NEWTON S PRINCIPIA. 17 



weights or powers are made inversely as those lengths, the 

 whole will be in equilibrio or balanced. This is the well 

 known and fundamental principle of the lever, the founda 

 tion of mechanics ; and it applies also to the wheel and 

 axle and the pulley. The fundamental properties of the 

 screw, the wedge, and the inclined plane are deduced in 

 like manner from this important proposition. So may 

 all the properties of the centre of gravity, and the method 

 of finding it ; for, in fact, the fulcrum of the lever is the 

 common centre of gravity of two bodies equal to the 

 two weights, and placed at the opposite ends of the 

 lever; and the line joining the bodies is divided in the 

 inverse proportion of those bodies. It also is easily shown 

 that the common centre of gravity of two or more bodies 

 is not moved, nor in any way affected, by their mutual 

 actions on each other, but it either remains at rest, or 

 moves forward in a straight line. So are the relative mo 

 tions of any system of bodies, whether the space they 

 occupy is at rest, or moves uniformly in a straight line. 



The Scholium to the Laws of Motion first considers 

 very briefly the motion of falling bodies which descend 

 with a velocity uniformly accelerated, that velocity which 

 is given to them by the attraction of the earth during 

 the first instant continuing and having at each succeeding 

 instant a new impulse added. The acceleration, therefore, 

 is as the time; and they move through a space propor 

 tional to the velocity and the time jointly, consequently 

 proportional to the square of the time, since the velocity is 

 itself proportional to the time.* 



* Velocity is as time, i. e., v is as m t $ space is as velocity x time, 

 or s as v x t ; therefore space is as time x time, or as square of time, that 

 is, s is as m t x t, or m t 2 . The proportion of the space fallen through 

 by the force of gravity (or moved through by any body uniformly acce 

 lerated) to the square of the times, is also demonstrated thus. Let the 



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