Principia Mathematica by Newton

[rudransh verma]

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?

 

[BvU]

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.

$\$

 

[ipsky]

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!

 

[phyzguy]

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?

 

[haushofer]

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.

 

[Office_Shredder]

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.

 

[jtbell]

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.

 

[vanhees71]

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).

 

[rudransh verma]

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:

Is it the same book https://www.amazon.com/dp/0520088174/?tag=pfamazon01-20

Also why is the book this thick. Newtons laws, gravitation and calculus

 

[Frabjous]

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.

 

[jtbell]

Is it the same book https://read.amazon.in/kp/embed?asi...e=kpe&ref_=cm_sw_r_kb_dp_5ADMP8EG6JWSQ1XZNAEB

That's the one!

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

 

[vanhees71]

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".

 

[rudransh verma]

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!

 

[Hall]

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 $\Delta t \to 0$".

 

[Office_Shredder]

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.

 

[jtbell]

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.

 

[rudransh verma]

Everything else is derived (proved) from them

What is proved?

 

[vanhees71]

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".

 

[rudransh verma]

@vanhees71 Great! So Newtons 3 laws + Euclidean geometry changed the world.
What about gravitation ? Where is law of gravitation fits in principia?

 

[vanhees71]

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.

 

[jtbell]

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.

 

[Ssnow]

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

 

[smodak]

These two are really good.
1. Newton's Principia for the Common Reader
2. Magnificent Principia