Moving Force. 219 
deret, ac proinde miraculosa foret.” * This 
short but comprehensive argument contains 
every thing that can be urged in support of 
any of the principles which are termed laws 
of nature; and it is not easy to understand 
upon what grounds of experience or analogy 
this principle of continuity has ever been 
rejected. 
The laws of uniformly accelerated or re- 
tarded motions having been demonstrated by 
Galileo, the same principle was extended by 
Newton to motions produced by varying 
forces, where the acceleration or retardation 
cannot be uniform; and in the 39th prop. of 
the first book of the principia, it is demon- 
strated, that when a body is urged in one 
direction by a varying force, the square of 
the velocity which it has acquired in any 
given space, measured from the beginning of 
its motion, will be as the curvilinear area 
which is formed by the aggregate of the 
increments of the space drawn into right 
lines denoting the pressures exerted. at each 
increment. 
As far therefore as the measure of force, 
which is composed of the pressure into the 
space through which it acts, can be applied to 
* Dialogus de Systemate Mundi. Lugdani 1641, p. 11. 
This was first published at Florence in 1632. 
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