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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?

wythagoras
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copper
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  • This question is answered under Who discovered the power rule for derivatives? http://hsm.stackexchange.com/questions/3024/who-discovered-the-power-rule-for-derivatives/3025#3025 – Conifold Apr 30 '16 at 23:04
  • There are many historical books: Carl Boyer, Margaret Baron, Niccolò Guicciardini,... – Mauro ALLEGRANZA May 01 '16 at 08:04

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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."

Mark Yasuda
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