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Philosophiae Naturalis Principia Mathematica was first published in 1687. In it, Newton states his laws of motion, forming the foundation of classical mechanics; his law of universal gravitation; and a derivation of Kepler's laws of planetary motion. The Principia is considered one of the most important works in the history of science. By the end of the century, no one could deny that a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally . In formulating his physical theories, Newton developed and used mathematical methods now included in the field of calculus. But the language of calculus as we know it was largely absent from the Principia; Newton gave many of his proofs in a geometric form of infinitesimal calculus, based on limits of ratios of vanishing small geometric quantities. In a revised conclusion to the Principia, Newton used his expression that became famous, Hypotheses non fingo ( I feign no hypotheses ). This classic translation by Andrew Motte was described by Newton scholar I. Bernard Cohen as still of enormous value in conveying to us the sense of Newton's words in their own time, and it is generally faithful to the original: clear, and well written .

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