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The Mathematical Principles of Natural Philosophy

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The Mathematical Principles of Natural Philosophy

In 1687 Isaac Newton published Philosophiae Naturalis Principia Mathematica, usually known simply as the Principia, at the urging and expense of the astronomer Edmond Halley. The book set out three laws of motion, an object at rest or in uniform motion stays that way unless a force acts on it, force equals mass times acceleration, and every action has an equal and opposite reaction, together with the law of universal gravitation: every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

What made the Principia extraordinary was not any single law but the demonstration that one set of rules governed motion everywhere, an apple falling in an English orchard and a planet tracing its orbit around the sun answered to the same equation. Newton derived Johannes Kepler's earlier empirical laws of planetary motion as consequences of his own gravitational law, showing that Kepler's careful cataloguing of how the planets moved followed necessarily from a deeper physical cause. He wrote the whole argument in the geometric style of classical mathematics rather than the calculus he had developed to find it, a choice that made the proofs harder to follow but easier for contemporary readers trained in Euclid to accept.

The Principia's authority held for more than two centuries, and its core predictions still hold today at the scales of everyday engineering and ordinary astronomy, only at speeds near light or in very strong gravitational fields does Einstein's general relativity supersede it. Newton himself considered the work unfinished business rather than a final word, revising it twice more in his lifetime, and its method, stating a small number of general laws and showing that the observed world follows from them, became the template for physical science that followed.

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