[ +35 J 
Having now clearly proved, that the moving 
Forces are not proportional to the Squares of the 
Velocities, I proceed next to demonftrate, that 
they are proportional to the Velocities themfelves: 
And, in order thereto, I fhall, as I have hitherto 
done, make ufe of no other Principles or Axioms, 
than fuch as are admitted on both Sides, or, at leaft, 
have never yet been controverted a priori by either 
Party. 
Axiom IV. 
Springs of unequal Lengths, when bent alike, have 
equal Preflures. 
We fpeak here of Springs equal in all Refpeds, 
except the Length only 5 and, by being bent alike, 
we mean, that they are fo comprefled, as that the 
Lengths they are now reduced to, are exadly propor- 
tional to their natural Lengths, or to the Lengths 
they are of when no way comprefied. 
In this Condition, if one be diredly oppofed to 
the other, they will mutually fuftain each other's Pref- 
fure, fo as to maintain a perfed c/ Equilibrium : Or, 
if each be placed feparately in a vertical Situation,, 
they will fufiain equal Weights. And in one or the 
other of thefe Cafes, it is evident, that they muft 
exercife equal Preflures. 
Axiom V. 
Equal Preflures in equal Times produce equal 
moving Forces, 
