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 the celestial sphere. Similarly it may be shown that the ultimate cause of all genesis and destruction can be traced to the motion of the sphere. But the motion of the sphere must likewise have been effected by an agent (Prop. XVII.) residing either without the sphere or within it; a third case being impossible. In the first case, if the motor is without the sphere, it must either be corporeal or incorporeal: if incorporeal, it cannot be said that the agent is without the sphere; it can only be described as separate from it; because an incorporeal object can only be said metaphorically to reside without a certain corporeal object. In the second case, if the agent resides within the sphere, it must be either a force distributed throughout the whole sphere so that each part of the sphere includes a part of the force, as is the case with the heat of fire; or it is an indivisible force, e.g., the soul and the intellect (Props. X. and XI.). The agent which sets the sphere in motion must consequently be one of the following four things: a corporeal object without the sphere; an incorporeal object separate from it; a force spread throughout the whole of the sphere; or an indivisible force [within the sphere].

The first case, viz., that the moving agent of the sphere is a corporeal object without the sphere, is impossible, as will be explained. Since the moving agent is corporeal, it must itself move while setting another object in motion (Prop. IX.), and as the sixth element would likewise move when imparting motion to another body, it would be set in motion by a seventh element, which must also move. An infinite number of bodies would thus be required before the sphere could be set in motion. This is contrary to Proposition II.

The third case, viz., that the moving object be a force distributed throughout the whole body, is likewise impossible. For the sphere is corporeal, and must therefore be finite (Prop. I.); also the force it contains must be finite (Prop. XII.), since each part of the sphere contains part of the force (Prop. XI.): the latter can consequently not produce an infinite motion, such as we assumed according to Proposition XXVI., which we admitted for the present.

The fourth case is likewise impossible, viz., that the sphere is set in motion by an indivisible force residing in the sphere in the same manner as the soul resides in the body of man. For this force, though indivisible, could not be the cause of infinite motion by itself alone: because if that were the case the prime motor would have an accidental motion (Prop. VI.). But things that move accidentally must come to rest (Prop. VIII.), and then the thing comes also to rest which is set in motion. (The following may serve as a further illustration of the nature of accidental motion. When man is moved by the soul, i.e., by his form, to go from the basement of the house to the upper storey, his body moves directly, while the soul, the really efficient cause of that motion, participates in it accidentally. For through the translation of the body from the basement to the upper storey, the soul has likewise changed its place, and when no fresh impulse for the motion of the body is given by the soul, the body which has been set in motion by such impulse comes to rest, and the accidental motion of the soul is discontinued). Consequently the motion of that supposed first motor must be due to some cause which does not form part of things composed of two elements, viz., a moving agent