Totally agree about Newton and his 3 ways. I remember reading in Burton's History of Mathematics:
"Newton developed 3 different versions of his calculus, apparently searching for the best approach; or maybe each version served a different purpose.
- 'Infinitesimals': largely a geometric approach,
- 'Fluxions': a kinematic approach,
- 'Prime and ultimate ratios': his most rigorous, "algebraic" approach.
The 3 methods weren't always kept apart when solving problems. See: DT Whiteside, Mathematical Papers Isaac Newton."
You might enjoy Tristan Needham's book on Visual Differential Geometry where he really dives into Newton's geometric approach.
Thanks for the other links... must go through them. Lots of gold there.
"Newton developed 3 different versions of his calculus, apparently searching for the best approach; or maybe each version served a different purpose.
- 'Infinitesimals': largely a geometric approach, - 'Fluxions': a kinematic approach, - 'Prime and ultimate ratios': his most rigorous, "algebraic" approach.
The 3 methods weren't always kept apart when solving problems. See: DT Whiteside, Mathematical Papers Isaac Newton."
You might enjoy Tristan Needham's book on Visual Differential Geometry where he really dives into Newton's geometric approach.
Thanks for the other links... must go through them. Lots of gold there.