Principia Mathematica

I was only willing to show by those examples the great extent and certainty of the third Law of motion.

For if we estimate the action of the agent from its force and velocity conjunctly,

and likewise the reaction of the impediment conjunctly from the velocities of its several parts,

and from the forces of resistance arising from the attrition, cohesion, weight, and acceleration of those parts,

the action and reaction in the use of all sorts of machines will be found always equal to one another.

And so far as the action is propagated by the intervening instruments,

and at last impressed upon the resisting body,

the ultimate determination of the action will be always contrary to the determination of the reaction.

For if we estimate the action of the agent from its force and velocity conjunctly,
→「the action of the agent = F(its force) * V(its velocity)」

「the reaction of the impediment = V(the velocities of its several parts) * F(the forces of resistance arising from the attrition, cohesion, weight, and acceleration of those parts)」

「the action in the use of all sorts of machines = the reaction in the use of all sorts of machines」

「the ultimate determination of the action=ーthe determination of the reaction」
「the ultimate determination of the action⇔the determination of the reaction」

In physics, the third Law of motion is below.
「F=ーF」
F is force.
F is vector.

To every Action there is always opposed an equal Reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.