My question is: what did Newton mean in stating that he was a Baconian? This is complicated by the fact that very few philosophers have an accurate understanding of Baconian empiricism - what Hooke called Bacon's "logic engine." Bacon's exclusionary method may hold a clue. He developed something close to what today is called a neo-hermeneutic method of successive approximations (like fuzzy set theory). Bacon held that because Nature could not speak English (nor any demotic language) one had to invent a "code" that was transitive between Nature and the human mind. Bacon's solution was to "try" nature the way he tried a law case in which there was no direct evidence - only circumstantial evidence.
With circumstantial evidence one starts with hypotheses and collects evidence by which each one can be tested and those that do not fit the evidence can be excluded. This process eliminates every other explanation of the evidence but the "true" one - the verifiable hypothesis that remains after the evidence has excluded all others.
Newton tried, in the beginning, a similar exclusionary approach. This may have been behind what he meant in May 1666 in writing that "I had entrance into the universe method of fluxions." Was this the way he found entry into the inverse method that told him how fluxions worked?
Next, what did he mean by the "analysis by experiment" method he used to discover that if one used a prism to isolate a beam of light and showed it through a second prism it did not split up but retained what he called its "homogeneal" character?
Did he use prisms in a Baconian "inductive support" (L. Jonathan Cohen), non-statistical probability method? Bacon himself used a legal term to described the method: "adminicle support".
This explains not only how Newton came to his correct conclusions but also how he came to the ones that later (on better evidence) proved to be incorrect ones: for example, the conclusion that one could never make a lens free from chromatic aberrations
In Newton's answers to his critics he seems to be saying that he derived his conclusions by Baconian adminicle support method. Years later he wrote that during those early two years :
"I was in the prime of my age for invention and minded Mathematics and Philosophy."
I've wondered why Newton used older geometric methods in explaining what he had discovered by The Calculus. Did he think this could make it more readily understandable? Did he want to keep precise knowledge of The Calculus to himself? Or had he made the discovery originally by using a Baconian (adminicle) type of geometric empiricism ....
There is something unexplained in Newton's choice of that mode of explanation.
SirBacon.org - Sir Francis Bacon's New Advancement of Learning