Newton’s mathematical language is favoring Greek synthetic geometry – masking its novel character. Although Cartesian mathematics formed a fundament of a mathematical description of motion, and even though Descartes first found the law of inertia, Newton soon distanced himself from Descartes’s achievements and severely criticized him. Barrow understood these curves as trajectories of moving bodies. He had studied Oughtred’s Clavis mathematicae, Wallis’s Arithmetica infinitorum and Descartes’s Géometrie in Frans van Schooten’s Latin edition and thus knew his new tool of Analytic geometry which was used to describe curves by mathematical equations. Newton was well informed about recent developments in mathematics and physics in the 1660s. Many thoughts had been expressed by the author in previous published and unpublished letters and works, including De motu corporum (1684) which served as a basis for the first and the third book of the Principia. Among the most prominent examples are Newton's axioms on the motion of bodies, his universal law of gravitation, and its application to planetary motion. Notions like force ( vis), impulse, gravitation, or inertia were quantified and experienced a unified theory and explanation. For the first time, the same simple rules applied to and explained celestial and terrestrial phenomena.Īlthough in many ways prepared by Kepler, Descartes, Huygens, Barrow, Halley or Hooke, this approach culminates in the Principia mathematica. Its title announces the paradigm shift in physics (or natural philosophy): Mathematics has become the language in which phenomena were to be described. Newton’s seminal work Mathematical Principles of Natural Philosophy is considered to be the standard text for classical mechanics (Newtonian mechanics) as well as for the modern scientific method in general. Philosophiae naturalis principia mathematica (3d ed. Philosophiae naturalis principia mathematica (1st ed. Philosophiae naturalis principia mathematica
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