V 
256 MOVING FORCli. 
Cases of diffi- excederet, ac proinde miraculosa foret*”. This short, but com- 
dootVi'iu-s' of pi'chensive, argument contains every thing that can be urged 
moviii<j lorco. in support of any of the principles which are termed Jaws 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 retarded motions hav- 
ing been demonstrated by Galileo, the same principle was ex- 
tended 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 vary- 
ing force, the square of the velocity which it has acquired in 
any given space, measured from the beginning of its motion, w'ill 
be as the curvilinear area w'tiich 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 tire measure of force, which is com- 
posed of the pressure into the .space through which it acts, can 
be applied to the estimation of the forces of moving bodies, 
it is, properly speaking, the doctrine of Galileo and of New- 
ton. 
But we have seen, that the same principle has been still far- 
, ther extended, and applied to explain the phenomena of force 
producing changes of figure in masses of matter. 
No indications of force are more constantly presented to our 
notice than those- which consist of mechanical changes of 
figure. The fabrication of every thing that is useful or con- 
venient to us, is accomplished chiefly by the application of 
mechanical force to produce change of figure. The grinding 
of corn, the expressing of oil from seed, the sawing of timber, 
the hammering and rolling of metals, the driving of piles, are 
all examples of mo\ing force producing changes of figure; 
' and although, in all these cases, the efteets pioJuced are cf a 
co.uplicated kind, yet the moving forces by which they are 
• Dia'.ogiis e’e Sjsteniate Mun li. Lnpduni, 16J1, p.'ll. Tli’S wts 
fir t pubiished at Florence in lo32. 
produced 
