28 votes
Accepted

How did Isaac Newton write the integral symbol?

Newton used both vertical bars ($\overset{|}{x}$) and rectangles ($\boxed{x}$) to denote integrals in his Quadratura curvarum published in 1704. Here, the bar notation is used on the bottom of page 9 ...
Scene's user avatar
  • 396
21 votes

Did Newton know about non-inertial frames?

TL;DR Yes, but... 1) Inertial frames To say that Newton had the modern conception of even inertial frames (based on the laws of motion), is an overstatement. Theoretically, he did not need them ...
Conifold's user avatar
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12 votes
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When did "neighbourhood of a point" first appear in the history of Taylor series?

The terminology "neighbourhood of a point" (in German, "Umgebung einer bestimmten Stelle") with its current meaning, dates back at least to 1841 when Weierstrass wrote his Zur ...
user6530's user avatar
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7 votes

How did Isaac Newton write the integral symbol?

The section II.4 Integral Calculus in Analysis by Its History by E. Hairer and E. Wanner begins with quotations, one of them from a letter by Newton: Newton, letter to Keill, April 20, 1714: And ...
Markus Scheuer's user avatar
6 votes

Origin of Riemann-Stieltjes Integral

The Riemann-Stieljes was introduced by Thomas Stieltjes in his long paper (or book) on continued fractions, Recherches sur les fractions continues, Mém. Sav. étr. 32, Nr. 2, 197 S. (1904). The purpose ...
Alexandre Eremenko's user avatar
6 votes
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Which geometer first compared a length (one dimensional) to an area (two dimensional)?

Al Khwarizmi, one of the first written sources of the general solution to quadratics, does exactly that: I observed that the numbers which are required in calculating by Completion and Reduction are ...
SRobertJames's user avatar
6 votes

How good was Newton at definite integration?

Newton integrated in the 'Principia' at least three rate-expressions related to features of the motion of the moon. (Newton's convention for denoting such rates was to call them 'hourly motions'): (a) ...
terry-s's user avatar
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6 votes
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What were the obstacles that made the discovery of calculus very late?

I would like to make several points with regard to this interesting question. The discovery of some Taylor series of trig functions by the Kerala school is a very impressive early breakthrough. ...
Mikhail Katz's user avatar
  • 5,496
5 votes

When did "neighbourhood of a point" first appear in the history of Taylor series?

According to Miller's Earliest Known Uses, "neighborhood of a point" first appears in Cayley's 1877 paper (in a different context), and then in Harnack's calculus text (1891), where it is ...
Conifold's user avatar
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5 votes

Who was the first person in history to calculate the limit $\lim\limits_{n\to\infty}\left(1+\dfrac{1}{n}\right)^n$?

I followed up on a pointer given by @nwr in comments that Jacob Bernoulli first encountered $e$ in the context of computing continuous compound interest. Sure enough, the article "The number $e$&...
njuffa's user avatar
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5 votes
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Who was the first person in history to calculate the limit $\lim\limits_{n\to\infty}\left(1+\dfrac{1}{n}\right)^n$?

First of all, what does it exactly mean to "calculate" this limit? The limit equals to $e$, but this is the definition of $e$. So one only has to prove that the limit exists, and then denote ...
Alexandre Eremenko's user avatar
5 votes

What were the "weird" things people were doing in calculus at the time of Marx?

Besides infintesimals, there are other ideas and concepts that mathematicians used to work with up until roughly 1940, that have not been properly formalized in modern mainstream mathematics, like the ...
Michael Bächtold's user avatar
4 votes
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Where can I find the Royal Society report on the controversy over the invention of differential calculus?

At request of Leibniz himself, the Royal Society appointed a commission which had the task of dealing with a dispute that followed an article by John Keill published in 1710 in "Philosophical ...
BakerStreet's user avatar
4 votes
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Can the so-called completeness of real numbers be understood as closure under limits in the real number system?

Concerning the "connection to the history of mathematics" that you mentioned: There has been a fairly clear concept of what we call a real number only since Simon Stevin. In particular, the ...
Mikhail Katz's user avatar
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4 votes

Origin of Riemann-Stieltjes Integral

An important use of the Stieltjes integral, after its creation by Stieltjes, was its use by Riesz in $1909$ to describe the continuous dual space of $C([0,1])$, the space of real-valued continuous ...
KCd's user avatar
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3 votes
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When did derivative mean not only "slope of tangent" but also "instantaneous rate of change"?

"Fermat was interested in minima and maxima, and realized these occur when the tangent has zero slope. When was it realized that this slope of tangent was the same thing as an instantaneous rate ...
Mikhail Katz's user avatar
  • 5,496
2 votes

Did any mathematicians of the time (the 17th Century) try out an intermediary between Bernoulli's and Nieuwentijdt’s infinitesimals?

These are assorted comments too long for a comment. Boyer is unreliable and should not be used as a source. Bernoulli's "proof" of the existence of infinitesimals was rejected by Leibniz, ...
Mikhail Katz's user avatar
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