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In August 1684, more than a decade after Newton was elected Lucasian professor of mathematics, Edmund Halley came to Cambridge to consult with him about the law of gravitation, specifically seeking to resolve the question of whether the law of attraction was that of the inverse square, and, if so, what the orbit of a planet would be. Newton answered that it was an ellipse and sent a demonstration of his findings that November, also working out the substance of several propositions in the first book of the Principia. These, along with notes on the laws of motion, were published by the Royal Society in February 1685 as the paper De Motu.
Spurred on by Halley's visit, Newton undertook to attack the whole problem of gravitation and publish his results. Of the three fundamental principles applied in the Principia, it is generally agreed by science historians that the notion that every particle attracts every other particle in the universe was formed as early as 1666. The law of equable description of areas, and the fact that if the law of attraction were that of an inverse square the orbit of a particle about the center of force would be conic were proved in 1669. Finally, the discovery that a sphere attracts an external point as if the whole mass were collected in its center was made in 1685.
The draft of the first book was completed before the summer of 1685, although it was not presented to the Royal Society until April 1686, and covers the motion of particles or bodies in free space. The second book was completed by the summer of 1686, and treats the concept of motion in a resisting medium, as well as hydrostatics and hydrodynamics, with special applications to waves, tides, and acoustics. Newton spent the next 10 months writing the third book of the Principia, applying the theorems of the first book to the chief phenomena of the solar system to determine the masses and distances of the planets and their satellites.
Financed primarily by Halley, the actual printing of the entire work was not completed until the summer of 1687. While nearly all competent critics admitted the validity of Newton's conclusions, it took some time before the findings in the Principia altered prevailing beliefs of educated men; in fact, it was nearly half a century before his work was completely assimilated into the field of mathematics. Within 10 years of its publication, it was generally accepted in Britain as giving a correct account of the laws of the universe, and similarly accepted on the European continent within 20 years, except in France, which clung to the Cartesian hypothesis until 1738, when Newtonian theory was championed by Voltaire.
The man who stood on the shoulders of giants died at Kensington, London, on March 20, 1727, and is buried at Westminster Abbey, but his influence on science and mathematics remained unparalleled until the onset of the 20th century. Lagrange described the Principia as the greatest production of the human mind, admitting to feeling dazed at such an illustration of what man's intellect might be capable. Gauss, who used the Latin magnus or clarus for other great mathematicians or philosophers, reserved the prefix summus for Newton alone.
Newton himself was much more modest when estimating his own work. "I do not know what I may appear to the world," he wrote. "But to myself I seem to have been only like a boy, playing on the seashore and diverting myself, in now and then finding a smoother pebble, or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."
Birthdays for July:
July 5 — Gerard 't Hooft (1946)
July 17 — Georges Lemaitre (1894)
July 18 — Hendrik A. Lorentz (1853)
July 28 — Pavel A. Cerenkov (1904)
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