The Principia is just as much a book of problems as it is a book of solutions to problems.
Newton in his calculus made use of power series in a systematic way.
The Newton's cardinal importance in the history of cosmology lies in his understanding of physical space. According to him, Euclidean space is an
To justify this, he assumed
that the fixed stars can be a basis of "inertial frame."
His bucket experiment, elucidated in the Scholium to Book 1 of the Principia, is an attempt to support the existence of absolute motion.
Setting aside the theoretical matters, what is peculiar about the Principia is that Newton adhered to the Euclidean style, and used laboriously
even though he was well acquainted with Descartes' work, which was, as a matter of course, more appropriate for the presentation.
He testified, writing about himself in the third person,
"By the help of the Analysis, Mr. Newton found out most of Propositions of his Principia Philosophiae : but because the Ancients for making things certain admitted nothing into Geometry before it was demonstrated synthetically, he demonstrated the Propositions synthetically, that the System of Heavens might be founded upon good Geometry. And this makes it now difficult for unskillful Men to see the Analysis by which those Propositions were found out" (Phil.Trans. R. Soc., 29 (1715), 173-224).
Apart from the style of the Principia, this epoch-making work (and its offspring) was "the theory of everything" in the centuries to follow as far as the classical description of the world is concerned. Indeed, Newton's laws seemed to tap all the secrets of nature, and hence to be the last word in physics.
It was in the 19th century that physical phenomena inexplicable by the Newtonian mechanics were discovered one after another. A notable example is electromagnetic phenomena which are in discord with his mechanics in the fundamental level. Moreover various physicochemical phenomena called for entirely new explanations as well, and eventually led to quantum physics.