Motion in General

DEFINITION 1

1. Motion is the translation of a body from the place it occupies to another place. True rest is a body remaining at the same place.

Corollary 1

2. Therefore the ideas of the body remaining at rest and of moving to other places cannot be entertained together, except that they occupy a place.

Whereby the place or position the body occupies shall be a property of the body, that can be said to be possible only for that body, and that the body is either moving or at rest.

Corollary 2.

3. This idea of moving or of being at rest is a property of a body that relates to all bodies.

All bodies are either moving or at rest.

DEFINITION 2.

4. The place is a part of the immense or boundless space which constitutes the whole world.

In this sense, the accepted place is the ‘absolute place’ as opposed to a relative place.

Corollary 1.

5. A body is:

• moving if it successively occupies one part and then another, of this immense space.
• at rest if it continues to be present at the same place always

Corollary 2.

6. This absolute space has fixed boundaries.

The relation with those boundaries is the ‘position’.

Bodies are:

• at rest if they maintain the same positions with respect to these boundaries.
• moving if they change their positions

Scholium 1.

7. Absolute motion and absolute rest are states.

These are the true definitions of these quantities, since they are compliant with the laws of motion.

We are unable to form a fixed idea of this because of:

• the immense nature of space
• its unbounded nature

Instead of this immense space and boundaries, we define a finite space and the limits within which bodies can move.

From this we can indicate the states of motion and of rest of bodies.

We say that a body is:

• in a state of rest if it keeps the same situation with respect to its boundaries
• in a state of motion if it changes with respect to them

Scholium 2.

8. The boundaries of this immense and infinite space are purely mathematical.

These can be summoned to establish our correct understanding because metaphysical speculations contradict it.

if we do not assert to give fixed and motionless boundaries to infinite space; but instead assert that space may have or may not have attending boundaries, then we can still postulate that such absolute motion and absolute rest may be represented in such a space, such as we are about to contemplate; and that such a finite space may indicate the state of motion or of rest of a body.

The mind can abstract for us from the universe a void of infinite extend.

We can consider bodies to be arranged in that space so that, if they retain the same position, then they are in a state of absolute rest.

But if on the other hand they are passing from one part of space to another then this indicates that they are moving.

DEFINITION 3.

9. Relative motion is the change in the position of a body that it is agreeable to assume within a space.

Relative rest means that the body stays in the same place with respect to the same space.

Thus taking the earth for this space, we say that those bodies are at rest that maintain their own unchanging places on the earth.

We are accustomed to say only those to be moving that proceed [p. 4] from one place to another with respect to the earth.

In a similar manner for a ship’s movement, those bodies that remain relatively at rest stay in the same place on the ship, while these are relatively moving that change their position on the ship.

Corollary 1

10. Relative motion and relative rest agree with absolute motion and rest, when the space and the body, with respect to which the motion and the state of rest are indicated, actually are at rest with respect to the immense and infinite space.

For if the earth is actually considered at rest [in the absolute sense], these things which are at rest and these things which are moving, are also at rest or are moving in the absolute sense.

Corollary 2.

11. But relative motion and relative rest disagree [with their absolute counterparts] if that space is moving.

For if the earth is not at rest with respect to the infinite space, neither those bodies which are at rest with respect to the earth are in a state of absolute rest, and also the absolute motions of bodies are different from their relative motion.

A body moving relative to the earth can be in a state of absolute rest.

Scholium.

12. There are innumerable different states of relative motion or rest of bodies: indeed as one or another space is assumed, the relative motion and the state of rest are decided in that space, and all will produce relative motion from the state of rest of another.

Thus the fixed stars are moving with respect to the earth, while any one of these is at rest with respect to the others.

As the fixed stars move with respect to the earth, so also do the planets [p. 5]. Moreover in the following derivations I wish both absolute motion and rest to be understood [to be the reference frame], unless I advise that relative motion is to be considered, and that will be brought to your attention.