Timeline for History question - why h in the definition of derivative?
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| Dec 27, 2021 at 20:29 | comment | added | Clive Long | $h$ serves the same purpose as $\delta x$. But further, $h$ represents the height of the trapezium that "stands on" the x-axis "above" h. The sum of the area of the trapezia (between limits) approximates the area between the upper and lower limits of the integral and "in the limit" (hand-waving) is the value of the area / definite integral. I have no historic reference to back this up, and this explanation as to why $h$ was used may be "after-the-fact" to justify the use of $h$ - but I like it - and now I have shared with you. | |
| Dec 27, 2021 at 20:29 | comment | added | Clive Long | For this very old question, we were taught (in UK) in our introductory calculus class on differentiation from first principles (of a single-variable function, x). $\Delta x$ represents any change in the value of the variable x. $\delta x$ represents any "small" change in the value of the variable x that is decreased in size and approaches zero "in the limit" (cue hand-waving here). | |
| May 2, 2012 at 14:59 | history | edited | Papiro | CC BY-SA 3.0 |
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| Apr 29, 2012 at 3:17 | comment | added | I. J. Kennedy | The places where Boyle is mentioned in the answer, is it supposed to by Boole? | |
| Apr 29, 2012 at 2:17 | history | edited | Papiro | CC BY-SA 3.0 |
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| Apr 28, 2012 at 11:42 | comment | added | Papiro | @Jeff: Taylor's work about increments is available at 17centurymaths.com/contents/taylorscontents.html. Also, there is a work from L. Feigenbaum, (tufts.edu/as/math/feigenbaum.html) published by Springer (springerlink.com/content/h720142152632171) but I have no access to it. | |
| Apr 27, 2012 at 15:26 | comment | added | Jeff McGowan | Interesting, and thanks so much. One thing I would love to see is the original reference of Taylor which Sloman refers to... | |
| Apr 27, 2012 at 15:25 | vote | accept | Jeff McGowan | ||
| Apr 27, 2012 at 14:23 | comment | added | Papiro | Laplace writes: "Nous désignerons ordinairements les variables des fonctions par les dernières letters de l'alphabet, x, y, etc., et las constantes par les premières a, b, c, etc..." | |
| Apr 27, 2012 at 14:15 | comment | added | Papiro | @Michael I think you are correct. Please, see ref. of Lacroix's book, first paragraph, pp. 599: "... corresponding to the increment h ...". | |
| Apr 27, 2012 at 14:08 | history | edited | Papiro | CC BY-SA 3.0 |
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| Apr 27, 2012 at 13:59 | comment | added | Michael Renardy | It would seem reasonable to speculate that i stands for increment. It may have been changed to h later to avoid conflicts of notation. | |
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| Apr 27, 2012 at 10:26 | history | made wiki | Post Made Community Wiki by Papiro | ||
| Apr 26, 2012 at 19:37 | history | edited | Papiro | CC BY-SA 3.0 |
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| Apr 26, 2012 at 19:32 | history | answered | Papiro | CC BY-SA 3.0 |