 So, for Hume, Newton uses experiment to arrive at explanations. Thus, he seems to echo and accept Newton’s claim about “hypotheses non fingo” (see the relevant section in the  entry on Newton).  Once such “principles” or explanations have been arrived at experimentally, Hume sees Newton as adopting them boldly, even if they are unusual or surprising. Hume appears to have assimilated the importance of Newton’s third rule of reasoning (see  section 4.5  below). Moreover, Hume is discerning the (broad) outlines of Newton’s commitment to the method of analysis and synthesis (Newton’s Opticks, Query 31; for discussion, see  section 4.7).  But in Hume’s account there is no mention of the importance of mathematics in Newton’s methodology (see  section 4.6).  Hume lack of interest in this aspect of Newton’s methodology may be a consequence of his education (see  section 2).