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" The third, viz. that the squares of the periodic times are proportional to the cubes of the mean distances... "
History of Astronomy - Page 53
by George Forbes - 1909 - 200 pages
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Kepler

Walter William Bryant - 1920 - 74 pages
...exactly the sesquiplicate proportion of the mean distances of the orbits," or as generally given, " the squares of the periodic times are proportional to the cubes of the mean distances." Kepler was evidently transported with delight and wrote, " What I prophesied two and twenty years ago,...
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Elementary Functions and Applications

Arthur Sullivan Gale, Charles William Watkeys - Functions - 1920 - 457 pages
...planetary motion states that for different planets the squares of the times of describing their orbits are proportional to the cubes of the mean distances from the sun. That is ^ = jy ELEMENTARY FUNCTIONS 15. If the distance of the earth from the sun changed from 93,000,000...
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Astronomy: A Revision of Young's Manual of Astronomy, Volume 1

Henry Norris Russell, Raymond Smith Dugan, John Quincy Stewart - Astronomy - 1926 - 514 pages
...early in the seventeenth century, and constitutes his famous harmonic law, the squares of the periods are proportional to the cubes of the mean distances from the sun, which may readily be verified from the table. This relation was shown by Newton to be a consequence...
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A Short History of Physics

Harry Fawcett Buckley - Physics - 1927 - 288 pages
...any two planets is exactly the sesquiplicate proportion of the mean distances of the orbits," that is the squares of the periodic times are proportional to the cubes of the mean distances. In the introduction to his De Motibus Stella Martis he endeavoured to account for the motions of the...
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Proceedings of the Royal Philosophical Society of Glasgow, Volumes 55-56

Royal Philosophical Society of Glasgow - Science - 1927 - 402 pages
...distances of the various planets from the sun, and the times which they take to revolve round the sun — the squares of the periodic times are proportional to the cubes of the mean . T,2 1? T* distances, ie — r= — * = — s = etc. rrr 1 1 l2 l3 From these laws of Kepler, Newton...
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Selected Writings (Values in a Universe of Chance)

Charles Sanders Peirce - Philosophy - 1966 - 484 pages
...maturest deliberation a poor girl eighteen years younger than himself. At forty-six, he discovered the "third law," that the squares of the periodic times...are proportional to the cubes of the mean distances, not a discovery involving any difficult reasoning, yet leading at once, had he only been able to see...
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The Peripatetic University: Cambridge Local Lectures 1873-1973

Edwin Welch - Education - 1973 - 254 pages
...one of the foci. (2) A line joining the planet and the sun sweeps out equal areas in equal times. (3) The squares of the periodic times are proportional to the cubes of the mean distances from the sun. Explain the meaning of the various technical words used in these laws. 6. What is it that renders an...
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Mathematical Modelling

Jagat Narain Kapur - Mathematics - 1988 - 276 pages
...If Ti, T2 are the time periods of two planets with orbital radii ri, r2, then 7?/Г| = r]lr\, (8) so that the squares of the periodic times are proportional to the cubes of the radii of the orbits. (c) Motions of Satellites Satellites move under the attraction of the Earth in...
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Proceedings of the Royal Irish Academy, Volume 3

Antiquities - 1893 - 1072 pages
...attraction = centrifugal force = Equating these, we find /ao = 4JV, (1) which represents Kepler's well-known third law that the squares of the periodic times are proportional to the cubes of the distances. Let us now take a molecule of chlorine, and represent it a* follows : If now, then, /*!...
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Space and Time, Matter and Mind: The Relationship Between Reality and Space-time

Wolfram Schommers - Science - 1994 - 186 pages
...one focus. 2. The vector radius from the sun to the planet sweeps over equal areas in equal times. 3. The squares of the periodic times are proportional to the cubes of the major axes. These three laws distinctly reflect that the geocentric world view no longer had a basis...
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