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I came across this today while looking for works on the method of Newton's reasoning. It is a fascinating subject and the article is illuminating.

Newton seems to have inferred, and tested by many experiments, that certain constrained motions consisted of two components: an initial velocity; and a centripetal motion.

He seems to have been (or was) the first person to derive a mathematical statement of the centripetal motion. He found this was also true of the celestial motions observed by Kepler and Halley, and inferred it was true of any orbital motion.

I was astonished to find in Principia that Newton explicitly does not define a cause, seen in Definition 8. He says that "force" is only a mathematical statement of effect, and not an explanation of cause. Gravity is not a cause, but an effect, the cause of which is completely unknown.

The Axioms or Laws seem to play the role of a theory, which Newton demonstrates to be true of all known observations of motion. The real axioms come in Book III Rules of Philosophizing, because there is no reason to accept that celestial motion has the same "cause" unless you accept Rule 2: "Accordingly, to natural effects of the same kind, the same causes should be assigned, as far as possible". Otherwise the celestial motion could be an interesting coincidence.

John Heinmiller

Newton calls his principles the Three Axioms and not the Three Laws for a very simple reason. He calls them axioms because they are fundamental to his thinking. They are necessarily first principles, much like Euclid's five axioms are, they can never be proved to perfection though they can be disproved by a single observation, again like Euclid's five axioms and all of his calculations are dependent upon these, again like Euclid's five axioms.

If we get rid of even one of his three first principles, we have to redo almost all of Newton's calculations, for they will suddenly not make any sense. We have to assume that bodies remain in a specific state of motion unless a force is applied to it, we have to assume that the force acts in a specific way and we have to assume that there is an equal and opposite reaction, to do otherwise is to render each and every one of the calculations in Newton's great Principia becomes mere exercises of mathematics, without any meaning in real life. This gives the three principles a fundamental importance beyond anything in the rest of the book.

I know that a lot of people prefer to call his three principles laws instead of axioms. But Newton was entirely correct because, just as Euclid's five axioms were so fundamental to his entire geometry, Newton's three axioms are absolutely and totally fundamental to his physics. They are the first principles, the root foundation, without which all of his calculations and analysis are absolutely meaningless.

Eric Schliesser

Newton calls his three Axioms also Laws: Axiomata sive leges Motus.

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Here's a link to my past blogging (and discussions involving me) at: New APPS.


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