 | University of Cambridge - 1805 - 310 pages
...with its density after any number of turns. ' 4. Find the principal focus of a sphere, the radiu•t of the sphere and the ratio of the sines of incidence...revolve in an ellipse, it is required to find the law o£ the force tending to the focus. 6. Divide the given angle into two other angles, so that their... | |
 | Isaac Newton - Curves, Plane - 1850 - 184 pages
...velocity in this spiral at P = velocity in circle at the same distance. PBOP. X. PROBLEM V. Let a body revolve in an ellipse; it is required to find the law of centripetal force, tending to the centre of the ellipse. Let CA, CB be semi-axes of the ellipse, GP,... | |
 | Richard Abbatt - Astronomy - 1870 - 72 pages
...coincides with P. If a body revolves in a spiral cutting all the radii SP, SQ, &c., in a given angle ; it is required to find the law of the force tending to the centre of the spiral. (See next fig.) Suppose the elementary angle PSQ to be given, then all the angles... | |
 | Floyd Karker Richtmyer - Physics - 1928 - 634 pages
...the motions of bodies. For example, Proposition XI of Book I solves the problem : If a body revolves in an ellipse, it is required to find the law of the centripetal force tending to the focus of the ellipse. The solution is the inverse-square law. Proposition... | |
 | Niccol- Guicciardini - Mathematics - 2003 - 296 pages
...l0) the force varies directly with distance. Let us see how Newton proves Proposition l0: Let a body revolve in an ellipse; it is required to find the law of centripetal force tending toward the centre of the ellipse.t Consider fig. 3.6. Here, points P, R,... | |
 | Jean-Claude Pecker - Nature - 2001 - 616 pages
...Ar, it would reach point R. Fig. 5.37 304 Fig. 5.38 Proposition XL Problem VI15. If a body revolves in an ellipse, it is required to find the law of the centripetal force tending to the focus of the ellipse. Let S be the focus of the ellipse16. Draw SP... | |
 | Julian B. Barbour - Science - 2001 - 778 pages
...Principia, there is a magical moment. Newton has just solved his great problem: If a body revolves in an ellipse; it is required to find the law of the centripetal force tending to the focus of the ellipse. He then comments that, as in a previous problem... | |
 | Harald Iro - Science - 2002 - 466 pages
...about 1680. 'In the first Book of "The Principia", in Proposition XI, Prublem VI ("1/ a body revolves in an ellipse; it is required to find the law of the centr,petal force iending to the foc0s of the ellipse"), Newton deduces the l1(distance) law solely... | |
 | Malcolm S. Longair - Science - 2003 - 592 pages
...1690s, he carried out extensive chemical experiments PROPOSITION XI. PROBLEM VI If a body revolves in an ellipse; it is required to find the law of' the centripetal force tending to the focus of the ellipse. Let S be the focus of the ellipse. Draw SP cutting... | |
 | Jason Allen Snart - Literary Criticism - 2006 - 226 pages
...already said. Take, for example, Book I of the Principia, Section III, Proposition 11: "Let a body revolve in an ellipse; it is required to find the law of the centripetal force tending toward a focus of the ellipse." Newton continues, "Let S be a focus of the... | |
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If a body revolves in an ellipse it is required to find the law of the centripetal force tending to the focus of the ellipse . . . . . . And therefore the centripetal force is inversely as the square of the distance. 
