Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/83

Rh obliquely, as the velocity of the perpendicular acent of the weight to the velocity of the hand that draws the rope, will utain the weight.

In clocks and uch like intruments, made up from a combination of wheels, the contrary forces that promote and impede the motion of the wheels, if they are reciprocally as the velocities of the parts of the wheel on which they are impre'd, will mutually utain the one the other.

The force of the crew to pres a body is to the force of the hand that turns the handles by which it is moved as the circular velocity of the handle in that part where it is impelled by the hand is to the progreive velocity of the Screw towards the pres'd body.

The forces by which the Wedge prees or drives the two parts of the wood it cleaves, are to the force of the mallet upon the wedge, as the progres of the wedge in the direction of the force impres'd upon it by the mallet, is to the velocity with which the parts of the wood yield to the wedge, in the direction of lines perpendicular to the ides of the wedge. And the like account is to be given of all Machines.

The power and ue of Machines conit only in this, that by diminihing the velocity we may augment the force, and the contrary: Ffrom whence in all orts of proper Machines, we have the olution of this problem; To move a given weight with a given power, or with a given force to overcome any other given reitance. For if Machines are o contriv'd that the velocities of the agent and reitant are reciprocally as their forces, the agent will jut utain the reitant: but with a greater diparity of velocity will overcome it. So that if the diparity of velocities is o great as to overcome all that reitance which Rh