Proofs of the Parts of the Third Law

41. Proof of the first part of this third rule.

The first part is demonstrated by the difference between motion considered in itself and its direction.

• This direction can be changed while the motion remains unchanged.*

This is because motion is a simple uncompounded thing. And so, it always perseveres as long as it is not destroyed by any external cause.

In the collision of a hard body, the resistance of that hard body prevents the moving body from remaining in the same direction.

But there is no cause which removes or reduces the motion itself.

This is because motion is not contrary to motion. Hence, it should not be reduced.

42. Proof of the Second Part

The other part is also demonstrated by the immutability of God’s operation, conserving the world now with the same action with which He once created it.

All things are filled with bodies.

Yet the motion of each body tends in a straight line.

God from the start:

• moved its various particles in different ways
• arranged them so that some particles would impel others and transfer their motions to them.

He conserves motion not by keeping motions of the particles of matter always fixed, but by letting those motions pass from one to another as they encounter each other.

Thus, this continuous alteration of creatures itself is an argument for the immutability of God.

43. Where does the power of every body to act or to resist come from?

This power to act or resist comes from nature of each body to remain in the same state.

This means that:

• whatever is connected to another has some force to prevent itself from being separated
• whatever is separated has the force to remain separated
• whatever is at rest has the force to persist in its rest, and resist all those things which could change it [and make it move]
• whatever is in motion has force to persist in its motion.

That force should be estimated by:

1. The magnitude of the body
2. The surface by which that body is separated from another
3. The swiftness of motion
4. The nature and mode of opposition in which different bodies encounter each other.

44. That motion is not the opposite of motion, but of rest; and determination in one direction against determination in the opposite direction.

One motion is not contrary to another motion of equal speed.

There are properly only 2 kinds of opposition found here:

1. One between motion and rest, or even between the fast and slow

2. One between one direction of motion towards a body at rest and another direction from the actual encounter with that body.