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'Proposition II. 
Moving Forces are proportional to the Mafifes and 
Velocities jointly. 
'Demonftration. 
Let there be two Springs, of the Lengths i and 
2, but equal in all other Refpe&s, and bent alike : 
And, in unbending themfelves, let the Spring i 
drive before it a Body whofe Mafs is 2 j and the 
Spring 2 another Body of the Mafs 1. 
Now, by Coroll. 11. of my general Theorem con- 
cerning the A&ion of Springs, thefe two Springs 
will unbend themfelves exactly in the fame Time? 
and, confequently, the Spring 2 will unbend itfelf 
with a Velocity double of that of the Spring 1 : 
And. by Coroil. 12. of the fame Theorem, it will 
give to the Body 1 a Velocity double of that, which 
the Body 2 will receive from the Spring 1. 
Alfo, as the two Springs were fuppofed to be bent 
alike at firft, and the Spring 2 unbends itfelf with a 
Velocity double to that of the Spring 1, it is mani- 
fell, that, during the whole Time of their Expanlion, 
they will be always bent alike, one to the other. 
Therefore, by Axiom IV. their Preffures will be 
conftantly equal one to the other: And hence, by 
Axiom V. the infinitely fmall moving Forces pro- 
duced by each of thefe Springs, in every infinitely 
fmall Part of Time, will be equal one to the other. 
Confequently, the Sums of thofe infinitely fmall 
moving Forces, that is, the whole moving Forces, 
produced by the two Springs, will be equal one to the 
other. And the Malfes of the two Bodies being 1 and 1, 
and 
