Maybe we can elaborate on what Pourciau said in his text.  Incidentally, Jesseph in his 2005 paper used the adjective "kinematic" to describe Newton's approach.  Other scholars use the term "kinetic".  I don't have access to Pourciau.  Does he document several instances or just one?  It is not surprising that other historians prefer to deny any limits in Newton.  This fits better with their ideology that Weierstrass invented analysis.