Book, Paragraph

 1  II, 3 |            The minute accuracy of mathematics is not to be demanded in
 2 III, 2 |       good itself. This is why in mathematics nothing is proved by means
 3 III, 2 |      Aristippus, used to ridicule mathematics; for in the arts (he maintained),
 4 III, 4 |        while the other objects of mathematics, e.g. a plane or a line,
 5 III, 6 |            because the objects of mathematics, while they differ from
 6  IV, 2 |         as that word is used; for mathematics also has parts, and there
 7  IV, 2 |         ones within the sphere of mathematics.~Now since it is the work
 8  IV, 3 |           the truths which are in mathematics called axioms, and into
 9   V, 14|          the unmovable objects of mathematics, the sense in which the
10  VI, 1 |     condition, and the objects of mathematics have first principles and
11  VI, 1 |        from these considerations. Mathematics also, however, is theoretical;
12  VI, 1 |    certain movable things) nor to mathematics, but to a science prior
13  VI, 1 |      immovable, and some parts of mathematics deal with things which are
14  VI, 1 |         theoretical philosophies, mathematics, physics, and what we may
15  VI, 1 |         of thing, while universal mathematics applies alike to all. We
16 VII, 10|  perceptible, i.e. the objects of mathematics.~We have stated, then, how
17 VII, 11|          Regarding the objects of mathematics, why are the formulae of
18 VIII, 1|          Forms and the objects of mathematics are substances. But there
19 VIII, 1|          Ideas and the objects of mathematics; for some say these are
20   X, 3 |     exemplified in the objects of mathematics. "Other or the same" can
21  XI, 1 |      Forms or with the objects of mathematics. Now (a) evidently the Forms
22  XI, 1 |       Forms, as of the objects of mathematics. I mean that these thinkers
23  XI, 1 |     thinkers place the objects of mathematics between the Forms and perceptible
24  XI, 1 |           treat of the objects of mathematics; for none of them can exist
25  XI, 1 |          matter of the objects of mathematics. Neither to physics (because
26  XI, 4 |         examine the principles of mathematics also. That when equals are
27  XI, 4 |     common to all quantities, but mathematics studies a part of its proper
28  XI, 4 |           in the same position as mathematics; for physics studies the
29  XI, 4 |           and so both physics and mathematics must be classed as parts
30  XI, 7 |           movement in themselves; mathematics is theoretical, and is a
31  XI, 7 |     theoretical sciences-physics, mathematics, theology. The class of
32  XI, 7 |          of things, but universal mathematics applies alike to all. Now
33 XII, 1 |          Forms and the objects of mathematics, and others positing, of
34 XII, 1 |          two, only the objects of mathematics. The former two kinds of
35 XIII, 1|     consider first the objects of mathematics, not qualifying them by
36 XIII, 1|        only whether as objects of mathematics they exist or not, and if
37 XIII, 1|        inquiry.~If the objects of mathematics exist, they must exist either
38 XIII, 2|         to suppose the objects of mathematics to exist thus as separate
39 XIII, 2|           case of the subjects of mathematics, which are divisible and
40 XIII, 2|      generation of the objects of mathematics show that we are right.
41 XIII, 2|           out that the objects of mathematics are not substances in a
42 XIII, 3|         universal propositions of mathematics deal not with objects which
43 XIII, 3| qualification that the objects of mathematics exist, and with the character
44 XIII, 4|           then for the objects of mathematics; we have said that they
45 XIII, 6|          which are the objects of mathematics are different from those
46 XIII, 6|           speak of the objects of mathematics and in a mathematical way-viz.
47 XIII, 6|           speak of the objects of mathematics, but not mathematically;
48 XIII, 8|          but think the objects of mathematics exist and the numbers are
49 XIII, 8|       time from the standpoint of mathematics and from that of universal
50 XIII, 9|           who make the objects of mathematics alone exist apart from sensible
51 XIII, 9|       themselves and not those of mathematics. And he who first supposed
52 XIII, 9|           and that the objects of mathematics exist, naturally separated
53 XIV, 3 |       evident that the objects of mathematics do not exist apart; for
54 XIV, 3 |           while the statements of mathematics are true and "greet the
55 XIV, 3 |         the spatial magnitudes of mathematics. It is evident, then, both
56 XIV, 3 |         number and the objects of mathematics, press this difficulty,
57 XIV, 3 |       existence of the objects of mathematics only, and if spatial magnitudes
58 XIV, 3 |        nothing, as the objects of mathematics contribute nothing. But
59 XIV, 3 |          to change the objects of mathematics and invent doctrines of
60 XIV, 3 |           to unite the objects of mathematics with the Ideas. And those
61 XIV, 6 |      collect from the theorems of mathematics all have this meaning. Hence
62 XIV, 6 |      indicate that the objects of mathematics are not separable from sensible