  Sections 12 and 13 treat attractive forces between bodies that result from — are composed out of — centripetal forces between each of the individual microphysical particles forming them. Section 12 treats spherical bodies, and Section 13, non-spherical bodies. As Newton anticipated, this was the part of Book 1 that would arouse the strongest complaints from readers committed to the view that all forces involve contact between bodies. On top of this, nowhere in Book 1 did the mathematics become more demanding than here. These two sections give primary attention to inverse-square forces and forces that vary linearly with distance, but, just as earlier in Book 1, some results pertain to forces that vary in other ways, included among which are results pointing to experiments that might differentiate between inverse-square and any alternative to it. In the Scholium to Proposition 78 Newton singles out the result of this inquiry that he regarded as most notable: