fresh_42 said:
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.
fresh_42 said:
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\,\}##.
The principia naturalis start with definitions:
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.
