Motion in General

Definition 1: Motion

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: Place

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.

It is irrelevant whether infinite space has fixed and motionless boundaries or not.

This is because we can still postulate that space can have absolute motion and absolute rest in it.

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

Bodies are in a state of:

• absolute rest if they retain the same position in space
• motion if they are passing from one part of space to another

Definition 3: Relative Motion

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.

Let us take the earth for this space.

Those bodies are at rest if they maintain their own unchanging places on [relative to] the earth.

In a similar way, bodies remain relatively at rest on the same place on the ship, even if they are relatively moving as the ship changes its position.*

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.

If the earth is actually at rest, then the things which are at rest and those which are moving are also at rest or are moving in the absolute sense.

Corollary 2.

11. But if the earth is moving, then relative motion and relative rest disagree.

It would mean that:

• those bodies at rest on the earth are in a state of absolute rest, and
• 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.

The relative motion and the state of rest are decided in the space considered.

All will produce relative motion from the state of rest of another.

Thus, the fixed stars:

• are moving with respect to the earth
• are at rest with respect with the other fixed stars

The fixed stars move with respect to the earth.

Likewise, the planets move.

When I speak of motion and rest, I mean absolute motion and rest.

I will explicitly mention when I mean relative motion.