# How did Newton establish his famous third law of motion?

For every action,there is equal and opposite reaction . This is the famous Newton's third law of motion. But how did he come to this conclusion? We can prove 2nd law using calculus. But how did Newton prove this law? Or did he just used practical examples?

[According to me, it may be due to conservation of energy,but did Newton use this?]

• We do not prove laws of nature. We fail to falsify them. Oct 14, 2014 at 17:03
• You can't use calculus to prove there's an equal & opposite reaction. Given the force the Earth exerts on my body, for example, you can't use calculus to deduce that an equal and opposite force must be exerted on the earth. Oct 14, 2014 at 17:19
• Also I wonder how you managed to prove the second law. Oct 14, 2014 at 17:29
• Re "We can prove 2nd law using calculus": see physics.stackexchange.com/questions/2644/…
– user10851
Oct 14, 2014 at 17:30
• @stackErr, the author of the text you referenced made a mistake in reasoning. He confused two forces $A,B$ acting on the imaginary body of zero mass (which have to cancel each other per 2nd law) with the two forces $C,D$ acting on two different bodies of finite mass (which need not cancel per 2nd law). Oct 14, 2014 at 18:16