# Tag Info

28

It is a play of words by Charles Babbage. Deism was a religious belief or rather a movement promoting the idea that God exists but it does not interfere with whatever happens in this world. This old philosophy according to the Wikipedia "...asserts God's existence as the cause of all things, and admits its perfection (and usually the existence of ...

24

Newton's notation, Leibniz's notation and Lagrange's notation are all in use today to some extent they are respectively: $$\dot{f} = \frac{df}{dt}=f'(t)$$ $$\ddot{f} = \frac{d^2f}{dt^2}=f''(t)$$ You can find more notation examples on Wikipedia. The standard integral($\displaystyle\int_0^\infty f dt$) notation was developed by Leibniz as well. Newton did ...

17

Newton used anagrams which are not the usual ciphers. It is not designed for a secret communication, but only for proving at a later time that you knew something. So nobody is supposed to be able to decode the message until you tell what the message was. To do this, he used a simple procedure: he wrote a sentence (in Latin) and then just counted letters in ...

10

Several factors come together to suggest that the idea that "English mathematics [was] ever significantly behind -- by say 50 years, 100 years, or even centuries" (i.e. in the post-Newtonian 18th or early 19th centuries) is at best a sweeping over-generalization, although something very like it has clearly become a received view. Two recent valuable ...

10

It can certainly be agreed that Book 2 of the Principia has received less attention than Books 1 and 3. According to I B Cohen (1999):-- "Book 2 of the Principia differs from books 1 and 3 in a variety of ways. One of the most striking of these is the fact that its major contents, the theoretical and experimental study of the forces of resistance ...

9

Newton studied at school and at the university, but he mostly taught himself by reading. (At his secondary school he certainly learned Latin, Greek, the Bible and some arithmetic. In the universities, they mostly studied Aristotle at that time, which has nothing to do with mathematics). Besides textbooks that existed at that time he mastered Euclid, and ...

8

There are too separate issues here. The method of fluxions and fluents, Newton's version of calculus, is amply represented in Newton's extant papers, starting with 1669 On Analysis by Equations with an Infinite Number of Terms sent as a letter to John Collins, and disseminated by him to multiple correspondents, including Leibniz. The dotted shorthand was ...

8

Beyond the issue of notation, Newton experimented with a number of foundational approaches. One of the earliest ones involved infinitesimals, whereas later he shied away from them because of philosophical resistance of his contemporaries, often stemming from sensitive religious considerations closely related to inter-denominational quarrels. Leibniz also was ...

8

I suggest that the baseless suggestion offered in this question can best be answered by Einstein's own words about Newton, written in 1919. The background was the now-well-known eclipse expedition of 1919, in which the amount of deflection of light from stars close to the sun's limb had been observed during the eclipse. The results gave a probable ...

8

The first answer is excellent but just for context on the actual math: Newton notation for derivative of f(x): $\dot f(x)$ Leibniz notation for derivative of f(x): $\frac {df}{dx}$ Newton's notation is fine for very basic single variable derivation and generally the derivative for the described cases but the Leibniz notation is general purpose and ...

7

You should definitely take a look at the second chapter of Arnold's Huygens & Barrow, Newton & Hooke. The late Prof. Arnold summarized therein the difference between Newton's approach to mathematical analysis and Leibniz's as follows: Newton's analysis was the application of power series to the study of motion... For Leibniz, ... analysis was a more ...

7

Goldstine, A History of Numerical Analysis from the 16th through the 19th Century (1977), describes Kepler's approach (p. 47), which may be found in Kepler's Epitome Astronomiae Copernicanae (1618), Ch. 4, Bk. V., pp. 665f. It is an iterative numerical algorithm Kepler called regula positionum. Goldstine describes the steps of an example, which begins on p....

7

Hooke was not close (as far as we can judge from his surviving work) to what Newton accomplished. Yes, he conjectured the inverse square law. He understood correctly some simple qualitative features of the motion under this law. He probably performed some simple experiments suggesting these features. And he proposed to Newton to prove that the inverse square ...

7

You remember incorrectly. Calculus was found by Archimedes, Gregory of Saint-Vincent, Galileo, Kepler, Descartes, Pascal, Cavalieri, Fermat, Barrow, Wallis, Brounker, Huygens, Leibniz, J. Gregory, N. Mercator, Newton, Cotes, Taylor, Torricelli, Bernoulli brothers, to name only the most famous ones. As every big enterprise, this was a collective enterprise. ...

6

The article cited by the questioner incorrectly represents the limited amount of historical evidence that we have about the incident described. When the article is compared with the evidence, it can be seen that its account has been extensively fictionalized. Thus, it is an unsuitable basis on which to question anyone's truthfulness -- except perhaps that ...

6

The answer is more of a yes, but with many buts. Newton did not have the modern concept of function, it was introduced by Dirichlet in the 19th century, or even its predecessor as assignment of values according to a "law", as Euler defined it in the 18th. Fluent was closer to what was later called variable quantity, something like a temporally ...

6

It was not "the experiment". First, Newton considered "his" laws to be "common knowledge" already "abundantly" confirmed and accepted by experts (he names Galileo, Wallis, Wren, and Huygens). In Axioms, or Laws of Motion section of Principia, where they are laid down, he writes in particular:"Hitherto I have laid ...

5

The standard book about Newton's life is Never at Rest by Richard Westfall. On my opinion it is a very good book, it covers his life in great detail, and gives a general overview of his activities (not only in physics) but in astronomy, history, theology, alchemy, and as the Mint administrator. On physics, the latest English translation of Principia by Cohen ...

5

Kepler's Proofs will get you started on your quest. This article mentions 987 folio pages of arithmetic; you should also look at the tables and methods of Copernicus.

5

It would probably not have been easy for a contemporary mathematician to formulate a direct critique that Newton was difficult to understand without also 'reflecting' unwanted discredit on the skill or level of understanding of the critic. I can't recall seeing such a direct critique, but what can be found perhaps more easily are statements pointing more-or-...

5

Numerical agreement was (at best) a fluke; quoth e.g. A. Berry, A short history of astronomy (1898, p. 235): The amount of the precession as calculated by Newton did as a matter of fact agree pretty closely with the observed amount, but this was due to the accidental compensation of two errors, arising from his imperfect knowledge of the form and ...

5

We know relatively little about Newton's original model from 1668, modern versions draw lineage from the improved 1671 version. There is a record with its detailed description, with some comments on construction, although not the entire "process of building". Here is from Newton's telescope by Mills and Turvey. "The prime source of information on this ...

4

Although this question and the answers now have some age to them, I suggest that it's important not to overlook the mythical character of the assumption that underlies this question. The question explicitly supposes that 'calculus is missing from the Principia'. But that is not true: it is not missing, not only have skilled commentators from the 17th to the ...

4

A comprehensive scientific biography of Newton is "Never at rest" by Westfall. He tells the story, and expresses no doubt about it. The article in Wikipedia is an example of sloppy writing.

4

This will answer two out of three parts of the question: (a) 'Why didn't the church go after Isaac Newton?' It was not at all the whole church that was involved in the Galileo affair: it was the establishment of the Roman Catholic church of the time. In much of (mostly northern) Europe, the Roman Catholic church had no authority at all: the reformed ...

4

Part of the problem may be that Newton's roommate's name is spelled as Wickins or Wickens, not to be confused with bishop John Wilkins, Newton's older contemporary. Since they did live in the same room for 20 years Wickens's testimony would be precious indeed, but alas, as far as I know, the only things Wickens wrote concerning Newton were not about him but ...

4

Contribution of Newton to optics is enormous. He is considered a founding father of physical optics. I can only give some examples. His main discovery was that the sunlight can be dissolved into colors (spectrum). The discovery which lead to spectroscopy, and eventually to quantum mechanics. He also analysed what is called "Newton rings" (discovered by Hooke ...

4

I think the two other answers here when combined offer a complete explanation of Knuth's word game. He calls Leibniz notation "d-ism" to combine the English word "deism" with Leibniz's use of the prefix $d$ in $dx$ to suggest an infinitesimal change in $x$. So Leibniz would write $dx/dt$ for the rate of change of $x$ with respect to time $t$. Believing in ...

4

The fourth quote is found in the posthumous work "Anecdotes, Observations and Characters, of Books and Men" Vol 1 (page 158), by the historian Joseph Spence (1820). They are reported to have been uttered by Newton just before his death (1727) to Chevalier Andrew Michael Ramsey (though the latter was recorded to be in France at the time). The second probably ...

4

Your requirements are contradictive: there CANNOT BE a "detailed analysis" of mathematical ideas of all of Principia in 25-30 pages! One of the best reviews covering all three books of Principia that I know is the Guide to Newton's Principia by I. Bernard Cohen. It is attached to the new translation of Principia itself, U. of California press, 1999. The ...

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