Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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The greater
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city exactly
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penſates thegreater
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gravity.
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<
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>SAGR. </
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<
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>But do you think that the velocity doth fully make
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good the gravity? </
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<
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>that is, that the moment and force of a
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able of
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v. </
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<
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four pounds weight, is as great as that of one of an
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hundred weight, whenſoever that the firſt hath an hundred degrees
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of velocity, and the later but four onely?</
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<
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>SALV. </
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>Yes doubtleſs, as I am able by many experiments to
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demonſtrate: but for the preſent, let this onely of the ſtiliard
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ſuffice: in which you ſee that the light end of the beam is then
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able to ſuſtain and equilibrate the great Wool ſack, when its
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ſtance from the centre, upon which the ſtiliard reſteth and
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eth, ſhall ſo much exceed the leſſer diſtance, by how much the
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ſolute gravity of the Wool-ſack exceedeth that of the pendent
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weight. </
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<
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>And we ſee nothing that can cauſe this inſufficiencie in
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the great ſack of Wool, to raiſe with its weight the pendent
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weight ſo much leſs grave, ſave the diſparity of the motions which
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the one and the other ſhould make, whilſt that the Wool ſack by
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deſcending but one inch onely, will raiſe the pendent weight an
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hundred inclies: (ſuppoſing that the ſack did weigh an hundred
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times as much, and that the diſtance of the ſmall weight from the
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centre of the beam were an hundred times greater, than the
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ſtance between the ſaid centre and the point of the ſacks
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on.) And again, the pendent weight its moving the ſpace of an
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hundred inches, in the time that the ſack moveth but one inch
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onely, is the ſame as to ſay, that the velocity of the motion of the
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little pendent weight, is an hundred times greater than the
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city of the motion of the ſack. </
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<
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>Now fix it in your belief, as a
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true and manifeſt axiom, that the reſiſtance which proceedeth from
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the velocity of motion, compenſateth that which dependeth on
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the gravity of another moveable: So that conſequently, a
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able of one pound, that moveth with an hundred degrees of
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locity, doth as much reſiſt all obſtruction, as another moveable
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of an hundred weight, whoſe velocity is but one degree onely.
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<
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>And two equal moveables will equally reſiſt their being moved,
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if that they ſhall be moved with equal velocity: but if one be
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to be moved more ſwiftly than the other, it ſhall make greater
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ſiſtance, according to the greater velocity that ſhall be conferred
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on it. </
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<
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>Theſe things being premiſed, let us proceed to the
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nation of our Problem; and for the better underſtanding of
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things, let us make a ſhort Scheme thereof. </
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<
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>Let two unequal
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wheels be deſcribed about this centre A, [
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in Fig.
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7.] and let the
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circumference of the leſſer be B G, and of the greater C E H, and
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let the ſemidiameter A B C, be perpendicular to the Horizon; and
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by the points B and C, let us draw the right lined Tangents B F
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and C D; and in the arches B G and C E, take two equal parts
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B G and C E: and let the two wheels be ſuppoſed to be turn'd </
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