LECTURE 20 (265 a 28-266 a 9)

HE SHOWS WITH COMMON AND LOGICAL ARGUMENTS THAT CIRCULAR MOTION IS CONTINUOUS AND FIRST. ACCORDING TO THE OPINIONS OF THE ANCIENT PHILOSOPHERS LOCAL MOTION IS THE FIRST MOTION

1136. After the Philosopher has shown with proper arguments that circular motion is continuous and first, he here proves the same thing with logical and common arguments.

             He gives three arguments. In the first argument he says that it is reasonable that circular motion is one and eternally continuous, but straight motion is not. For in straight motion the beginning, mid-point, and end are determined, and all three of these are designated in the same straight line. Therefore, it is in this very line that motion begins and ends. For every motion rests at its termini, namely, either the terminus from which or the terminus to which (these two states of rest he distinguished above in Book V . But in a circular line the termini are not distinct. For there is no reason why one designated point of a circular line should be a terminus rather than another. For each one is similarly a beginning, a mid-point, and an end. And thus, in a certain sense whatever is moved in a circle is always at the beginning and at the end, insofar as any point of a circle can be taken as a beginning or an end. And in a certain sense it is never at a beginning or an end, insofar as no point of a circle is actually a beginning or an end.

             From this it follows that a sphere is in a certain sense in motion and in a certain sense at rest. For as was said in Book VI, while a sphere is in motion, it always remains in the same place with respect to the subject, and to this extent it is at rest. But it is always different with respect to reason [ratio], and to this extent it is moved.

             In a circular line itself, then, beginning, mid-point, and end are not distinguished since these three pertain to the centre. From the centre as from a beginning lines proceed to the circumference. And at the centre are terminated the lines which are projected from the circumference. The centre is also the mid-point of the whole magnitude, insofar as it is equidistant from every point of the circumference.

             Therefore, the beginning and the end of a circular magnitude are at the centre which is not touched by that which is moved in a circle. Therefore in circular motion there is no point where that which is moved rests when it arrives there. For that which is moved in a circle is always moved around the mid-point, and does not reach an end, since it is not moved to the mid-point which is the beginning and the end.

             Because of this, a whole which is moved spherically in a sense is at rest and in a sense is in continuous motion, as was said.

             From what has been said the argument can be formulated as follows. Every motion which is never at its beginning or end is continuous. But circular motion is a motion of this kind. Therefore, etc. And through the same middle it is proven that straight motion cannot be continuous.

             1137. Next where he says, 'Our next point . . .' (265 b 9), he gives the second argument. He says that the following two points follow each other conversely, namely, circular motion is the measure of all motions, and it is the first of all motions. For, as is shown in Metaphysics, X, all things are measured by the first ones in their genera. And so, this proposition is convertible: everything which is a measure is first in its genus; and everything which is first is a measure. But circular motion is the measure of all other motions, as is clear from what was said at the end of Book IV. Therefore, circular motion is the first of all motions. Or if it is granted that circular motion is the first of all motions because of the arguments set forth above, the conclusion is that it is the measure of other motions.

             1138. He gives the third argument where he says, 'Again, rotatory motion . . .' (265 b 11). He says that only circular motion can be regular since things which are moved in a straight line are moved irregularly from the beginning to the end.

             As was said in Book V, that motion is irregular which does not maintain equal velocity throughout the whole. This must occur in every straight motion. For in natural motion the greater the distance of the mobile object from the initial rest from which motion begins, the greater the velocity. And in violent motion the greater the distance from the final rest where the motion ends, the greater the velocity. For natural motion tends toward an end, and violent motion toward a beginning.

             But this does not take place in circular motion. The beginning and the end of a circle are not found inside the circulation, which forms the circumference, but outside of it, that is, at the centre, as was said. Hence there is no reason why a circular motion should be increased or diminished as if approaching a beginning or an end. For it is always at an equal distance from the centre which is the beginning and the end.

             From what was said in Book V, moreover, it is clear that regular motion is more one than irregular motion. Hence circular motion is naturally prior to straight motion. For to the extent that a thing is more one, it is to that degree naturally prior.

             1139. Next where he says, 'As to locomotion . . .' (265 b 16), he proves by means of the opinions of the ancient philosophers that local motion is the first of motions.

             He says that the sayings of all the ancient philosophers who made mention of motion attest to this truth. For they held that their principles move by local motion.

             First he explains the opinion of Empedocles who held that friendship and strife are the first moving principles: friendship unifies and strife separates. Unification and separation, however, are local motions.

             Secondly, he shows the same thing from the opinion of Anaxagoras, who posited intellect as the first moving cause whose work, according to him, is to separate what is mixed.

             Thirdly, he shows the same thing from the opinion of Democritus, who did not posit a moving cause, but said that all things are moved because of the nature of the void. But motion which is the result of the void is local motion, or something similar to local motion, for void and place differ only in reason [ratio], as was explained in Book IV. And thus, while they hold that things are first moved because of the void, they hold that local motion and no other is naturally first. They thought that other motions are consequent upon local motion. Following Democritus, they say that increase and corruption and alteration are the result of a certain unification and separation of indivisible bodies.

             Fourthly, he shows the same thing from the opinions of the ancient natural philosophers who posited only one material cause, either water, or air, or fire, or some intermediate. From that one material principle they derived the generation and corruption of things through condensation and rarefaction, which are the result of unification and separation.

             Fifthly, he shows the same thing from the opinion of Plato, who held that the soul is the first cause of motion. For Plato held that a self-mover, which is the soul, is the principle of all things which are moved. According to him, the proper function of animals and all living things is to move themselves with respect to place autokinesim, that is, with respect to per se local motion.

             Sixthly, he shows the same thing from what people say who speak in general and in common. For that alone is properly said to be moved which is moved in place. And if a thing which is at rest in a place undergoes increase or decrease or alteration, it is said to be moved in some way, but not simply.

             1140. Next where he says, 'Our present position . . .' (266 a 5), he summarizes what he has said, namely, there has always been motion and there always will be motion, and there is some first principle of eternal motion. We have shown which motion is first and which motion is eternal. We have shown that the first mover is immobile. For all of these points were explained in the preceding discussions.