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Prior to the publication of The ''Principia'', the philosophy of motion and change in the universe was largely a theoretical and non-mathematical enterprise. The dominating methodological approach both in the Aristotelian-scholastic and Cartesian natural philosophy, was one in which truths about the natural world were proposed as conjectural hypotheses. The They were often deduced from fundamental metaphysical principles that were deemed evidently true by human reason [[CiteRef::Janiak (2016)]][[CiteRef::Lennon and Dea (2014)]]. Influenced by the more experimental and mathematically oriented methodologies of Bacon, Galileo, and Boyle, Newton explicitly rejected the this method of hypotheses, and instead demanded that all propositions be deduced from the observed phenomena and then converted into general principles via '''induction''' [[CiteRef::McMullin (2001)]][[CiteRef::Janiak (2016)]][[CiteRef::Smith (2002)]]. In the second edition of The ''Principia'', Newton states:

Out of these four rules a new, engaged method for conducting science emerged that stood in stark contrast to the previous passive and theoretical Cartesian and Aristotelian-scholastic methods. Propositions are born from formulated based on observations of the natural sources world and placed back into the natural world to be tested empirically.[[CiteRef::Smith (2002)]] As the four rules were absorbed into the ensuing mosaic, the The calculus became deeply incorporated in the experimental method, as it was used to mathematically calculate empirical predictions from natural laws, and then evaluate how exactly the prediction matched the observed reality. Newton claimed to have derived his law of universal gravitation using this method as applied to Kepler's laws of planetary motion. In the Cartesian natural philosophy, the centripetal force had already been defined as the agent that pulled the moon towards the Earth, keeping its orbit circular rather than linear. Newton appealed to rules 1) and 2) to claim that the centripetal force, and the force that compelled objects to move downwards towards the Earth, were merely two different expressions of the same thing. Newton then went on to apply the third rule, and argue that this force, which he called gravity, must be a universal property of all material objects. From here, he went on to argue for the unification of superlunary and sublunary phenomena.[[CiteRef::Harper (2002)|pp. 183-184]]

Historical research indicates that the scientific community did not use Newton's own criteria in evaluating his work. Newton's theories did not become accepted outside of England until after its prediction of the oblate spheroid shape of the Earth was confirmed by expeditions to Lapland and Peru. Newton's theories became accepted via a hypothetico-deductive method based on confirmed novel predictions that distinguished it from the rival Cartesian vortices, rather than via Newton's own inductive methodmethodology. [[CiteRef::Barseghyan (2015)|p. 48-49]][[CiteRef::Terrall (1992)]][[CiteRef::McMullin (2001)]] According to McMullin, Newton's method methodology ran contrary to the consensus that had been emerging among natural philosophers of his time, in favor of hypothesis. [[CiteRef::McMullin (2001)]] Christiaan Huygens and John Locke are known to have taken the experimental philosophy, if not necessarily the full content of Newton’s theories, to heart.[[CiteRef::Janiak (2016)]]