# Definitions

by Isaac Newton 1. Mass is the amount of matter in a body

Air that is 2x density in a 2x space is 4x in mass.

• In 3x space, it becomes 6x in mass

This mass is known by the weight of the body because mass is proportional to weight. I have proven this through accurate pendulums.

This definition does not care about any medium that pervades the gaps within bodies.

1. The total motion of a body is the sum of all motions of its parts and is based on its velocity and mass
• A body with 2x mass at 1 velocity has 2x motion than a body of 1x mass at 1 velocity.
• A body with 2x mass at 2x velocity has 4x motion

he quantity of motion is the velocity of matter

1. Inertia is the innate force of matter for resisting movement when not moving, or for moving when already moving

This force can be considered both as:

• resistance in resisting external forces
• impulse in trying to transfer its force to another

All bodies are not always truly at rest.

1. Force is an external action exerted on the body in order to change its state

This Force is in the action only. It disappears when the action is over.

Upon reaching the new state, the body regains its inertia.

This Force can come from:

• impact
• pressure
• centripetal force
1. A centripetal force draws a body towards a center

Examples are:

• Gravity which draws bodies to the centre of the earth
• Magnetism, which attracts iron to magnets
• The force that makes planets travel in orbits
• The force of the sling that makes a stone, in a sling being whirled, stay with that sling. This is the same for things in orbit.

A projectile would travel in a straight line if air resistance and gravity were removed.

• The Earth’s gravity makes it go down back to the Earth

It will go farther if there is:

• less gravity or
• more velocity
1. The strength of the centripetal force is based on the center

Magnetism is less in a small magnet than a bigger magnet.

1. The increasing quantity of centripetal force
• Magnetism is less when far from a magnet and stronger when near a magnet.
• Gravity is stronger in the bottom of valleys, less on mountaintops, and even less away from Earth.

A larger body has more weight than a smaller one.

Weight is the tendency of a body to go to center. It is measured by a contrary force of the weighing scale that prevents it from going to the center.

The quantities of these forces can be called:

• accelerative (speed): this is the propensity of areas around the center to draw bodies to the center
• motive (motion): this is the total propensity of the body to go to the center
• absolute: this activates the motive force to go with the accelerative

I do not bother to know where such an absolute force come from. I just want to give them a mathematical form.

The accelerative force is relative to the motive force just as speed is relative to motion.

• The quantity of motion comes from speed drawn into the mass of the central body.
• The motive force comes from the accelerative force drawn into the same mass of the central body.

The sum of the accelerative forces in each space is the total motive force.

Hence, the accelerative gravity of mountains is different from those in valleys. Likewise, the resulting motive gravity, as weight, is also different.

This accelerative force, I call attraction. This motive force, I call impulse.

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