Questions tagged [newton]

For questions about Isaac Newton (1643-1727), mathematician and physicist, and his works

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Online resources for 19th century physics textbooks

I remember seeing Newton's force equation written in a 19th century textbook as $F=(M+m)/R^2$ (instead of $Mm$). I don't remember if they used $G$. Do you know a collection of 19th century physics ...
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Deflection of the pendulum arm in Cavendish experiment

I'm trying to find how Cavendish calculated the deflection of the arm due to the gravitational attractions of the weights. He gives for the deflection B=6.18 divisions. "Motion of the arm on ...
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Newton's Corollary #1 to the Laws of Motion (Principia)

I'm currently working through selected portions of Newton's Principia, but I'm already stuck in trying to understand his explanation for the first corollary (i.e., Corollary I) to the laws of motion. ...
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Is Newton's Gravitational Constant G a force?

The Constant of Gravitation $G$ was first defined by Boys in 1894: Employing the C.G.S system of measurement, the Newtonian Constant is equal to the force of attraction in dynes between two balls ...
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Question from Whiteside V. 1 - what did Newton mean by a:b :: c:d notation?

I'm reading volume 1 of Whiteside's 'Mathematical Papers of Isaac Newton,' and on pp. 383-384, Newton reaches a conclusion on his "Example 1st" in the statement "55:-54 :: p:q..." -...
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Did Newton know the chain rule?

I heard someone say recently that Newton didn't know the chain rule. Is that true? I know Newton didn't share our current conception of functions, the real line, limits, etc., so if he did use ...
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Did the concept of mass exist before Newton?

I have been learning Newton's laws, and I am confused about the different formulations of the laws, the definitions of the quantities in the modern version, and the definitions of the quantities ...
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Are there any direct comments by Isaac Newton on Leibniz's living force / vis-viva?

The living force or the vis-viva is a quantity usually attributed to Leibniz (although there were a few other people who identified it as a conserved quantity in certain collisions earlier). Many ...
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Ideas about the speed of light between Galileo and Romer?

I know that the great Galileo made no real progress measuring the speed of light -- he disappointingly suggested that it might be infinite. I read that he concluded (based on his attempts to measure ...
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Identification of Rare Newton Statue

I'm not sure where else to post this. No matter how inventive my Google searches, I am unable to locate an active webpage containing this rare statue of Isaac Newton that I stored on my computer a ...
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How to understand Poincaré's interpretation of Newton's anagram "aaaaabbbeeeeii"

In Science and Method, page 37, Poincaré (as translated by Francis Maitland) states, The story goes that Newton once communicated to Leibnitz an anagram somewhat like the following: aaaaabbbeeeeii, ...
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What led to the formula $W=\vec{F} \cdot \overrightarrow{d s}$? [closed]

For me the concept of energy in physics is the least intuitive one as in all the books on Physics that I have read so far. The concept of energy have been the least intuitive one as I cannot ...
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In which units did Sir Isaac Newton define force at that time as SI system didn't existed then? [duplicate]

Sir Isaac Newton led the foundation of his famous laws of motion during the 17th Century but at that time SI system hadn't existed. So in which units did he define force? Did he define it in some ...
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In Newton's cannon image, where do the shapes drawn into the sphere come from?

I find quite interesting the choice for the shapes drawn into the sphere that resembles continents. Was this choice arbitrary or do we know if there is some justification behind it?
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About Newton's apple

I read: Suddenly – boink! -an apple hits him on the head. “Aha!” he shouts, or perhaps, “Eureka!” In a flash he understands that the very same force that brought the apple crashing toward the ground ...
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When did the word "Real number" begin to be used as an official terminology to refer to both rational and irrational numbers?

I am really curious about and struggling with finding when the word "Real number" began to be used as an official terminology to refer to both rational and irrational numbers. In Wiki, it ...
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Did Newton ever use filtered or prism-dispersed colored light to view "Newton's rings" or other thin-film interference effects?

First please enjoy this wonderful answer to How did Newton explain his interference rings without wave optics? which describes the story behind what we now call Newton's rings. Below I show an example ...
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History of interpolation methods - Newton

I'm interested in reading more about how Newton developed his method of interpolation and also the proofs he developed to this topic. I'm currently reading "Analysis by its history" which ...
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Was Kants theory of space and time inspired by that of colour?

Kants theory of space, time and causality is that they are the very forms of experience and ground all the other phenomena that we can experience. He called them the forms of sensibility. Kant studied ...
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How did Newton originally formulate the Law of Cooling?

I am searching for Newton's original formulation of the Law of Cooling. In his article (p.140-143), Newton said: "For the heat which the hot iron communicates in a given time to cold bodies ...
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8 votes
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Who was buying prisms in 1665?

In his recollections Newton describes how he made his greatest discovery: In August 1665, Sir I., who was not then not 24 brought at Sturbridge fair a Prism to try some experiments upon Descartes's ...
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How did the idea of a formal derivation emerge?

Infinitesimal calculus and the introduction of derivatives is often linked to Newton and Leibniz. I was wondering, when and why the idea of studying formal derivatives (e.g., of a formal polynomial) ...
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Did Newton discuss and/or use the principle of moments?

This question comes from a point of view of a student in current times. The general curriculum for a physics student presents that a static analysis of a simple system requires that the forces in each ...
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What was Newton's statement of the universal law of gravitation?

Newton explained the inverse square law in Principia. On looking through an English translation, though, I'm having difficulty pulling out a single quote that is Newton's clearest statement of the ...
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Is there an English translation of Newton’s De Analysi?

I’m looking for an English translation of Newton’s De analysi. (Alas, my Latin is weak.) I’m rather dismayed by the fact that I can’t appear to find one. How is it possible that one of the most ...
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6 votes
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Can anyone find Newton's calculation error in Principia, Book III, Proposition XIX?

Musing about the historical evolution of the notation for the gravitational constant ($f$, $G$, $\kappa$, $\kappa^2$), I found myself digging for the first time in my life into Newton's Principia, ...
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Is it true that Newton used the gedankenexperiment of a cannonball revolving around the earth to find the inverse square law of gravity?

I have often heared that Newton compared the centripetal acceleration of an (imaginary) cannonball revolving around the earth just above the surface with the centripetal acceleration of the moon and ...
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Mr. Newton at the Royal Mint

I would like to ask how Isaac Newton specifically applied mathematics to reducing forgeries and improving coinage while he was Master of the Royal Mint. Thank you.
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What was Newton's road to his discovery of "Puiseux series" and "Newton polygon"?

In my opinion, one of Isaac Newton's greatest achievements in the "purer" aspects of mathematics was his discovery of Puiseux series; power series with fractional exponents. According to p.6 ...
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What did Newton's teacher contribute to the Fundamental Theorem of Calculus?

Isaac Barrow was one of the professors who taught Isaac Newton at Cambridge. According to this page, he is said to have made contributions to the Fundamental Theorem of Calculus that was devised by ...
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Newton's evaluation of 1 + 1/3 - 1/5 - 1/7 + 1/9 + 1/11

I had asked the following question on MSE here, and I was directed to this exchange. There is a nice solution in the comments there, but perhaps someone here can add some additional insight? How ...
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5 votes
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Why do we use Leibniz's “version” of calculus instead of Newton's?

I understand that they invented calculus independently at roughly the same time, but why do we use Leibniz's terminology/notation rather than Newton's? For example, why don't we use "fluxion"...
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Newton as the first one to establish numerical analysis as a new field of study

I was reading about the history of Newton's Method. Newton used a cubic equation, $x^3 - 2x - 5 = 0$, to show the efficacy of his method around 1670. I was wondering that why Newton would choose this ...
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What mathematics did Isaac Newton learn at school?

Since Sir Issac Newton invented a lot of modern mathematics, what mathematics did he already know? Since he was standing on the shoulders of giants which giants was he speaking of? I presume he knew ...
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Where can I find Lagrange’s original equilateral triangular solution for arbitrary masses?

This answer to What kind of triangle is formed by three unequal masses in a circular restricted three body orbit? explains that In the Newtonian limit, an equilateral 3-body solution exists for any ...
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How did Newton prove his third law of motion?

I guess it is an experimental law, so what was the experiment?
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What was Sir Issac Newton's thoughts on the origin of the Universe?

Newton founded the Law of Gravitation based on the observations of Kepler and Galilei. He later invented the mathematical framework which eventually helped him formulate his theory of gravitation. ...
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What made Newton realize that the law of gravitation was 'universal'? [duplicate]

Newton's law of gravitation operative near the earth is the same law causes the earth and the other planets to go around the sun and other heavenly phenomena. Was it a giant leap of faith by Newton or ...
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2 votes
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The Mathematical Principles of Natural Philosophy

Please, advise a good review of Isaac Newton's work "The Mathematical Principles of Natural Philosophy" with a detailed analysis of his mathematical ideas. Smth about 20-25 pages. Thank you in ...
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Did Newton invent convex hulls?

The convex hull of a set of points appears recognizably in a 1676 letter from Newton to Henry Oldenburg describing Newton polygons. Is there an earlier precedent for convex hulls or is this their ...
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2 votes
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Glass ball drop experiment

Several years ago, I remember reading about an experiment, and I thought it was in Newton's Principia, so the experiment was conducted in that time frame. The experiment involved timing the fall of a ...
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Is there a record of how Newton built his telescope?

Did Newton write down his process of building a reflector telescope? Even with modern knowledge and technology, building one is no easy task so I'm curious of exactly what Newton did.
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Are these Newton's quotes apocryphal?

I have stumbled upon the following alleged Newton's quotes, but I could not find them in any of their works. No great discovery was ever made without a bold guess. No sciences are better attested ...
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What problem led to the discovery of Calculus?

As far as I remember, Calculus was invented/discovered/founded by Newton. What was he trying to achieve that made him find the limit of differences approaching zero? How far did he get into Calculus? ...
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What if Newton's bucket had been a sphere?

My question is about Newton's bucket experiment. If a sphere filled (say) one-third with water is rotated very very fast, will the water eventually spread out across and coat the entire interior ...
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1 vote
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Did Newton already have F= ma (or equivalent) before finding his gravity equations?

Newton's gravity equations are in an F = ma configuration. Multiply the acceleration formula by m, you get the force formula. So did he have F = ma (or some equivalent - I think the concept of ...
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How did Newton measure forces in his experiments to establish the laws of motion?

I wanted to know about the experiments that Newton performed which led to the formulation of laws of motion. In particular I am interested in the following: How did he measure the forces in order to ...
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17 votes
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What does it mean by "d-ism of Leibniz" and "dotage of Newton" in simple English?

I am reading this article by Donald E. Knuth and get stuck by this sentence: Our mathematical language continues to improve, just as “the d-ism of Leibniz overtook the dotage of Newton” in past ...
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What was Isaac Newton's contribution to optics?

What was Isaac Newton's contribution to optics? I know that he believed in the corpuscular theory of light. Did he know about the laws of reflection ad refraction?
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Refraction in Newton's Corpuscular Theory of Light [duplicate]

Newton's theory of light stated that a light travelled in a straight line as small particles. When these particles travelled in a medium, they experienced an attractive force with the particles of the ...
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