What is Force?

60. As for circular motion, many think that, with increasing true circular motion, a body necessarily tends more and more away from the axis.

But this arises from the fact that, since circular motion can be regarded as originating at every moment from two directions, one along the radius, the other along the tangent;

if impetus is increased in this last direction only, then the moved body will move away from the center, and the orbit will cease to be circular.

But if the forces are equally increased in both directions, the circular motion will remain, but accelerated by an endeavor which will no more argue that the forces of receding from the axis have been increased than those of approaching it.

Water rotated in a bucket ascends to the sides of the vessel because, when new forces are applied in the direction of the tangent to any particle of water, equal new centripetal forces are not applied at the same instant.

The rotating water does not mean that absolute circular motion is necessarily recognized by the forces of moving away from the axis of motion.

Moreover, in what way these words, “forces of bodies and endeavors,” are to be understood, is sufficiently and more than sufficiently evident from the premises.

61. A curve can be considered as consisting of infinite straight lines.

• This is useful in geometry.

Likewise, circular motion can be regarded as originating from infinite rectilinear directions.

• This is useful in mechanical philosophy.

However, it is not therefore to be affirmed that it is impossible for the center of gravity of any body to exist successively in the individual points of a circular periphery, no account being taken of any rectilinear direction, either in the tangent or in the radius.

62. Some people define the true places of bodies by parts of absolute space.

They think that the motion of a stone in a sling, or of water rotated in a bucket, is circular motion.

This is not correct.

This is because it is compounded of motions not only of the bucket or sling, but also of the earth’s:

• daily rotation around its own axis
• monthly revolution around the common center of gravity of the earth and moon
• annual revolution around the sun.

Therefore any particle of the stone or water describes a line far removed from a circle.

Nor is there really that centrifugal endeavor which is believed to exist.

Thhis is because it does not regard any single axis in relation to absolute space, supposing that such a space exists.

Therefore it cannot be called a single endeavor to which truly circular motion corresponds as its proper and adequate effect.

63. Motion can only be recognized or measured by sensible things.

Absolute space does not impinge on the senses. So it must be utterly useless for the distinction of motions.

Besides, determination or direction is essential to motion, but this consists in relation. Therefore it is impossible for absolute motion to be conceived.

64. Furthermore, since for the diversity of relative place the motion of the same body is various, nay, something can be said to move in one respect and to be at rest in another; for determining true motion and true rest, by which ambiguity may be removed and the mechanics of philosophers, who contemplate the system of things more broadly, may be consulted, it will have been sufficient to use the relative space enclosed by the heaven of fixed stars, regarded as at rest, in place of absolute space.

But motion and rest defined by such relative space can be conveniently used in place of absolute motion and rest, which cannot be distinguished from them by any symptom.

For however forces are impressed, whatever endeavors there may be, let us grant that motion is distinguished by actions exerted on bodies; nevertheless, it will never follow from this that that absolute space and place exist, and that its change is true place.

65. The laws of motions, and their effects, and the theorems containing their proportions and calculations, for different figures of paths, likewise for different accelerations and directions, and for media more or less resisting, all these stand firm without the calculation of absolute motion.

As is evident even from the fact that, since according to the principles of those who introduce absolute motion, it is not permissible to know by any symptom whether the entire fabric of things is at rest or moves uniformly in a straight line, it is clear that the absolute motion of no body can be known.

66. For perceiving the true nature of motion the following are helpful:

67. Distinguish between mathematical hypotheses and the natures of things

68. Beware of abstractions

69. Consider motion as something sensible, or at least imaginable

70. Be content with relative measures.

If we do these things, at the same time all the clearest theorems of mechanical philosophy, by which the recesses of nature are unlocked and the system of the world is subjected to human calculations, will remain unimpaired, and the contemplation of motion will be freed from a thousand minutiae, subtleties, and abstract ideas. And let these remarks about the nature of motion suffice.

67. What is the cause of the communication of motions?

Most people think that an impressed force in a moving body is the cause of motion in it.

However, it is clear from the premises that they do not assign a known cause of motion, distinct from the body and the motion.

Force is not a certain and determined thing, from the fact that the greatest men put forth very different, indeed contrary, opinions about it, the truth in the consequences nevertheless being preserved.

Newton says that impressed force consists in action alone, and is an action exerted on a body to change its state, and does not remain after the action.

Torricelli contends that a certain accumulation or aggregate of impressed forces is received by percussion into a moving body, and remains there and constitutes impetus.

Borelli and others say almost the same thing.

Newton and Torricelli seem to conflict with each other. Nevertheless, the matter is explained quite conveniently by both.

For all forces attributed to bodies are as much mathematical hypotheses as attractive forces in the planets and the sun.

But mathematical entities do not have a stable essence in the nature of things as they depend on the notion of the definer; whence the same thing can be explained in different ways.

68. Let us establish that new motion is conserved in a struck body, either by:

• an inherent force or
• an impressed force

The inherent force perseveres the body in its state either of:

• uniform motion or
• rest in a straight line

The impressed force is received into the struck body during the percussion and remains there.

The inherent and impressed force is the same to the thing, the difference only in names.

Similarly, when the striking moving body loses, and the struck body acquires motion, it matters little to dispute whether the acquired motion is numerically the same as the lost motion, for it leads into metaphysical and utterly nominal minutiae about identity.

Therefore, whether we say that motion passes from the striker to the struck, or that motion is generated anew in the struck and destroyed in the striker, it comes down to the same thing.

In either case, one moving body loses motion, the other acquires it, and nothing besides.

69. The mind agitates and contains this entire corporeal mass.

• It is the true efficient cause of motion and of its communication.

In physical philosophy, however, it is necessary to seek the causes and solutions of phenomena from mechanical principles.

Therefore, a thing is explained physically not by assigning its truly active and incorporeal cause, but by demonstrating its connection with mechanical principles: of which kind is that, “action and reaction are always contrary and equal,” from which, as from a source and primary principle, the rules concerning the communication of motions are drawn, which have already been discovered and demonstrated by modern thinkers, to the great benefit of the sciences.

70. That principle could have been declared in another way.

If the true nature of things rather than abstract mathematics is considered, it will seem more correct to say that in attraction or percussion the passion of bodies, rather than the action, is equal on both sides.

For example, a stone tied to a horse by a rope is drawn towards the horse as much as the horse towards the stone: also, a moving body impacting another at rest undergoes the same change as the body at rest.

As for the real effect, the striker is likewise struck, and the struck is likewise striking.

But that change is on both sides, both in the body of the horse and in the stone, both in the moving and in the resting body, a mere passion.

But it is not established that a force, power, or corporeal action is truly and properly the cause of such effects.

A moving body impinges on one at rest; yet we speak actively, saying that it impels this one: nor absurdly in mechanics, where mathematical ideas rather than the true natures of things are considered.

71. In physics, sense and experience, which reach only to apparent effects, have a place.

In mechanics, the abstract notions of mathematicians are admitted.

In first philosophy, or metaphysics, incorporeal things, the causes, truth, and existence of things are treated.

The physicist contemplates the series or successions of sensible things, by what laws they are connected, and in what order, observing what precedes as cause and what follows as effect.

In this way we say that a moving body is the cause of motion in another, or impresses motion on it, also draws or impels it.

In which sense corporeal secondary causes ought to be understood, no account being taken of the true seat of forces, or active powers, or the real cause in which they reside.

Furthermore, the primary axioms of mechanical science, beyond body, figure, motion, can be called mechanical causes or principles, regarded as causes of the consequences.

72. Truly active causes can be drawn from the darkness in which they are enveloped only by meditation and reasoning, and known to some extent. But it pertains to first philosophy, or metaphysics, to treat of them. But if to each science its own province is assigned, its limits defined, and the principles and objects that pertain to each are accurately distinguished, it will be permissible to treat them with greater ease and clarity.