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6

It is hard to say what "official" means exactly, it is not like there was a bureau of terminological standards. But "real numbers", "real values" and "real quantities" were certainly widely used long before Dedekind, and the erasure of the distinction between rationals and irrationals where it is not relevant is even ...


6

I do not think it is a virtue to make unsupported assertions just because we happen to believe them now. Following available evidence does not makes one not smart or disappointing, that is how science should be done. Galileo deserves credit for moving the question from armchair speculations to observations and experiments, and honestly surmising what they ...


5

See more detail about this anagram (there were actually two of them) here: https://mathoverflow.net/questions/140327/arnold-on-newtons-anagram Whatever the literal translation of the anagrams is, Newton indeed discovered a method of solving "all equations" algebraic, differential, functional, whatever. The method consisted in plugging a power ...


5

The motivation for applying derivatives to polynomials over general fields is their use in detecting multiple roots: if $K$ is a general field, a polynomial $f(x)$ in $K[x]$ has no repeated roots if and only if $f(x)$ is relatively prime to $f'(x)$ in $K[x]$. Formal derivatives on polynomials in $K[x]$ for a general field $K$ were introduced by Steinitz in ...


4

Maybe some of Newton's prisms were preserved. An article by A.A. Mills (1981) shows images. He writes: Newton appears to have purchased all his prisms: there is no intimation that he made any of them, although he was obviously skilled at grinding lenses and mirrors. This availability of ready-made glass prisms is rather puzzling, for the period in question ...


3

Following up on Carl Witthoft's lead, I found another image at this link. To locate the image, you can search the page for the text "第五章:科技筑梦" to avoid lots of scrolling. The image, shown below, provides the full background text: 没有大胆的猜测 就没有伟大的发现 (paraphrasing google translate, this comes out to: "Without bold guesses, there is no great ...


3

Perhaps this is a lead: I found an article which includes the following text [emphasis mine] . The campus of Broad Group in Changsha was designed to reflect Zhang Yue’s eclectic influences and his passion for the environment. It encompasses a sprawling organic garden that provides up to half of the food consumed by his workers, and the grounds are dotted ...


3

I'm not a historian, but I have to answer this because the previous answers have gotten it completely wrong. Leibniz's $\displaystyle \frac{df}{dx}$ is not equal to $f'(x)$. I think there are two main differences between Newton's calculus and Leibniz's: Newton's calculus is about functions. Leibniz's calculus is about relations defined by constraints. In ...


3

See Sir Isaac Newton's two treatises of the quadrature of curves and analysis by equations of an infinite number of terms (1745).


2

Chrandrasekhar's Newton's Principia for the Common Reader p. 370: 104. Proposition VII: the universal law of gravitation We have now reached the climactic point of Philosphie naturalis Principia Mathematica. After establishing the preceding propositions, particularly, Propositions IV and VI, Newton, at long last, is ready to enunciate his law of gravitation....


2

The first main point to make in answer is : beware Newton myths -- there are far too many of them, and people have made money and (flaky) reputations fabricating catchpenny fake history about Newton. The 'apple' story has been plenty embroidered over time. But there is a source, a notebook handwritten by Newton's friend William Stukeley. It was written ...


2

This explanation helped me understand Newton's language and answered my question: "the excess of the degrees of the heat … were in geometrical progression when the times are in an arithmetical progression (by 'degree of heat' Newton meant what we now call 'temperature', so that 'excess of the degrees of the heat' means ‘temperature difference')." ...


2

The definitions related to Newton's laws of motion do not require the use of any units. The concepts of force, velocity, distance and time are expressed in general terms. Units are unnecessary.


2

It's very doubtful that the engraving/diagram had anything to do with Newton. "The system of the world" was a posthumous publication from 1728-9 onwards. It was derived (with a little editorial amendment including a new title) from a manuscript of 1685 of Newton's (written out by his secretary/amanuensis but bearing corrections in Newton's hand). ...


1

Mirowski P., More heat than light (1989 Cambr.UP), Chap.2. pp.11-98 The history of the energy concept.< It's a great book for various other reasons.> For Ernst Mach, energy was more or less defined as the ability to do work. Although "work" could mean many things to many people, Mach felt it was merely an historical accident that the term ...


1

There seem to be alternative versions of this illustration: this one from page 6 of the Second Edition of On the System of the World [from the ResearchGate site]. I've always just taken this to be a "generic" planet for illustrative purposes. I've been looking for information on the engraver, in case anything was ever said about the intent of the ...


1

After a bit of research I stumbled across this paper which might be a good starting point. As often in mathematics, Newton discovered his method of divided differences through pattern finding whereby the paper gives a slightly adjusted approach after some examination of Newton's thoughts which will give you a good idea why his method works.


1

Full details in my paper: Historical Development of the Newton-Raphson Method, published in SIAM Review in 1995. Deuflhard's paper is basically a summary of that work.


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