also would be numbers and units. But if they had
108 XIV, 2 |             few (from which proceed numbers), long and short (from which
109 XIV, 2 |             question, regarding the numbers, what justifies the belief
110 XIV, 2 |          this reason that he posits numbers), but who posits mathematical
111 XIV, 3 |            Ideas to exist and to be numbers, by their assumption in
112 XIV, 3 |         they saw many attributes of numbers belonging te sensible bodies,
113 XIV, 3 |            be numbers-not separable numbers, however, but numbers of
114 XIV, 3 |     separable numbers, however, but numbers of which real things consist.
115 XIV, 3 |           Because the attributes of numbers are present in a musical
116 XIV, 3 |     construct natural bodies out of numbers, things that have lightness
117 XIV, 3 |             raised just now, why if numbers are in no way present in
118 XIV, 3 |            out of or they use other numbers, which makes no difference.
119 XIV, 3 |          cannot in any way generate numbers other than those got from
120 XIV, 3 |  unchangeable things, so that it is numbers of this kind whose genesis
121 XIV, 4 |        account of the generation of numbers merely to assist contemplation
122 XIV, 4 |          element, and an element of numbers, is impossible. Powerful
123 XIV, 4 |             Again, if the Forms are numbers, all the Forms are identical
124 XIV, 4 |            the One itself, and that numbers partake of it in a more
125 XIV, 4 |       partly because they treat the numbers as the first substances,
126 XIV, 5 |             existing things are the numbers, should have first distinguished
127 XIV, 5 |      determined at all in which way numbers are the causes of substances
128 XIV, 5 |       pebbles, as some people bring numbers into the forms of triangle
129 XIV, 5 |       because harmony is a ratio of numbers, and so is man and everything
130 XIV, 5 |             Evidently it is not the numbers that are the essence or
131 XIV, 5 |           but a ratio of mixture of numbers, whether these are corporeal
132 XIV, 6 |             is that things get from numbers because their composition
133 XIV, 6 |          expressed by the adding of numbers, not by mere numbers; e.g.
134 XIV, 6 |             of numbers, not by mere numbers; e.g. it is "three parts
135 XIV, 6 |            should not some of these numbers be squares, some cubes,
136 XIV, 6 |            same. But why need these numbers be causes? There are seven
137 XIV, 6 |           lauded characteristics of numbers, and the contraries of these,
138 XIV, 6 |            that goodness belongs to numbers, and that the odd, the straight,
139 XIV, 6 |            the potencies of certain numbers, are in the column of the
140 XIV, 6 |          Again, it is not the ideal numbers that are the causes of musical
141 XIV, 6 |           the like (for equal ideal numbers differ from one another
142 XIV, 6 |      trouble with the generation of numbers and can in no way make a