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Although i've already accepted one answer, i added this answer in order to clarify what is known about Gauss's work towards the general Gauss-Bonnet theorem and what is a matter of speculation; this distinction is not clear in Mark Yasuda's answer, and one might get from it incorrect impression about the roots of Gauss differential geometric ideas. Gauss ...

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It is discussed in multiple manuscripts, letters and publications from 1675 to 1701. According to Fracois Ziegler's post on MO Did Leibniz really get the Leibniz rule wrong?, Leibniz originally thought $d(uv)=du\,dv$ in a special case, but corrected his mistake the same month in the manuscript Methodi tangentium inversae exempla (November 11, 1675). Later ...

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Leibniz states the product rule in his first paper on the calculus (1684). It's in the middle of the fist page (page 467) as can be seen here: https://www.maa.org/press/periodicals/convergence/mathematical-treasure-leibnizs-papers-on-calculus-differential-calculus and also in English translation (top of page 2) here: http://www.17centurymaths.com/contents/...

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Following the advice of Dave Renfo in comments, I looked up the 1990 interview with Tụy in the Mathematical Intelligencer. The article is fascinating, and I'd recommend it. Sadly, it gives a pretty brief account of the founding of the Society, and none of the journal. Koblitz: And you were able to do mathematics during all this? Tụy: Yes, in fact our ...

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Dugas’ History of Mechanics (French ed 1958) starts with Aristotle followed by Archimedes. Then Hellenistic and Arabic science, followed by Middle Age and Renaissance. Thus it is old but quite comprehensive.

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Because otherwise historians had to admit that Christianity, by destroying the ancient civilization, caused a regress. Even if after the fall of the Roman Empire the population experienced some relief, ultimately the whole Western world stagnated and sunk culturally. Quantitative data is available through Ian Morris project (Why the West Rules - For now, ...

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That formula was stated (albeit in a rather different notation) and derived in section 149 of Galloway (1839, A treatise on probability, Adam and Charles Black), of which Google Books has the full text available. That work appears to be a republication as a book of an article from the 7th edition of Encyclopaedia Britannica, which was published in 1827. I ...

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The law of propagation of error is discussed at length in Text-book on geodesy and least squares, prepared for the use of civil engineering students by Charles L. Crandall, 1907. There is also a paper "The essentials of error theory for practical engineers" by L. B. Tuckerman, in the Nebraska Blue Print, v. 13 (1914), pp.61-84 that discusses the &...

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This terminology does appear in English 100+ years ago, and is arguably archaic, but just means "types" or "kinds".

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Such terms as “given in species” are defined in Euclid’s Data (Greek, English): III. Rectilineal figures are said to be given in species, which have each of their angles given, and the ratios of their sides given. (English version, R. Simpson, 1810, p. 367) [Species is the translation of eidos, shape or form; see LSJ, εἶδος, def. A.2.b.]

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It's because of Diracs use of it in QM. After QM was a revolutionary new theory of physics and so had immense visibility because of this. This is very similar to how Einstein popularised the study of non-Euclidean geometry by his use of such in his revolutionary theory of space and time. After all, non-Euclidean geometry had been known since Gauss's time but ...

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Jeff Miller's very valuable collection of the origins of mathematical expressions has the entrie "Integration around a closed path": Dan Ruttle, a reader of this page, has found a use of the integral symbol with a circle in the middle by Arnold Sommerfeld (1868-1951) in 1917 in Annalen der Physik, "Die Drudesche Dispersionstheorie vom ...

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It's an early recognition of duality in set theory. Domain vs Codomain suggests a relationship that is missing from domain and range. This is hidden in set theory as functions are biased in that they are not symmetrically defined. Nor is it easy to conceptualise one to many functions naturally, and dually to many to one functions, which they do naturally. ...

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Proportion is the key concept that underlies most of mathematics. In its modern guise, it's described as the straight line or linearity. Now consider that the epitome of motion in Newtons theory is straight line motion. Further consider that Einstein then described motion in GR as straight lines on a curved surface. More, consider that calculus is simply the ...

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