## Dt

and this really serves as Newton's definition of mass.48 It measures a body's resistance to a change in motion, i.e. its inertia.

The third law, when combined with the second, gives Newton's version of Descartes' law of the conservation of motion. If two bodies A and B interact, with A exerting a force FB on B and B exerting a force FA on A, Newton's third law says that, in the absence of any other forces,

Combining this with the second law, we obtain the law of conservation of momentum, mA Va + mB Vb = c, where c is a constant vector.

Much of the Principia is concerned with the motion of bodies under the influence of central forces or, as Newton called them, 'centripetal forces'. In this we see that Newton had realized crucially that it was much simpler to consider things from a frame of reference in which the point of attraction was fixed rather than from the point of view of the body in motion. In this way, centrifugal forces - which were not forces at all in Newton's new dynamics -were replaced by forces that acted continually toward a fixed point.

After stating the laws on which his dynamics was based, Newton went on to prove eleven lemmas that showed how to apply methods from the calculus to geometrical problems involving curved lines - his so-called method of 'first

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