# Classical Isaac Newton's Principia

## Have you read the Philosophiae Naturalis Principia Mathematica?

• ### Never heard of it before

• Total voters
31

#### Auto-Didact

A physics YouTuber by the name of Tibees recently posted two wonderful videos on Sir Isaac Newton's magnum opus, the Philosophiae Naturalis Principia Mathematica.

The videos are this one

and this one

My interest was instantly peaked making me wonder how many people here have actually read Newton's Principia? I remember back in my uni days that from asking about a hundred people in the physics department, the amount that had read it could be counted on one hand.

Related Science and Math Textbooks News on Phys.org

#### fresh_42

Mentor
2018 Award
I guess my Latin is too bad. But I have read Noether and Einstein. Does that count?

I have had a look on the English as well as the German version, but it's very old fashioned and even the type setting is something you first will have to get used to.

#### Auto-Didact

I guess my Latin is too bad. But I have read Noether and Einstein. Does that count?
No!!!

#### vanhees71

Gold Member
The Latin is not the problem since there are some translations in modern languages available. I tried to read an English translation and found it very hard to understand, because Newton doesn't apply his own great invention of calculus but Euclidean (non-analytic!) geometry. So to really understand the Principia I'd have to translate it myself from non-analytic geometry to modern analytic calculus-based math, and this has been done by Euler already in a masterful way. At the end mechanics is described entirely by Hamilton's principle, as is any fundamental model of physics so far.

#### HallsofIvy

Homework Helper
"Piqued", not "peaked"!

Staff Emeritus
"Number", not "amount"!

#### fresh_42

Mentor
2018 Award
The question is: Why?

There is no need to read it. Any modern book on mechanics will provide more insights than Newton does. If at all, it is interesting for historians and of course in its Latin version.

#### jtbell

Mentor
I have this, but haven't worked my way through it systematically, just dipped into it occasionally:

Close to 1000 pages. Half is a modern English translation of the original, and half is a guide to it.

#### mathwonk

Homework Helper
I owned a copy of the florian cajori translation for many years until I moved and unfortunately left it behind. My friend Mike Spivak recently wrote a book laying out his attempts to understand it, in his usual marvellous style. I suggest looking at it if you are interested in reading Newton. In general I always recommend taking a stab at reading great books such as the principia, by great minds, as you always get something out of it that cannot be got otherwise. here is amazon's listing of Mike's book:

#### fresh_42

Mentor
2018 Award
Gauß' Disquisitiones Arithmeticae starts with:

Theorema: Propositis $m$ numeris integris successivis
$$a,\,a+1,\,a+2\, \ldots a+m-1$$
alioque $A$, illorum aliquis huic secundum modulum $m$ congruus erit, et quidem unicus tantum.

It is not really the Latin which makes it difficult. It is the distance to the modern way of writing it:

Theorem: The equivalence classes of $\mathbb{Z}/m\mathbb{Z}$ are uniquely represented by $a+\{\,0,1,\ldots,m-1\,\}$.

Def 1: Quantitas materiae est mensura eiusdem orta ex illius densitate magnitudine conjunctim.
Def 1: The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.

Now tell me what he defined!

#### smodak

LOl the grammar and spelling police .... :)

Staff Emeritus
LOl the grammar and spelling police .... :)
Actually it's diction.

#### Auto-Didact

The question is: Why?

There is no need to read it. Any modern book on mechanics will provide more insights than Newton does. If at all, it is interesting for historians and of course in its Latin version.
My Latin is good, but not that good. That's not important since reading it in English or another language certainly counts. Newton describes much more in his Principia than just Mechanics, especially in the beginning of the book: he is describing his thought process, his methodology not just how to think, but how to reason about natural philosophy from a purely mathematical point of view.

Of his methodological description, nothing has changed so far in how to do physics; the only change is in the content of the theories themselves, which is frankly speaking from a theoretical methodological standpoint almost completely irrelevant. Everyone (in physics) already knows that Hamiltonian/Lagrangian mechanics is an equivalent formulation, but I'd say that is completely beside the point; that's almost like arguing that a modern TV adaptation of some book is better than an original book and therefore one needn't read the book.

Maybe it's just me, but I think reading original canonical texts is something that is important in the development of a theorist; it forces one to be both careful and focused when trying to describe novel conceptualizations before instantly jumping to a mathematization. I can imagine experimentalists not caring about this, but I personally never cared what they wanted w.r.t. methodological traditions since they tend to have a very narrow understanding of the theoretician's/mathematician's point of view.

I'm the first to admit that reading the Principia or not won't necessarily make you a better physicist in the direct practice of physics itself, definitely not w.r.t. experimenting. As a foundational theorist however there aren't many better works available: understanding the Principia as a foundational work can give you a much better perspective in the methodological structure of foundational research, something I think that many physicists are severely lacking in.

Moreover, it also shows how far physics has come in such a short time and also gives some insight into what reasoning skills we have actually lost along the way (naive physicists will say this is irrelevant because our modern formulation is better). Make no mistake, the modern mathematics of physics is nothing but fluff to a master of the trade; I have no doubt whatsoever if Newton were alive and practicing today he would steamroll 99.9% of alive theoreticians, especially w.r.t. foundations, like nobody's business.
Gauß' Disquisitiones Arithmeticae starts with:

Theorema: Propositis $m$ numeris integris successivis
$$a,\,a+1,\,a+2\, \ldots a+m-1$$
alioque $A$, illorum aliquis huic secundum modulum $m$ congruus erit, et quidem unicus tantum.

It is not really the Latin which makes it difficult. It is the distance to the modern way of writing it:

Theorem: The equivalence classes of $\mathbb{Z}/m\mathbb{Z}$ are uniquely represented by $a+\{\,0,1,\ldots,m-1\,\}$.

Def 1: Quantitas materiae est mensura eiusdem orta ex illius densitate magnitudine conjunctim.
Def 1: The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.

Now tell me what he defined!
Newton is speaking his equations out using natural language: "the quantity of matter (i.e. mass) is the conjunction of density and bulk (i.e. volume), i.e. $m = \rho V$. Many pre-20th century science and engineering texts are written in this manner; this is how physics was done before Newton invented mathematical/theoretical physics.

To be able to speak out mathematical statements in this manner is a skill that is still thought in some high schools, but the skill itself seems to have more or less to diminished greatly over time among many physicists since they reflexively jump to equations; today it seems that both mathematicians and philosophers are much better at this than physicists.

This is somewhat of a shame because in other sciences and practices, e.g. in medicine, this method of speaking often is codified into both a communication and reasoning method. Doing applied mathematics successfully in such other fields (e.g. mathematical sociology) often requires precisely a mastery of this descriptive ability before any equations can be found.

This descriptive and communicative ability is not just applicable and useful in other sciences but actually in new theories/frameworks from both mathematical and theoretical physics, in interdisciplinary fields and in much of classical engineering/industry/business as well; you can imagine that being able to do this gives one tonnes of unique work opportunities. Once others in those fields see that this is possible the demand for capable physicists tends to increase enormously within that professional endeavor, given of course that there are physicists/applied mathematicians who are actually able to meet such demands successfully.

#### fresh_42

Mentor
2018 Award
By the way, did anybody read this one: https://en.wikipedia.org/wiki/Universal_Natural_History_and_Theory_of_the_Heavens?

I just learnt that his description of how planets formed is even today close to modern astronomy. And this was a philosopher. Incredible!

Wikipedia said:
With his theory, Kant comes closer to today's ideas about cosmogony than Pierre-Simon Laplace, who developed his hypothesis on the formation of the planets in 1796, 41 years later, independently of Kant. Nevertheless, both theories are often summarized as Kant-Laplace theory about the formation of the solar system (cosmogony).

By direct measurements Kant's assumption about the variety of galaxies could be proved by Edwin Hubble in the 1920s.

#### Auto-Didact

By the way, did anybody read this one: https://en.wikipedia.org/wiki/Universal_Natural_History_and_Theory_of_the_Heavens?

I just learnt that his description of how planets formed is even today close to modern astronomy. And this was a philosopher. Incredible!
I never read it in full, but I did read a few more recent monographs summarizing Kant's contribution and impact on natural science and mathematics.

In fact, it was only after reading about Kant's theoretical exposition of Newtonian physics as a world view that I became convinced that philosophy was extremely useful to science; Kant basically gave us almost all the conceptual and therefore logical limitations of Newtonian theory in the form of falsifiable hypotheses, which others (such as Einstein et al.) made more explicit and then falsified.

It should go without saying, but most of the greatest physicists and mathematicians of the late 19th century and early 20th century were hugely influenced by his work. If we had someone of the likes of Kant today - or better yet, had Poincaré not met an untimely death - there would probably be no problems in the foundations of QT today.

#### fresh_42

Mentor
2018 Award
I never read it in full, but I did read a few more recent monographs summarizing Kant's contribution and impact on natural science and mathematics.
Att.: off topic.

Just a funny side note. Kant also influenced normal people's lives. He used to have a walk every day at the same time. It is said, that people set their clocks when they saw him.

#### MathematicalPhysicist

Gold Member
I thought of reading Maxwell's treatise on Electricity and Magnetism the other day, but not now.

Anyone wants to read how physics was in Aristotle's time?!

#### Auto-Didact

Anyone wants to read how physics was in Aristotle's time?!
I never read Aristotle's Physics; despite the word itself being the book's title and counter to what scholars claimed for many centuries even millenia, I'd say that Aristotelian physics clearly isn't the same subject or discipline that we would call physics today. This break started with Galileo and was cemented by Newton, Leibniz, Fermat et al.

The simple fact is that Aristotles' metaphysics is far too drastically different from the ontology of Newtonian/Kantian physics - i.e. the existence of laws of physics as we still think about it today - to consider his physics as being the same discipline as classical/modern physics, despite any shared subject matters between the disciplines such as a theory of motion, matter, etc.

#### MathematicalPhysicist

Gold Member
I never read Aristotle's Physics; despite the word itself being the book's title and counter to what scholars claimed for many centuries even millenia, I'd say that Aristotelian physics clearly isn't the same subject or discipline that we would call physics today. This break started with Galileo and was cemented by Newton, Leibniz, Fermat et al.

The simple fact is that Aristotles' metaphysics is far too drastically different from the ontology of Newtonian/Kantian physics - i.e. the existence of laws of physics as we still think about it today - to consider his physics as being the same discipline as classical/modern physics, despite any shared subject matters between the disciplines such as a theory of motion, matter, etc.
I agree, but science existed also before Newton's and Galileo's time; just a different dogma.
A dogma that didn't stress observation over theoretical thinking.
One might argue that part of theoretical physics community went back to stressing theory over experimental evidence.

#### Auto-Didact

Your description is consistent with how the history of science is usually presented within many if not most science major programmes. Personally, I think it is a somewhat mistaken view from a simplified post-hoc-ergo-propter-hoc view of history - biased by the knowledge that we have today - instead of a view based in strong historicity, which is trying to understand the past.

Most scientists tend to get very uncomfortable once people start talking about falsified theories, sometimes even getting outright defensive whereby they try to overcompensate for these 'sins of the past'. From my observations of colleagues and students over the years, I tend to see that they are ashamed and openly hear them say 'how could people back then be so ignorant/stupid? I would have never made such a mistake!' while this is actually very far from a proper evaluation of the intellect of the past.

In any case, whether true or not it seems that based on an acceptance by many of the 'theoretical dogma'-explanation, today almost all other sciences stress the importance of experiments almost to the exclusion of theory. You would be hardpressed to find almost any theoretical science divisions outside physics departments and even more hardpressed to find any where the theoreticians weren't primarily trained as physicists or applied mathematicians.

This development is quite unfortunate since this is going from one extreme (theory is more important) to the other (experiment is more important), while clearly there can be a more healthy balance, as demonstrable by the very existence of the practice of physics.
This is codified by the special role that mathematics plays in the foundations of physics, namely as the very structure behind physical laws. In fact, physics is the only science which truly has scientific laws; all other scientific laws aren't fundamental and if they are they tend to turn out to be laws of physics as well.

The key role of mathematics way down into the fundamental conceptualizations of physics is what makes physics unique among the sciences and what gives physics such a special place among the sciences; this is why physics is also the only science where ontology is important, because the ontology of almost all other sciences usually defer to what are physical laws, whether discovered or still undiscovered. I don't think it is going to far to say that the laws of physics ARE the real subject of physics, with everything else just fluff.

Many laws in other sciences, e.g. natural selection, often turn out to only be 'lawful' due to the phenomenon mathematically conforming to some universality class, making the underlying physics almost invisible, especially if the observer lacks the prerequisite knowledge i.e. a strong theoretical foundation. This explains why such theories and their respective sciences lack pristine mathematical models and languages as is customary in the practice of physics.

All of this is becomes even more apparent when one realizes that the word 'theory' doesn't have the same meaning in other sciences as it has in physics. In most other sciences, theory roughly means 'a(ny) widely accepted explanation of empirical data', while in physics something only becomes a theory based on very stringent mathematical prediction criteria, which usually precede an experiment to an arbitrarily high degree of accuracy.

"Isaac Newton's Principia"

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