# How did Newton find the relationship between force, mass and acceleration? [duplicate]

I have been told always that $F$ is directly proportional to acceleration.

My question is that for finding such a relationship there should be source that produces desired force and in which the force can be adjusted i.e. Twice, thrice and more. But the problem is initially before the discovery of laws of motion how can one say that a force is twice the other, how can he even judge the relationship between two forces without knowing the quantitative definition of force?

## marked as duplicate by Brandon Enright, John Rennie, tpg2114♦, Alfred Centauri, Qmechanic♦Nov 13 '13 at 18:08

• Duplicate of physics.stackexchange.com/q/2644 – Kyle Kanos Nov 13 '13 at 15:53
• @kyle kanos that question does not answers the question above – user28804 Nov 13 '13 at 15:57
• It does as stated from the title of this question. – Ignacio Vergara Kausel Nov 13 '13 at 16:17
• Another possible duplicate: physics.stackexchange.com/q/70186/2451 – Qmechanic Nov 13 '13 at 16:22
• @user28804: I disagree. Lubos's answer provides the answer to your question in his last 3 paragraphs. Please read it again. – Kyle Kanos Nov 13 '13 at 16:33