Galileo's law of inertia (at least what I've learned) is
"A body moving with constant velocity will continue to move in this path in the absence of external forces".
And Newton's first law says
"A body moving with constant velocity will continue to move with the same velocity provided that the net force acting on the body is 0.
So how are these two laws different? Both laws are telling us that a body in uniform motion will continue to move in uniform motion until the net force on the body is 0.
And if they are the same thing, then why isn't Galileo given credit for the above law? We call the law "Newton's first law of motion" when in fact Galileo discovered the above law through his experiments with inclined planes.
Best Answer
This is not uncommon in the world of physics. Different scientists might discover certain parts of a theory and some other scientist might come later and be able to incorporate all the previous known bits of knowledge into a more complete, full theory.
Even in case of relativity, many parts of it were discovered by other scientists/mathematicians before Einstein. But Einstein was the first one to take all of those, add his insight and combine all of it into a whole, consistent, complete theory that provided a much better explanation than any theory before that.
In case of Newton as well, although Galileo's law of inertia, predated Newton, Newton was the first to combine that with Newton's 2nd and 3rd law, combined with his brilliant work in calculus and was able to develop a complete theory of mechanics that was better than any other theory till then.
For what it's worth, I have seen many physics books where chapters on Newton's laws give honorable mention to the fact that Galileo came up with his law of inertia, years before Newton.