It is plain that the three quantities, s, v, t, are the three intrinsic principles of movement. In fact, the velocity, v, is the act, or the form, of movement; whence the epithet of uniform applied to all movement of constant velocity; the amount, s, of space measured is the term actuated by the said velocity; the time, t, is the duration of the movement, that is, its actuality; for as movement is essentially successive, its actuality also is successive, and constitutes a length of time. Here, then, we have most distinctly the three principles of movement. Let us remark that the first member of the equation is the ratio of the term to its act, and therefore represents the essence of movement; whilst the second member exhibits the duration of its existence. The sign of equality between the two members does not mean that the essence of movement is the same thing as the existence of movement, but only that both have the same quantitative value. For it should be remarked that, although a ratio is usually defined as "the quotient of a quantity divided by another of the same kind," nevertheless the quotient is not exactly the ratio, but its result or value; and is not the equivalent of the ratio in quality, but in quantity only. In pure mathematics, which are exclusively concerned with quantities, the distinction between the ratio and its value may not be important; but when a ratio is viewed in its metaphysical aspect, the distinction is of great consequence. For a metaphysical ratio is not looked upon as the ratio of two quantities, of which the one is the measure of the other, but as the ratio of two realities, of which the one actuates the other, and which, though belonging to the same kind of being, are, however, of a relatively opposite character, as is evident from the very example we are considering. The space, s, and the velocity, v, are, in fact, conceived as quantities of the same kind, only because velocity is mathematically expressed in terms of the space measured through it in a unit of time; yet velocity is certainly not space, but is that by which matter is compelled to move through space; so that while the extent of the space measured in a unit of time corresponds to the velocity with which it is measured, velocity itself has no extension, but intensity only. Hence the ratio of space to velocity, metaphysically considered, is a ratio of extension to intensity, or of potency to act, as we shall presently explain.
The third proof of our proposition is very simple. The intrinsic principles of being must correspond to its extrinsic principles, each to each respectively. For were any of the extrinsic principles not represented in the principiated being by something real proceeding from it, and corresponding to it, such an extrinsic principle evidently would principiate nothing, and would be no principle at all. Now, we have seen that the extrinsic principles of primitive being are three. It is evident, therefore, that its intrinsic principles likewise must be three. The extrinsic principles, as before stated, are God's volition of bringing something into existence, the term of its eduction, and the creative power exerted in its production. Hence it follows that every thing created must contain within itself an act as the product of the Creator's action, a term as an expression of the term of its eduction, and an actuality as the accomplishment and fulfilment of the volition of bringing it into existence.
We may here remark that the act of the created being is produced by God as its efficient cause, proceeds from God's omnipotence as its efficient principle, and is produced through action as the proximate reason of its causation and principiation.
The term of the created being, on the contrary, comes out of mere nothingness, acquires its reality through the mere position of an act, is not made, but actuated, and therefore has no efficient cause, but only a formal principle, the reality of which is the sole reason why the term is called real, and the disappearance of which would leave nothing behind. As a spherical form, by the necessity of its own nature, gives existence to a geometric centre, without need of an efficient cause, so does the essential act to its essential term. Let the spherical form be annihilated, and the centre will be gone; let the essential act vanish, and the essential term will have vanished together with it.
Finally, the actuality of the created being proceeds from the act and the term as making up its formal source, or the principium formale quod; while the formal reason, or the principium formale quo, of its proceeding is the actuation of the latter by the former, and the completion of the former in the latter; for to actuate a term is to give it actuality, and to be actuated is to become actual; and therefore the result of such an actuation is the actuality of the act in its term, and of the term in its act, or the complete actuality of the created essence and of the created being.
Thus the whole being, by its act, its term, and its complement, points out adequately and with the utmost distinction the three extrinsic principles whence it proceeds.[278]
The fourth proof is as follows: Every created being possesses an intrinsic natural activity and an intrinsic natural passivity. It possesses activity; for every creature must have an intrinsic natural aptitude to reveal, in one way or another, the perfections of its Creator, as such is the end of all creation; but to reveal is to act; and, therefore, every creature possesses its intrinsic aptitude and determination to act—that is, activity. It also possesses passivity; for all contingent beings are changeable, and therefore capable of receiving new intrinsic determinations; and such an intrinsic capability is what we call passivity, or potentiality. The consequence is, that every creature possesses something by reason of which it is active, and something on account of which it is passive; which amounts to saying that every creature possesses its intrinsic principle of activity, or, as it is styled, its act, and its intrinsic principle of passivity, or, as we call it, its potency or its potential term. Hence the well-known fundamental axioms of metaphysics: "Every agent acts by reason of its act," and "Every patient suffers on account of its potency."[279] Now, since the same being that can act can also be acted on, it is evident that that by reason of which it can act, and that on account of which it can be acted on, are the principles of one and the same actual essence, and therefore conspire into one formal actuality, which completes the essence into being. Accordingly, in all creatures, or primitive complete beings, we must admit act and potency as the constituents, and actuality as the formal complement, of their essence.
These four proofs more than suffice to show that all primitive complete beings consist of act, term, and complement as their intrinsic principles. But, as I am satisfied that on the right understanding of such principles the soundness of all our metaphysical reasonings finally depends, I think it necessary, before we proceed further, to make a few considerations on their exact notion, character, and attributions.
The term of a primitive being owes its reality to its act. Before its first actuation, it had no being at all; it was only capable of acquiring it, and therefore was, according to the language of the schools, a reality in mere potency; since everything that has no being, but can be actuated into being, has received the name of pure potency.[280] Now, pure potency, though it is nothing real, is infinite and inexhaustible; not that nothingness can have any such intrinsic attribute, but simply because no limit can be assigned to the possible eduction of beings out of nothing through the exercise of God's infinite and inexhaustible power. And it must be added that such a potency is thus infinite not only with regard to the substances that can be created out of nothing, but also with regard to the accidents which can be produced in those substances, and with regard to the modes resulting from the reception of such accidents. This being admitted, it is evident that, when the term of a created being acquires its first reality, a pure potency is actuated by an act; but is not actuated to the full amount of its actuality, which is infinite and inexhaustible. Indeed, no act gives to its potency the plenitude of all being; but every act gives that being only which corresponds to its own specific nature. And therefore the term of a primitive being, though actuated in its first actuation as much as is needed to make it the real term of a determinate essence, remains always capable of further and further actuation; in other words, such a term is still, and always will be, entirely potential in regard to all other acts compatible with the nature of the first by which it is actuated.
Hence we come to the conclusion that every created being, for the very reason of its having been educed out of nothing, retains potency, as the stamp of its origin, in its essential constitution. All creatures, then, are essentially potential, and therefore imperfect; as potency means perfectibility. God alone is free from potency, as he is the only being that did not come out of nothing.