Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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of Direction
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A
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D H and
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A
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E I are Right
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A
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ngles, we ſuppoſe that
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theſe two
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F
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orces I and H weigh alike upon the Center
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A
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as if they
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were nearer to the Center, at the equal Diſtances
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A
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B and A C,
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and we alſo ſuppoſe the ſame if theſe very
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F
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orces were ſuſpended
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both together in
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A,
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the
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A
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ngles of Directions being ſtill Right
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A
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ngles.</
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<
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>PROPOSITION I.</
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>Theſe Principles agreed upon, we will eaſily demonſtrate,
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in Imitation of
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Archimedes,
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that upon a ſtraight Balance
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the
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F
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orces, of which and of all their parts the Lines of Dire
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ction are parallel to one another, and perpendicular to the Balance,
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ſhall couuterpoiſe and make an
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Equilibrium,
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when the ſaid
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F
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orces
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ſhall be to one another in Reciprocal proportion of their Arms,
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which we think to be ſo manifeſt to you, that we thence ſhall de
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rive the Demonſtration of this Univerſal Propoſition to which we
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haſten.</
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<
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>PROPOS. II.</
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<
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>In every Balance or Leaver, if the proportion of the
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F
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orces is
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reciprocal to that of the Perpendicular Lines drawn from the
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Center or Point of the
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F
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ulciment unto the Lines of Direction
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of the
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F
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orces, drawing the one againſt the other, they ſhall make
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an
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Equilibrium,
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and drawing on one and the ſame ſide, they ſhall
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have a like Effect, that is to ſay, that they ſhall have as much
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F
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orce
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the one as the other, to move the Balance.</
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<
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>In this
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F
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igure let the Center of the Balance be
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A,
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the
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A
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rm
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A
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B,
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bigger than
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A
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C, and firſt let the
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L
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ines of Direction B D, and E C
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be perpendicular to the
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A
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rms
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A
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B and
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A
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C, by which Lines the
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F
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orces D and E (which may be made of Weights if one will) do
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draw; and that there is the ſame rate
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of the
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F
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orce D to the Force E as there
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is betwixt the
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A
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rm
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A
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C to the Arm
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A
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B: the Forces drawing one againſt
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the other, I ſay, that they will make an
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Equilibrium
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upon the Balance
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C
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A B.
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<
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>For let the
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A
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rm C
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A
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be prolonged
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unto F, ſo as that
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A
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F may be equal to
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A
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B: and let C
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A
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F be conſidered as a
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ſtreight Balance, of which let the Center be
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A
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: and let there be
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ſuppoſed two Forces G and H, of which and of all their parts the
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Lines of Direction are parallel to the Line C E, and that the
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Force G be equal to the Force D, and H to E, the one, to wit G, </
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</
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