The second law
The first law says an unbalanced force produces an acceleration. The second law says how much acceleration.
Newton's second law
The acceleration produced in an object is directly proportional to the unbalanced force applied to it, and inversely proportional to the mass of the object.
The two statements separately
Directly, with force
Decrease or increase the magnitude of the force by some ratio, and the acceleration decreases or increases by that same ratio.
a ∝ F
Double the force and the acceleration doubles.
Inversely, with mass
Increase the mass by some ratio and the acceleration falls by that ratio; decrease the mass and it rises.
a ∝ 1 ÷ m
Double the mass and the acceleration halves.
Putting them together
Both statements are true at once, so let us bring them into one relationship.
The two together
a ∝ F
a ∝ 1 ÷ m
so, a ∝ F ÷ m
Which makes (F ÷ m) ÷ a a constant. On the next page we define the unit of force so that this constant comes to 1, turning the law into a simple equation.