Proposition VII.
Things which are changeable are, at the same time, divisible. Hence everything that moves is divisible, and consequently corporeal; but that which is indivisible cannot move, and cannot therefore be corporeal.
Proposition VIII.
A thing that moves accidentally must come to rest, because it does not move of its own accord; hence accidental motion cannot continue for ever.
Proposition IX.
A corporeal thing that sets another corporeal thing in motion can only effect this by setting itself in motion at the time it causes the other thing to move.
Proposition X.
A thing which is said to be contained in a corporeal object must satisfy either of the two following conditions: it either exists through that object, as is the case with accidents, or it is the cause of the existence of that object; such is, e.g., its essential property. In both cases it is a force existing in a corporeal object.
Proposition XI.
Among the things which exist through a material object, there are some which participate in the division of that object, and are therefore accidentally divisible, as, e.g., its colour, and all other qualities that spread throughout its parts. On the other hand, among the things which form the essential elements of an object, there are some which cannot be divided in any way, as, e.g., the soul and the intellect.
Proposition XII.
A force which occupies all parts of a corporeal object is finite, that object itself being finite.
Proposition XIII.
None of the several kinds of change can be continuous, except motion from place to place, provided it be circular.
Proposition XIV.
Locomotion is in the natural order of the several kinds of motion the first and foremost. For genesis and corruption are preceded by transformation, which, in its turn, is preceded by the approach of the transforming agent to the object which is to be transformed. Also, increase and decrease are impossible without previous genesis and corruption.
Proposition XV.
Time is an accident that is related and joined to motion in such a manner that the one is never found without the other. Motion is only possible in time, and the idea of time cannot be conceived otherwise than in connexion with motion; things which do not move have no relation to time.
Proposition XVI.
Incorporeal bodies can only be numbered when they are forces situated in a body; the several forces must then be counted together with substances
