Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/82

38 will with its whole weight bear upon and pres the middle part towards the other extreme part EGF; and therefore the force with which EGI, the um of the parts HKI and EGKH, tends towards the third part EGF, is equal to the weight of the part HKI, that is, to the weight of the third part EGF. And therefore the weights of the two parts EGI and EGF, one towards the other, are equal, as I was to prove. And indeed if thoe weights were not equal, the whole earth floating in the nonreiting aether would give way to the greater weight, and, retiring from it, would be carried off in infinitum.

And as thoe bodies are equipollent in the congres and reflexion, whoe velocities are reciprocally as their innate force: o in the ue of mechanic intruments, thoe agents are equipollent, and mutually utain each the contrary preure of the other, whoe velocities, etimated according to the determination of the forces, are reciprocally as the forces.

So thoe weights are of equal force to move the arms of a Ballance, which during the play of the ballance are reciprocally as their velocities upwards and downwards: that is, if the acent or decent is direct, thoe weights are of equal force, which are reciprocally as the ditances of the points at which they are upended from the axis of the ballance; but if they are turned aide by the interpoition of oblique planes, or other obtacles, and made to acend or decend obliquely, thoe bodies will be equipollent, which are reciprocally as the heights of their acent and decent taken according to the perpendicular; and that on account of the determination of gravity downwards.

And in like manner in the Pully, or in a combination of Pullies, the force of a hand drawing the rope directly, that is to the weight, whether acending directly or Rh