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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?


marked as duplicate by Conifold, Community May 2 '16 at 19:14

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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

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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