NEWTON. 195 



perties of the conic sections had largely occupied the attention of the 

 ancient geometers, and now, after these properties had remained for 

 ages little more than mathematical curiosities, they were unexpectedly 

 applied in the investigation of the widest and grandest laws of all the 

 science of nature. By combining the truths long before reasoned out ' 

 by the old Grecian sages with his own original methods, Newton esta- 

 blished the following proposition a most important one in the theory 

 of the universe : a body projected in a straight line, and subjected to the 

 action of a central force, will revolve in some one of 'the conic sections ', if the 

 intensity of the force be inversely as the square of the distance from its 

 centre, which will be at a focus of the curve. Whether the particular 

 conic section be a circle, an ellipse, or a parabola, depends on the ratio 

 of the tangential (or projecting) to the centripetal (or deflecting) force. 

 The illustrious author of the "Principia" traces out a vast number of 

 consequences. He deduces the laws by which the velocities of bodies 

 moving in elliptical orbits must necessarily be regulated. He shows 

 in what periods such orbits must be completed, and demonstrates (as 

 a necessary consequence) the remarkable relation that the squares of 

 the periodic times are to each other as the cubes of the major axes. 

 As half the major axis of its elliptical orbit is the mean distance of each 

 planet from the sun, the reader will recognize in this last mathematical 

 deduction the third of Kepler's laws (page gr), as in the equality of 

 the areas he has already doubtless perceived the second law. Here 

 were the observed and unexplained facts of the German astronomer 

 deduced a priori by the English philosopher from simple dynamical 

 principles. 



These considerations having been founded only upon the mechanics 

 of small particles of matter, the author of the "Principia " goes on to 

 examine the effects of attractions of particles on each other ; and he 

 shows that, supposing such particles to attract each other with a force 

 inversely proportional to the square of the distances between them, and 

 to be aggregated in spherical masses, these spheres would be subject to 

 the same laws of attraction, etc., as the particles, and that the resultant 

 attraction would be directed to the centre of the spheres, and would 

 be proportional to their masses, divided by the squares of the distances 

 between their centres. 



The special glory of Newton is the system of the world which he 

 founded on the idea of universal gravitation. We may here leave for 

 the present out of consideration those approaches to the notion of gra- ' 

 vitation which had been made by several philosophers before Newton. 

 Germs of the idea of universal gravitation may, as in the case of many 

 other modern conceptions, be discovered among the ancients. In the 

 poem of Lucretius, already referred to (page 44), it is assigned as a 

 reason for supposing the world to be infinite, that otherwise all the 

 bodies composing it would have approached each other, and all would 

 have at length united together in one mass. Kepler, and later Hooke 



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