Credit: Cambridge University Library 1 of 6. Newton's own annotated copy of Principia Mathematica 2 of 6.

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The notebook of Isaac Newton showing his personal expenses c. Credit: The Fitzwilliam Museum, Cambridge. The notebook of Isaac Newton showing code writing listing his sins before and after Whitsunday Read this next. Annotating history: thoughts of an Elizabethan scholar revealed.

## Isaac Newton's Life

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### Nature of science

Fitzwilliam Museum. Trinity College. King's College. Related organisations. Royal Society.

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Newton made contributions to all branches of mathematics then studied, but is especially famous for his solutions to the contemporary problems in analytical geometry of drawing tangents to curves differentiation and defining areas bounded by curves integration. Not only did Newton discover that these problems were inverse to each other, but he discovered general methods of resolving problems of curvature, embraced in his "method of fluxions" and "inverse method of fluxions", respectively equivalent to Leibniz's later differential and integral calculus.

Newton used the term "fluxion" from Latin meaning "flow" because he imagined a quantity "flowing" from one magnitude to another. Fluxions were expressed algebraically, as Leibniz's differentials were, but Newton made extensive use also especially in the Principia of analogous geometrical arguments. Late in life, Newton expressed regret for the algebraic style of recent mathematical progress, preferring the geometrical method of the Classical Greeks, which he regarded as clearer and more rigorous.

Newton's work on pure mathematics was virtually hidden from all but his correspondents until , when he published, with Opticks , a tract on the quadrature of curves integration and another on the classification of the cubic curves.

His Cambridge lectures, delivered from about to , were published in Newton had the essence of the methods of fluxions by The first to become known, privately, to other mathematicians, in , was his method of integration by infinite series. In Paris in Gottfried Wilhelm Leibniz independently evolved the first ideas of his differential calculus, outlined to Newton in Newton had already described some of his mathematical discoveries to Leibniz, not including his method of fluxions. In Leibniz published his first paper on calculus; a small group of mathematicians took up his ideas.

In the s Newton's friends proclaimed the priority of Newton's methods of fluxions. Supporters of Leibniz asserted that he had communicated the differential method to Newton, although Leibniz had claimed no such thing. Newtonians then asserted, rightly, that Leibniz had seen papers of Newton's during a London visit in ; in reality, Leibniz had taken no notice of material on fluxions. A violent dispute sprang up, part public, part private, extended by Leibniz to attacks on Newton's theory of gravitation and his ideas about God and creation; it was not ended even by Leibniz's death in The dispute delayed the reception of Newtonian science on the Continent, and dissuaded British mathematicians from sharing the researches of Continental colleagues for a century.

According to the well-known story, it was on seeing an apple fall in his orchard at some time during or that Newton conceived that the same force governed the motion of the Moon and the apple.

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He calculated the force needed to hold the Moon in its orbit, as compared with the force pulling an object to the ground. He also calculated the centripetal force needed to hold a stone in a sling, and the relation between the length of a pendulum and the time of its swing. These early explorations were not soon exploited by Newton, though he studied astronomy and the problems of planetary motion.

Correspondence with Hooke redirected Newton to the problem of the path of a body subjected to a centrally directed force that varies as the inverse square of the distance; he determined it to be an ellipse, so informing Edmond Halley in August Halley's interest led Newton to demonstrate the relationship afresh, to compose a brief tract on mechanics, and finally to write the Principia. Book I of the Principia states the foundations of the science of mechanics, developing upon them the mathematics of orbital motion round centres of force.

Newton identified gravitation as the fundamental force controlling the motions of the celestial bodies. He never found its cause. To contemporaries who found the idea of attractions across empty space unintelligible, he conceded that they might prove to be caused by the impacts of unseen particles. Book II inaugurates the theory of fluids: Newton solves problems of fluids in movement and of motion through fluids.

From the density of air he calculated the speed of sound waves. Book III shows the law of gravitation at work in the universe: Newton demonstrates it from the revolutions of the six known planets, including the Earth, and their satellites. However, he could never quite perfect the difficult theory of the Moon's motion. Comets were shown to obey the same law; in later editions, Newton added conjectures on the possibility of their return. He calculated the relative masses of heavenly bodies from their gravitational forces, and the oblateness of Earth and Jupiter, already observed.

He explained tidal ebb and flow and the precession of the equinoxes from the forces exerted by the Sun and Moon. All this was done by exact computation. Newton's work in mechanics was accepted at once in Britain, and universally after half a century. Since then it has been ranked among humanity's greatest achievements in abstract thought. It was extended and perfected by others, notably Pierre Simon de Laplace, without changing its basis and it survived into the late 19th century before it began to show signs of failing.

See Quantum Theory; Relativity. Newton left a mass of manuscripts on the subjects of alchemy and chemistry, then closely related topics.

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## Sir Isaac Newton's Principia | Nature

Most of these were extracts from books, bibliographies, dictionaries, and so on, but a few are original. He began intensive experimentation in , continuing till he left Cambridge, seeking to unravel the meaning that he hoped was hidden in alchemical obscurity and mysticism. He sought understanding of the nature and structure of all matter, formed from the "solid, massy, hard, impenetrable, movable particles" that he believed God had created.

Most importantly in the "Queries" appended to "Opticks" and in the essay "On the Nature of Acids" , Newton published an incomplete theory of chemical force, concealing his exploration of the alchemists, which became known a century after his death. Newton owned more books on humanistic learning than on mathematics and science; all his life he studied them deeply.

Newton sought to reconcile Greek mythology and record with the Bible, considered the prime authority on the early history of mankind. In his work on chronology he undertook to make Jewish and pagan dates compatible, and to fix them absolutely from an astronomical argument about the earliest constellation figures devised by the Greeks.