How did Newton exactly prove his famous three laws of motion? I have a science project on the discovery of Isaac Newton. I want to highlight in most detail the famous Three Laws of Motion that Newton claims to have devised. However, looking everywhere on the web and even on this website, I can't seem to find a definite answer on exactly how he proved his laws. I'm looking for evidence of any experiments he conducted, or his contributions. I understand that some of his laws were based off of other scientists, but I'm uncertain who, and where his contribution to their ideas come in. Any help on this topic would be much appreciated.
 A: It wasn't so much that Newton discovered those laws. Rather, he made much, much better use of them than had been the case before.
Take what we have come to refer to as Newton's second law:
Galilei had offered the point of view that gravity causes change of motion such that the velocity increases linear with time. Well, there is only one law of motion that will result in velocity increasing linear with time: F=ma
The thing is, for a long time it wasn't necessary to restate that velocity-increases-linear-with-time in the form of F=ma
Huygens created setups with two hard balls for collision experiments. (Think of the type of setup called 'Newton's cradle', but with two swinging balls.) Huygens had no way of measuring the velocity of these collision objects, but he could use the height through which they had swung as a measure of the velocity the ball had to have, given how gravity works. Huygens collided hard objects, which had - to him - the advantage that he only had to keep track of momentum. Huygens worked around the limitations of not being able to measure velocity directly. Huygens could set up the height over which ball 1 had swung down. And he could see how ball 2, when hit by ball 1, would consistently swing back up to a particular height.
In those times, rather than expressing the laws of motion in equations of motion, it was common to express the findings in terms ratio of quantities. For example: if the mass ratio of ball 1 and ball 2 is such then the momentum transfer in a collision will be such.
For the amount of momentum transfer Huygens assumed - correctly - a principle of conservation of momentum.
Newton describes that he reproduced the setups that Huygens used. Newton describes that he devised ways to account for loss of velocity due toforms of friction. Newton describes that his collision setups corroborated conservation of momentum in collision setups.

In effect all of the three laws had been recognized before, but not necessarily explicitly stated.
Newton brought things into focus. So his fame is very much deserved, that is not at issue.

About history of physics:
Generally I would describe the available history of physics, as presented by physicists, as mythological.
Good history of physics does exist, but only by historians of science.
Here's what I think happens: when a physicist writes a textbook then when writing a 'historical introduction' he writes from memory what he has read in the textbook he learned from, but the story tends to get altered in alignment with the expectation pattern of the author.
The 'historical introduction' sections in physicst textbooks are totally unreliable. You cannot trust any of it. For history of physics one must read the works of historians of science.

See also:
Question raised on the 'history of science and mathematics' stackexchange: Origin of F=ma
A: It began with Aristotle who distinguished between natural and violent motion and who also defined a notion of force, force being an agent that causes change and this by contact. In fact, his notion of change was much broader than motion encompassing alteration and coming to be and passing away. However, he did say that change was primarily motion. Natural motion is the motion of an object when no force is applied and violent motion is the motion when a force is applied. We can see from this that natural motion is a precursor to inertial motion.
Now, Aristotle had said that change only occurs when a force is impressed and stops when no longer impressed. This is completely correct. However, he made an error when applying it to motion since he did not have the concept of affine space. Hence he suggested that an object only moves when a force is impressed upon it and comes to rest when this force stops acting on it. (Had he the concept of affine space, he would not have regarded change of position (that is velocity) as actual change, but that change of velocity (that is acceleration) is true change).
Philoponus, a Christian theologian and Aristotelian philosopher in the sixth century modified this theory to argue that the applied force imparts an impetus to the object which means that it will still carry on moving. However, this impetus was temporary meaning that this violent motuon eventually came to a stop.
Then in the 12th C, Avicenna argued that the impetus was in fact permanent and that an object came to a stop because of external forces like the friction of air. He thus established impetus as the precursor to momentum. Avicenna led the restablishment of Aristotelian thought in Islam and it was due to his influence it was also revived in Western Europe, particularly in Paris and Oxford. Jean Buridan, a 14th C French philosopher working in Paris established Avicenna's impetus theory in Western science (though it is often thought, wrongly, he originated the impetus theory).
Through Buridan it was then inherited by Newton. So this is the precursor to inertial motion in the first law, and the concept of force and momentum in the second law and likewise in the third.
It has been said that the only original contribution by Newton to his three laws is the third law. This can be rendered plausible if one considers it in the light of atomic theory and considers all atoms are alike. Newton was well aware of atomic theory through Gassendi back to Lucretious and then to Democritus. I don't know whether this is the route that Newton himself took.
One final point, it is often said that modern physics broke with Aristotelian physics. As the above makes quite clear, it is a continuation in the same sense that Einsteins physics did not break with Newtonian physics but was a continuation of the same tradition.
