Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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Force in B ſuſtaineth a part of the Weight D double to it ſelf, its
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Diſtance from the Fulciment A, that is, the Line B A being dou
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ble to the Diſtance A C at which the Grave hangeth: But becauſe
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the two Forces in B and C are ſuppoſed to be equal to each other:
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Therefore the part of the Weight D, which is ſuſtained by the
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Force in B, is double to the part ſuſtained by the Force in C. </
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>If
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therefore, of the Grave D two parts be made, the one double to
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the remainder, the greater is ſuſtained by the Force in B, and the
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leſſer by the Force in C: But this leſſer is the third part of the
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Weight D: Therefore the Moment of the Force in C is equal to
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the Moment of the third part of the Weight D; to which, of
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conſequence, the Force B ſhall be equal, we having ſuppoſed it
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equal to the other Force C: Wherefore our intention is manifell,
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which we were to demonſtrate, how that each of the two Powers
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C and B is equal to the third part of the Weight D. </
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>Which be
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ing demonſtrated, we will paſs forwards to the Pulleys, and will
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deſcribe the inferiour Gyrils of A C B, voluble about the Center
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G, and the Weight H hanging thereat, we will draw the other up
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per one E F, winding about them both the Rope D F E A C B I,
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of which let the end D be faſtned to the inferiour Pulley, and to
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the other I let the Force be applyed:
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Which, I ſay, ſuſtaining or moving the
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Weight H, ſhall feele no more than the
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third part of the Gravity of the ſame. </
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>For
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conſidering the contrivance of this Ma
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chine, we ſhall find that the Diameter A B
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ſupplieth the place of a Leaver, in whoſe
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term B the Force I is applied, and in the
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other A the
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F
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uiciment is placed, at the mid
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dle G the Grave H is hanged, and another
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F
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orce D applied at the ſame place: ſo that
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the Weight is faſtned to the ^{*} three Ropes
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I B,
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F
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D, and E A, which with equal Labour
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ſuſtain the Weight. </
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>Now, by what hath
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already been contemplated, the two
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F
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orces
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D and B being applied, one, to the midſt of the Leaver A B, and
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the other to the extream term B, it is manifeſt, that each of them
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holdeth no more but the third part of the Weight H: Therefore
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the Power I, having a Moment equal to the third part of the
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Weight H, ſhall be able to ſuſtain and move it: but yet the Way
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of the
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F
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orce in I ſhall be triple to the Way that the Weight ſhall
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paſs; the ſaid Force being to diſtend it ſelf according to the
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Length of the three Ropes I B,
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F
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D, and E A, of which one alone
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meaſureth the Way of the Weight H.</
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