In this Principia, Newton takes a rather complex viewpoint.
Following a number of definitions (including one for mass, his "quantity of matter" and
one for momentum, his "quantity of motion") he axiomatizes his laws of motion so
F=ma is taken to be exactly true. However, his definition of mass
(see following paragraph) was informed by his (dynamic)
pendulum experiments, given in the Principia's Book 3 , Proposition 6 , by which he concluded that balancescale
weight W is proportional to inertial mass m: