Part 9

i. e. a mundane period being finished.

See the Introduction to my Translation of the Timæus of Plato.

Traité de l’Astronomie Indienne et Orientale, par Monsieur Bailly, published in 1787.

SELECT THEOREMS IN PROOF OF THE PERPETUITY OF TIME, AND OF THAT WHICH IS NATURALLY MOVED WITH A CIRCULAR MOTION.

EXTRACTED FROM THE SECOND BOOK OF PROCLUS ON MOTION.

HYPOTHESES.

Every natural body is moveable according to place.

Every local motion is either in a circle, or in a right line, or mixed from these.

Every natural body is moved according to one of these motions.

Every natural body is either simple or compounded.

Every simple motion is the motion of a simple body.

Every simple body is moved with one motion according to nature.

DEFINITIONS.

That is heavy which is moved towards the middle.

That is light which is moved from the middle.

That is said to be moved in a circle which is continually borne from the same to the same.

Contrary motions are from contraries to contraries.

One motion is contrary to one.

Time is the number of the motion of the celestial bodies.

The motion is one which is without difference according to species, and belongs to one subject, and is produced in a continued time.

THEOREM 1.

Things which are naturally moved in a circle are simple.

Demonstration.—Let AB be that which is naturally moved in a circle. I say that AB is simple: for, since the motion in a circle is a simple motion; but every simple motion is the motion of a simple body; hence AB is a simple body. Things, therefore, which are naturally moved in a circle are simple.

THEOREM 2.

Things naturally moved in a circle, are neither the same with those moved in a right line, nor with those which are composed from things moved in a right line.

Demonstration.—Let AB be that which is naturally moved in a circle. I say that it is not the same with those things which are moved in a right line. For, if it is the same with any one of these, it must either be naturally moved upwards or downwards. But every simple body is moved with one simple motion according to nature. Hence, that which is naturally moved in a circle, is not the same with anything moved in a right line. But neither is it the same with anything compounded. For it has been shown that everything which naturally moves in a circle is simple; but that which consists from things moved in a right line is a composite. AB therefore, which is naturally moved in a circle, is neither the same with things moved in a right line, nor with those composed from these.

THEOREM 3.

Things which are naturally moved in a circle, neither participate of gravity nor levity.