I think it's fairly clear that both Archimedes and DaVinci were into understand and formulating natural phenomana, but they also went further and then applied that science. They couldn't have done what they did without having the understanding, because they sure as hell couldn't get the principles off anyone else.
Galileo was a theorectical scientist. That's because he could afford to be. People would pay him for his theorectical ideas. No one was paying Archimedes or DaVinci simply to come up with interesting theories.
U could indeed call Galaleo 1 of the 1st modern scientists becuase he was paid simply to think.
Stephen E