"Galileo discovered ..." is definitely referring to Galileo's experimental work.
Thus your assertion depends on what Newton mean with "By the first two Laws and the first two Corollaries, " prefixing that statement. I can think of a few interpretations:
The presence of a comma between the 2 phrases suggests the first interpretation. That is: Galileo did experiments that were governed by the first 2 laws and first two corollaries and got the expected results.
- Galileo's discoveries were because the first 2 laws and first two corollaries existed but had not yet been formulated by Newton.
- Galileo's experiments were tests of the first 2 laws and first two corollaries which he had already formulated.
- Galileo's experiments were tests of the first 2 laws and first two corollaries and he formulated them later.
If Newton had mentioned where Galileo had published the equivalent of the first 2 laws and first two corollaries then options 2 or 3 are more likely.
Perhaps you can provide the citation that Newton seems to have forgotten?
I think the statement Newton made was fairly clear. He provided the principles, or fundamental explanations, behind what Galileo (and others since) had observed by experiment. There isn't anything controversial in it - Newton did the maths that explains why Galileo saw this happen.
The Galileo in this thread is fishing for an argument that doesn't exist.
Athon