88 Mechanick Pomery. Book IV.

Te Demonſtration. That the Pully A be placed in E, thepower ought tobe moved as much as the length of the ChordsC k, G D, for from the point C to D, is the ſame diſtance asbetween Fand G; but CF, GP taken together, are doublethe ſpace A E, io which the motion of the weight B is equalas appears, therefore the motion of the power is double themotion of the weight; but(by the firſt principle of Mecha-nicks) as often as the motion of the power is double the mo-rion of the weight, the whole force of the power is doubled;therefore in our caſe the force of the power is doubled in Or-der to ſuch weight, or Which is the fame, the weight is di-miniſht an half part, which was to be demonſtrated.

But if in ſtead of the Hook C, there be added one powerwhich ſhall be equally moved with the pouer D, We a ſhallfind by tryal only an half part of the weight, in the ſamemanner as if they bore two weights equally diltant, hung to aBeam or Leaver. N

PRO POF. VII.A Theorem.

A Pomer applied to 4 mowpeable Pully, liminiſbes anHalf part, in reſpelt of a Meigbt hung on one end of4 Rope.

Eg. 74. JF in ſtead of iche weight B being hung, a power beapplied to the ſame Pully, and the weight hung tothe Rope D,] ſay, the force of the Power is diminiſht an halfPart.Zhe Demonſtration. As] ſhewed before, the motion of theweight will be double che motion of the power, and there.fore(by the firſt principle of Mechanicks) the forces of thePower are leſtned, and the forces of the weight increaſed;which may likewiſe be ſaid of two weights, to wit, as whenthe weight Bof ro pounds is made in equlibrio inthe point D,or which way ſoever the Rope G D ſhall require 50 pounds.Corol-