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Do we know if he knew of the previous works done on this subject? Do we have any idea of his thought process? Do we even know anything about this?

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  • $\begingroup$ This question is answered under Who discovered the power rule for derivatives? hsm.stackexchange.com/questions/3024/… $\endgroup$ – Conifold Apr 30 '16 at 23:04
  • $\begingroup$ There are many historical books: Carl Boyer, Margaret Baron, Niccolò Guicciardini,... $\endgroup$ – Mauro ALLEGRANZA May 1 '16 at 8:04
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Here's a short answer $-$ others may be able to elaborate in more detail. On page 98 of George Simmons' book Calculus Gems: Brief Lives and Memorable Mathematics (published by the Mathematical Association of America), he summarizes the matter by stating that Newton wrote in a letter that his own early ideas about calculus came from "Fermat's way of drawing tangents." A more direct quote from the same letter can be found in the page 144 footnote of Sabra's Theories of Light: From Descartes to Newton, which reads "I had the hint of this method [of fluxions] from Fermat's way of drawing tangents, and by applying it to abstract equations, directly and invertedly, I made it general."

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