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Descartes included many revolutionary theories of the natural world in his mosaic, but he still largely relied on classical methods of theorizing and conjectured hypotheses in order to construct scientific propositions.[[CiteRef::Janiak (2016)]] Whereas in the early 17th century Galileo and Boyle had already begun to test proposed theories, Descartes still chose to use logical deductions in an attempt to prove empirical truths, instead of attempting any empirical testing or mathematical techniques.[[CiteRef::Janiak (2016)]] Many of Newton’s ideas were either adopted directly, or adapted from Descartes views of the natural world, however the method of hypotheses is one that Newton rejected outright, as he instead sought different methods for arriving at his conclusions.[[CiteRef::Janiak (2016)]]

Whereas Descartes did not rely on mathematical reasoning for his deductions of scientific propositions, Newton believed that mathematics was an imperative part of conducting natural philosophy.[[CiteRef::Janiak (2016)]] In Newton’s physics, material objects were not required to be in direct contact with each other in order for motion to occur. Instead, objects react to each other via a force, a new concept which Newton envisioned as a quantifiable property contained in all material objects, the amount of which is directly proportional to the quantity of matter contained in the object. Quantities of force and matter were thus introduced to the mosaic as ontological entities that were measurable. By applying Newton’s three laws of motion, material objects in the universe were compelled to accelerate through action at a distance. Additionally, the laws outlined the mathematical relations between this acceleration and the quantities of force and matter could be explained and predicted mathematically, thereby giving mathematics a new central role in the study of natural philosophy. In The ''Principia'', Newton made extensive use of mathematics in his argument for the unified theory of gravity.[[CiteRef::Smith (2009)]] The mathematical language used in The ''Principia'' was geometry, which was also the basis for many of the major models for celestial mechanics that were studied at the time, including the works of Ptolemy, Copernicus and Kepler.[[CiteRef::Smith (2009)]]