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body first, and then go on to consider the others.
The body which moves in a circle must necessarily be finite in every
respect, for the following reasons. (1) If the body so moving is infinite, the
radii drawn from the centre will be infinite. But the space between infinite
radii is infinite: and by the space between the radii I mean the area outside
which no magnitude which is in contact with the two lines can be conceived
as falling. This, I say, will be infinite: first, because in the case of finite radii it
is always finite; and secondly, because in it one can always go on to a width
greater than any given width; thus the reasoning which forces us to believe in
infinite number, because there is no maximum, applies also to the space
between the radii. Now the infinite cannot be traversed, and if the body is
infinite the interval between the radii is necessarily infinite: circular motion
therefore is an impossibility. Yet our eyes tell us that the heavens revolve in a
circle, and by argument also we have determined that there is something to
which circular movement belongs.
(2) Again, if from a finite time a finite time be subtracted, what remains
must be finite and have a beginning. And if the time of a journey has a
beginning, there must be a beginning also of the movement, and consequently
also of the distance traversed. This applies universally. Take a line, ACE,
infinite in one direction, E, and another line, BB, infinite in both directions.
Let ACE describe a circle, revolving upon C as centre. In its movement it will
cut BB continuously for a certain time. This will be a finite time, since the
total time is finite in which the heavens complete their circular orbit, and
consequently the time subtracted from it, during which the one line in its
motion cuts the other, is also finite. Therefore there will be a point at which
ACE began for the first time to cut BB. This, however, is impossible. The
infinite, then, cannot revolve in a circle; nor could the world, if it were
infinite.
(3) That the infinite cannot move may also be shown as follows. Let A be a
finite line moving past the finite line, B. Of necessity A will pass clear of B
and B of A at the same moment; for each overlaps the other to precisely the
same extent. Now if the two were both moving, and moving in contrary
directions, they would pass clear of one another more rapidly; if one were still
and the other moving past it, less rapidly; provided that the speed of the latter
were the same in both cases. This, however, is clear: that it is impossible to
traverse an infinite line in a finite time. Infinite time, then, would be required.
(This we demonstrated above in the discussion of movement.) And it makes
no difference whether a finite is passing by an infinite or an infinite by a
finite. For when A is passing B, then B overlaps A and it makes no difference
whether B is moved or unmoved, except that, if both move, they pass clear of
577
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Buch The Complete Aristotle"
The Complete Aristotle
- Titel
- The Complete Aristotle
- Autor
- Aristotle
- Datum
- ~322 B.C.
- Sprache
- englisch
- Lizenz
- PD
- Abmessungen
- 21.0 x 29.7 cm
- Seiten
- 2328
- Schlagwörter
- Philosophy, Antique, Philosophie, Antike, Dialogues, Metaphysik, Metaphysics, Ideologie, Ideology, Englisch
- Kategorien
- Geisteswissenschaften
- International
Inhaltsverzeichnis
- Part 1; Logic (Organon) 3
- Categories 4
- On Interpretation 34
- Prior Analytics, Book I 56
- Prior Analytics, Book II 113
- Posterior Analytics, Book I 149
- Posterior Analytics, Book II 193
- Topics, Book I 218
- Topics, Book II 221
- Topics, Book III 237
- Topics, Book IV 248
- Topics, Book V 266
- Topics, Book VI 291
- Topics, Book VII 317
- Topics, Book VIII 326
- On Sophistical Refutations 348
- Part 2; Universal Physics 396
- Physics, Book I 397
- Physics, Book II 415
- Physics, Book III 432
- Physics, Book IV 449
- Physics, Book V 481
- Physics, Book VI 496
- Physics, Book VII 519
- Physics, Book VIII 533
- On the Heavens, Book I 570
- On the Heavens, Book II 599
- On the Heavens, Book III 624
- On the Heavens, Book IV 640
- On Generation and Corruption, Book I 651
- On Generation and Corruption, Book II 685
- Meteorology, Book I 707
- Meteorology, Book II 733
- Meteorology, Book III 760
- Meteorology, Book IV 773
- Part 3; Human Physics 795
- On the Soul, Book I 796
- On the Soul, Book II 815
- On the Soul, Book III 840
- On Sense and the Sensible 861
- On Memory and Reminiscence 889
- On Sleep and Sleeplessness 899
- On Dreams 909
- On Prophesying by Dreams 918
- On Longevity and the Shortness of Life 923
- On Youth, Old Age, Life and Death, and Respiration 929
- Part 4; Animal Physics 952
- The History of Animals, Book I 953
- The History of Animals, Book II translated 977
- The History of Animals, Book III 1000
- The History of Animals, Book IV 1029
- The History of Animals, Book V 1056
- The History of Animals, Book VI 1094
- The History of Animals, Book VII 1135
- The History of Animals, Book VIII 1150
- The History of Animals, Book IX 1186
- On the Parts of Animals, Book I 1234
- On the Parts of Animals, Book II 1249
- On the Parts of Animals, Book III 1281
- On the Parts of Animals, Book IV 1311
- On the Motion of Animals 1351
- On the Gait of Animals 1363
- On the Generation of Animals, Book I 1381
- On the Generation of Animals, Book II 1412
- On the Generation of Animals, Book III 1444
- On the Generation of Animals, Book IV 1469
- On the Generation of Animals, Book V 1496
- Part 5; Metaphysics 1516
- Part 6; Ethics and Politics 1748
- Nicomachean Ethics, Book I 1749
- Nicomachean Ethics, Book II 1766
- Nicomachean Ethics, Book III 1779
- Nicomachean Ethics, Book IV 1799
- Nicomachean Ethics, Book V 1817
- Nicomachean Ethics, Book VI 1836
- Nicomachean Ethics, Book VII 1851
- Nicomachean Ethics, Book VIII 1872
- Nicomachean Ethics, Book IX 1890
- Nicomachean Ethics, Book X 1907
- Politics, Book I 1925
- Politics, Book II 1943
- Politics, Book III 1970
- Politics, Book IV 1997
- Politics, Book V 2023
- Politics, Book VI 2053
- Politics, Book VII 2065
- Politics, Book VIII 2091
- The Athenian Constitution 2102
- Part 7; Aesthetic Writings 2156