Aristotle
eternal: they act upon each other, and suffer from each other, with
contrary effects; they are destructive of each other. Besides, each
of them has a mode of motion natural and appropriate to it, but this
mode of motion is not eternal (because it is either to the centre or
to the circumference and therefore has a natural terminus). It is not
reasonable to suppose that any Mobile can be eternal, whose natural
mode of motion cannot be eternal (s. 3).
Thus the four elements are not eternal, but require to be renewed by
generation; therefore generation must come to pass. But, if
generation be necessary, more than one revolution of the celestial
body is indispensably required: two at least, if not more. For, if
there were no other revolution except that of the First Heaven, that
is consistent only with a perfectly uniform condition of the four
elements in relation to each other (s. 4).
When the question is asked, therefore, Why there are (not one only
but) several encyclical bodies? I answer: Because generation _must_
come to pass. There must be generation, if there be fire; there must
be fire and the other elements, if there be earth; there must be
earth, because something must remain stationary eternally in the
centre, if there is to be eternal revolution (s. 5).
CH. 4.--The Heaven is by necessity spherical: this figure is at once
both most akin to its essence and first in its own nature. I shall
begin with some observations respecting figures generally--plane and
solid, as to which among them is the first. Every plane figure is
either rectilinear or curvilinear; the former is comprehended by many
lines, the latter only by one. Now, since in every department one is
prior to many and simple to compound, the first of all plane figures
must be the circle. Moreover, since that is perfect which can receive
nothing additional from without, and since addition can be made to
every straight line, but none whatever to the line circumscribing a
circle, it is plain that this latter is perfect; and therefore the
circle is the first of all plane figures, and the sphere of all solid
figures (ss. 1, 2). This doctrine appears most reasonable when we set
out the different figures, each with a number belonging to it in
numerical order. The circle corresponds to One, the triangle to Two,
since its three angles are equal to two right angles; whereas, if we
assign number One to the triangle and place that first, we can find
no number fit for the circle: the circle will be no longer recognized
as a figure (s. 4).
Now, since the first figure belongs to the first body, which is that
in the extreme or farthest circumference, this body which revolves
constantly in a circle, will be spherical in figure. That which is
continuous with it even to the centre, will also be spherical; and
all the interior parts are in contact and continuity with it: the
parts below the sphere of the planets touch the sphere above them. So
that the whole revolving current, interior and exterior, will be
spherical; for all things touch and are continuous with the spheres
(s. 5).
There is another reason too why the universe is spherical in figure,
since it has been shown to revolve in a circle. I have proved before
that there exists nothing on the outside of the universe; neither
place nor vacuum. If the figure of the Kosmos, revolving as it does
in a circle, were any thing else but spherical--if it were either
rectilinear or elliptical--it could not possibly cover exactly the
same space during all its revolutions: there must therefore be place
and vacuum without it; which has been shown to be impossible (s. 6).
Farthermore, the rotation of the Heaven is the measure of motions,
because it is the only one continuous and uniform and eternal. Now in
every department the measure is the least, and the least motion is
the quickest; accordingly the rotation of the Heaven will be the
quickest of all motions (s. 7). But among all curved lines from the
same back to the same, the circumference of the circle is the
shortest, and motion will be quickest over the shortest distance.
Accordingly, since the Heaven revolves in a circle and with the
quickest of all motions, its figure must be spherical (s. 8).
We may also draw the same conclusion from the bodies fixed in the
central parts of the Kosmos. The Earth in the centre is surrounded by
water; the water, by air; the air, by fire. The uppermost bodies
surround the fire, following the like proportion or analogy; being
not continuous therewith, but in contact therewith. Now the surface
of water is spherical; and that which is either continuous with the
spherical or surrounds the spherical, must itself be spherical also
(s. 9). That the surface of the water is truly spherical, we may
infer from the fact, that it is the nature of water always to flow
together into the lowest cavities, that is, into the parts nearest to
the centre (s. 10).
From all the foregoing reasonings, we see plainly that the Kosmos is
spherical, and moreover turned with such a degree of exact sphericity
([Greek: kata\ a)kri/beian e)/ntornos ou(/tôs]), that no piece of
human workmanship nor any thing ever seen by us on earth can be
compared to it. For none of the component materials here on earth is
so fit for receiving perfect level and accuracy as the nature of the
First or Peripheral Body; it being clear that, in the same proportion
as water is more exactly spherical, the elements surrounding the
water become more and more spherical in proportion as they are more
and more distant from the centre (s. 11).
CH. 5.--Circular revolution may take place in two directions; from
the point A on one side towards B, or on the other side towards C.
That these two are not contrary to each other, I have already shown.
But, since in eternal substances nothing can possibly take place by
chance or spontaneity, and since both the Heaven and its circular
revolution are eternal, we may enquire what is the reason why this
revolution takes place in one direction and not in the other. This
circumstance either depends upon some first principle, or is itself a
first principle (s. 1). Perhaps some may consider it a mark either of
great silliness, or great presumption, to declare any positive
opinion at all upon some matters, or upon all matters whatever,
leaving out nothing. But we must not censure indiscriminately all who
do this: we must consider what is the motive which prompts each
person to declare himself, and with what amount of confidence he
affirms, whether allowing for human fallibility or setting himself
above it. Whenever a man can find out exact and necessary grounds for
the conclusions which he propounds, we ought to be grateful to him:
here we must deliver what appears to be the truth. Nature (we know)
always does what is best among all the practicable courses. Now the
upper place is more divine than the lower, and accordingly among
rectilinear currents, that which is directed upwards is the more
honourable. In the same manner, the current forwards is more
honourable than backwards; and the current towards the right more
honourable than that towards the left--as was before laid down. The
problem above started indicates to us that there is here a real Prius
and Posterius--a better and a worse; for, when we recognize this, the
difficulty is solved. The solution is that this is the best
practicable arrangement, viz., that the Kosmos is moved in a motion,
simple, never-ending, and in the most honourable direction ([Greek:
e)pi\ to\ timiô/teron], s. 2).
CH. 6.--I have now to show that this motion of the First Heaven is
uniform and not irregular ([Greek: o(malê\s kai\ ou)k a)nô/malos]):
I speak only of the First Heaven and of the First Rotation; for in
the substances lower than this many rotations or currents have
coalesced into one. If the motion of the First Heaven be irregular,
there will clearly be acceleration and remission of its motion, and
an extreme point or maximum ([Greek: a)kmê/]) thereof. Now the
maximum of motion must take place either at the terminus _ad quem_,
as in things moved according to nature; or at the terminus _a quo_,
as in things moved contrary to nature; or during the interval
between, as in things thrown ([Greek: e)n toi=s r(iptoume/nois]). But
in circular motion, there is neither terminus _a quo_, nor terminus
_ad quem_, nor middle between the two--neither beginning, nor end,
nor mean; for it is eternal in duration, compact as to length or
space moved over, and unbroken ([Greek: tô=| mê/kei sunêgme/nê
kai\ a)/klastos]). It thus cannot have any maximum or acceleration or
remission; and of course, therefore, it cannot be irregular (s. 1).
Besides, since every thing that is moved is moved by some thing, the
irregularity, if there be such, must arise either from the Movens, or
the Motum, or both: the power of the Movens, or the quality of the
Motum, or both, must undergo change. But nothing of the sort can
happen with the Motum, being in this case the Heaven; for it has been
shown to be a First, simple, ungenerable, indestructible, and in
every way unchangeable. Much more then is it reasonable to believe
that the Movens is such; for that which is qualified to move the
First, must be itself a First ([Greek: to\ ga\r prô=ton tou=
prô/tou kinêtiko/n]); that which is qualified to move the simple,
must be itself simple, &c. If then the Motum, which is a body,
undergoes no change, neither will the Movens, being as it is
incorporeal (s. 2). Accordingly the current, or motion ([Greek:
phora/]), cannot possibly be irregular. For, if it comes to pass
irregularly, its irregularity either pervades the whole, the velocity
becoming alternately more or less, or certain parts only. But, in
regard to the parts separately, there is certainly no irregularity:
if there had been, the relative distances of the stars one from the
other would have varied in the course of infinite time; now no such
variation in their distances has ever been observed. Neither in
regard to the whole is there any irregularity. For irregularity
implies relaxation, and relaxation arises in every subject from
impotence. Now impotence is contrary to nature: in animals, all
impotences (such as old age or decay) are contrary to nature; for all
animals, perhaps, are compounds put together out of elements each of
which has a different place of its own and not one of which is in its
own place. In the First Bodies, on the other hand, which are simple,
unmixed, in their own places, and without any contrary, there can be
no impotence, and therefore neither relaxation nor intensification,
which always go together ([Greek: ei) ga\r e)pi/tasis, kai\
a)/nesis], s. 3). Besides, we cannot with any reason suppose that the
Movens is impotent for an infinite time, and then again potent for an
infinite time; nothing contrary to nature lasts for an infinite time,
and impotence is contrary to nature; nor can it be for an equal time
contrary to nature and agreeable to nature--impotent and potent. If
the motion relaxes, it cannot go on relaxing for an infinite time,
nor go on being intensified, nor the one and the other alternately.
For in that case the motion would be infinite and indeterminate;
which is impossible, since every motion must be from one term to
another term and also determinate (s. 4: [Greek: a)/peiros ga\r a)\n
ei)/ê kai\ a)o/ristos ê( ki/nêsis. a(/pasan de/ phamen e)/k tinos
ei)/s ti ei)=nai, kai\ ô(risme/nên]--_i.e._, all motion must be
determined both in distance and direction).
Again, the supposition may be made that there is a minimum of time
required for the revolution of the Heaven, in less than which the
revolution could not be completed; just as there is a minimum of time
indispensable for a man to walk or play the harp. Admitting this