Should I Read Newton's Principia Mathematica?

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The discussion centers on the value of reading Newton's "Principia" for understanding classical physics and its historical context. Participants express skepticism about the necessity of reading the original text, suggesting that modern interpretations and educational resources provide clearer insights into Newton's work. Some recommend secondary literature, like Vladimir Arnold's works, which elucidate Newton's concepts more effectively than the original text. The complexity of Newton's geometrical language and the lack of rigorous calculus in the "Principia" are highlighted as barriers to comprehension. While reading the "Principia" may enrich historical understanding, it is deemed less essential for grasping the physics concepts that are better taught through contemporary methods. The conversation also touches on the evolution of mathematical notation and the significance of Newton's laws, emphasizing that they serve as foundational principles rather than predictive tools without empirical context. Overall, the consensus leans towards prioritizing modern educational approaches over direct engagement with the original text.
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I was wondering to read this book to get a better understanding of the classical world. I want to know what things are there that I can learn in this book? Is it worth it? Is it tough? Should I read it or it will be covered in undergraduate and graduate level of physics?
 
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Personal opinion: it's not worth the effort. Much better to learn from didactically responsible modern presentation and go back to the historical sources only when well introduced to the material and still interested in the history.

##\ ##
 
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I share the same opinion as @BvU. I was able to understand Newton's work better through books about Principia than Principia itself. I can recommend Vladimir Arnol'd's Huygens and Barrow, Newton and Hooke (Birkhauser Verlag, 1990). As a teenager I had naively attempted to read Three hundred years of gravitation (edited by Stephen Hawking and Werner Israel, Cambridge University Press, 1989). All I can say, it is worth an attempt!
 
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rudransh verma said:
I was wondering to read this book to get a better understanding of the classical world. I want to know what things are there that I can learn in this book? Is it worth it? Is it tough? Should I read it or it will be covered in undergraduate and graduate level of physics?
Do you propose to read it in the original Latin, or an English translation?
 
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It depends. If you're interested in history, it's a good idea to read it. If you're interested in the actual physics behind it, there is absolutely no reason I can think of why you should read such a work 300 years old.
 
This book is famous for being the *first* book covering gravitation and calculus, not the best book. In fact there are very few things in human history where the first attempt at something was also the best, or even particularly above average.
 
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ipsky said:
I was able to understand Newton's work better through books about Principia than Principia itself.
There is an edition of the Principia in a translation by Cohen and Whitman.

https://www.amazon.com/dp/0520088174/?tag=pfamazon01-20

Here's what I wrote about it in this forum more than ten years ago:

I have the Whitman/Cohen edition of Newton's Principia. I haven't worked through it "seriously" yet, but I think it's worth the extra cost because half of it is historical background and commentary. Newton's language (even with the modernized translation) and geometrical approach are so different from the way we teach/learn classical mechanics nowadays that most people (certainly including me) need all the help they can get when reading it.
 
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Well, reading Newton's principia at least shows you how much progress has been made within a few decades through the work by Euler, Lagrange, Laplace. Also one should not forget Newton's arch enemy, Leibniz, who hat decidedly the better notation for calculus and also the correct point of view of the meaning of inertial frames (i.e., that there's no absolute space or time).
 
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vanhees71 said:
Well, reading Newton's principia at least shows you how much progress has been made within a few decades through the work by Euler, Lagrange, Laplace. Also one should not forget Newton's arch enemy, Leibniz, who hat decidedly the better notation for calculus and also the correct point of view of the meaning of inertial frames (i.e., that there's no absolute space or time).
Let me double down on the future contributions of Euler, Lagrange and Laplace. There are many others; especially Hamilton. Even if you master the Principia, there will still be a lot of undergraduate mechanics for you to learn.

There are also math issues. Modern vector analysis was not established until the late 19th century. Calculus/analysis was not made completely rigourous until the early 20th century.
 
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  • #11
rudransh verma said:
That's the one!
rudransh verma said:
Also why is the book this thick. Newtons laws, gravitation and calculus
It's really two books in one. My copy has 974 pages. The first 370 are a "Guide to Newton's Principia" by the translators. And there's no calculus, at least not in a form that we would recognize easily today. Newton used concepts from calculus, but expressed them in geometrical language, not the "fluxions" that he invented. I found an interesting discussion of this on StackExchange:

https://hsm.stackexchange.com/questions/2362/why-is-calculus-missing-from-Newtons-principia
 
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Ironically Newton considered his "calculus of fluxions" not rigorous enough and thus took a lot of effort to explain his physics "more geometrico", as was considered the "right way".
 
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jtbell said:
And there's no calculus, at least not in a form that we would recognize easily today. Newton used concepts from calculus, but expressed them in geometrical language, not the "fluxions" that he invented.
So Newtons did not used calculus directly but concepts of it. He almost used geometry in a major sense that was widely accepted at the time. But for what? 🧐
Laws don’t have proofs!
 
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  • #14
rudransh verma said:
So Newtons did not used calculus directly but concepts of it. He almost used geometry in a major sense that was widely accepted at the time. But for what? 🧐
Laws don’t have proofs!
He couldn't say "let us assume the particle has moved a distance ##\Delta x ## in time ##\Delta t## and let ##\Delta t \to 0##".
 
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rudransh verma said:
Laws don’t have proofs!

Laws, by themselves, are also basically useless. Newton's laws of motion by themselves don't actually make any predictions until you predict something with it.
 
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rudransh verma said:
Laws don’t have proofs!
The three laws of motion are axioms in the geometrical or mathematical sense. See page 416: AXIOMS, OR THE LAWS OF MOTION. [AXIOMATA, SIVE LEGES MOTUS in the original Latin text.] Everything else is derived (proved) from them, and from Euclidian geometry, which Newton presumably assumed that his readers already knew.
 
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  • #17
jtbell said:
Everything else is derived (proved) from them
What is proved?
 
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E.g., Kepler's laws for the motion of two bodies interacting via the gravitational interaction, and that was what made the Principia famous in its time, and that's why Haley pursuaded Newton to write it up in the first place. Newton didn't consider it as really as important of his works as we consider it today. He was much more involved in studies of alchemy than in what with some right can be called the "birth of theoretical physics".
 
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@vanhees71 Great! So Newtons 3 laws + Euclidean geometry changed the world.
What about gravitation ? Where is law of gravitation fits in principia?
 
  • #20
I don't know, how Newton introduces his general universal law of gravitation in his principia, but of course in the logical development it's an empirical law within the general framework of Newtonian mechanics (aka the Newtonian spacetime model). Famously according to legend Newton had the ingenious idea that the force on a falling apple is the same force which holds the moon in its orbit around the Earth. He also knew about Kepler's Laws (particularly the 1st and 2nd one). This "empirical input" must inevitably lead to Newton's "inverse-square central-force law": Indeed from Kepler's 2nd Law it follows that there's angular-momentum conservation and thus that the force is a central force. The elliptic orbits with the Sun (Earth) in one focus of the elliptical orbit of the planets (the Moon) then imply the inverse-square law, i.e. Finally from Galilei's law of the independence of the acceleration in free-fall experiments of the falling mass, together with Newton's 2nd Law inevitably leads to
$$\vec{F}_{12} \propto \frac{m_1 m_2}{|\vec{r}_1-\vec{r}_2|^2} \frac{\vec{r}_1-\vec{r}_2}{|\vec{r}_1-\vec{r}_2|},$$
which also obeys Newton's 3rd Law, i.e.,
$$\vec{F}_{21}=-\vec{F}_{12}.$$
As I said, I don't know the precise arguments Newton brought forward in his Principia. I never tried to read it, because it's really hard to follow, because it uses a completely different mathematical language than we use today.
 
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  • #21
rudransh verma said:
What is proved?
Chapters 5 through 8 of the "Guide" which precedes the Principia itself, in your Amazon link, summarize the topics covered by the different parts of the Principia.
 
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  • #22
I think that to read "The Principia" will be instructive in order to understand the culture level of the time, in particular the mathematical language was not rigorous as today. There are some theorems very interesting, Newton was also a geometer and the language of Euclid geometry was the language of the time.
Ssnow
 
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