Talk:Fluxion
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Rejecting 'o'[edit]
I don't think the description of the 'example' is accurate. So far as I am aware, Newton does not say that 'o' itself can be ignored, but that quantities multiplied by o 'will be nothing in respect of the rest. Therefore I reject them...' (Method of Fluxions, p. 25). The secondary source given in note 7 no longer exists, so I cannot tell if it supports the description in the text. 2A00:23C5:6487:4701:C845:1F4B:E368:BBAE (talk) 20:08, 9 June 2020 (UTC)
The explanation as to why Newton's method worked and it was correct to discard the o-increments was first given by John Gabriel[edit]
https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020
No mathematician in Newton's time or after (with the exception of John Gabriel) was able to explain why the o-increments being discarded had nothing to do with infinitesimals and in fact the process of discarding the same is perfectly valid in mathematics for the very simple reason that the terms with o-increments are simply the difference between the tangent line and the non-parallel secant line slopes. An example of Gabriel's geometric theorem is explained using the "fluent" x^n. Above link explains. Turns out that tossing away the o-increments is equivalent to setting them to 0 and valid for the method. 172.92.105.191 (talk) 00:43, 21 October 2022 (UTC)