For example in the early days, when it was the only way to learn Newtonian mechanics? Was it good as a textbook?
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At the time Principia (1687) came out it was not something to be learned, it was something to make sense of. Many consider Principia a tough read not only because of new ideas, but also because of obscuring effect of Euclidean geometric language in which it was coached, see Why is calculus missing from Newton's Principia? But many ideas were already known in some narrow circles from works of Huygens, etc., and Newton's correspondence, and those close to him, like one of his early promoters Clarke, had extra insights. There was also competing Cartesian mechanics at the time (mostly qualitative but more intuitive) so it was not so much about teaching and learning in the early years as arguing and advocating between partisans on both sides.
Newton's derivation of Kepler's laws was impressive however, and the new mechanics soon gained wide recognition. One of the first textbooks, Gravesande's, appeared in 1720-21, and others soon followed. Even then many concepts (force momentum, etc.), and their role in mechanics, remained unclear and controversial. The so-called vis viva controversy, that started with Leibniz criticizing Descartes's unconserved "quantity of motion" and turned into a mechanical off-shoot of Newton-Leibniz priority dispute, engulfed most prominent physicists in the first half of 18th century, see What was the vis viva controversy, including its philosophical aspects? One positive outcome of it was clarification of the basic notions by Euler and D'alembert. It was reformulations in Euler's Mechanica (1736) and D'alembert's Traite de Dynamique (1743/58) that allowed new mechanics to be broadly understood, appreciated and learned.
There is something of a modern movement of teaching with original sources, especially in mathematics, here is a programmatic website. It is not so popular in physics apparently, see Why don't most physics programs study the primary sources? on Physcis SE, which explicitly involves Newton's Principia. Still, one of the users wrote "I think it is possible to assign the Principia as an elementary physics book, if the translation is authentic and modernized. It requires rewriting the whole thing from scratch, but without throwing away any of Newton's insights. These insights are mostly contained in the special problems he solves". I have my doubts, but Bressoud uses (modernized) parts of Principia as a motivational springboard for teaching advanced calculus in his Second Year Calculus: From Celestial Mechanics to Special Relativity. In particular, he presents both Newton's and modern derivation of the inverse square law from Kepler's laws in the opening chapter.
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$\begingroup$ Thank you for this wonderful answer. One thing which I don't understand is why the Principia is considered obscure. Is it because you need to have a lot of geometry knowledge ? What is it that makes it obscure ? $\endgroup$– copperApr 21, 2016 at 22:45
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$\begingroup$ @copper Many feel that Euclidean language obscures how results were arrived at, 17th century authors like Torricelli said the same thing about Euclid's Elements and other ancient works themselves. For a long time it was even accepted that Newton originally derived Principia results using his fluxional calculus, and then "coded" them into geometry, but modern scholarship disputes that hsm.stackexchange.com/questions/2362/… $\endgroup$– ConifoldApr 23, 2016 at 21:41
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$\begingroup$ Thank you again for your answer ! Just curiously, how does someone know as much as you do ? How is it possible ? $\endgroup$– copperApr 25, 2016 at 18:41
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1$\begingroup$ @copper Thank you for the compliment. Like all magic it involves a sleight of hand :-) I do not know most of what is written in my answers at any given time, maybe bare bones and where to look it up. Many themes and time periods come up in multiple questions, so in many cases I roughly know where to look for specifics when writing the answer. $\endgroup$– ConifoldApr 28, 2016 at 1:55
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Most definitely! Newton was hailed as a mathematical genius, especially in England. Principia was the textbook on a variety of subjects, including physics and mathematics. I know for a fact that his fluxions (what Newton called his calculus) was exclusively used at Cambridge for a century after he died, which comes from his Principia.
Sources: "Isaac Newton: Man, Myth, and Mathematics" by V. Frederick Rickey; "The Newton Leibniz Controversy Concerning the Discovery of the Calculus" by Dorothy Schrader
