Isaac Newton’s early documents on circular motion: can the dynamic reasoning in the “Principia” be found in them?

Os documentos iniciais de Isaac Newton sobre o movimento circular: O raciocínio dinâmico no “Principia” pode ser achado neles?

Some historians claim that Isaac Newton had already formulated the categories in the Principia twenty years earlier. This is based on two extant documents (1664–1665 and 1669). Derek Whiteside claims that second order differentials are essential categories in the book, and that Newton had not yet mastered them in the 1660s. Isaac Bernard Cohen states a desideratum: “I am certain it was Hooke’s method of analyzing curved motion that set Newton on the right track”. I show that differentials in the early documents are introduced by geometric arguments, lacking dynamic meaning; however in hindsight can a dynamic meaning be recognized in them. The drawing of an orbit in a letter from Newton to Hooke on December 13, 1679 indicates the breakthrough toward the Principia: I argue that the orbit was drawn by Hooke’s method, which proves Cohen’s desideratum.

Keywords
Mechanic orbits; Hooke’s method to draw orbits; Newton’s treatment of motion under central forces