Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
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<s>
drawing upon the Arm A
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F,
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and the other, to wit H, upon the Arm
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A C: now, by the firſt Propoſition, G and H ſhall make an
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Equili­
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brium
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upon the Balance C A F: But, by the firſt Principle, the Force
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D upon the Arm A B worketh the ſame effect as the Force G on
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the Arm A F: Therefore the Force D upon the Arm A B maketh
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an
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Equilibrium
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with the Force H upon A C: And the Force H
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drawing in the ſame manner upon the Arm
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A
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C as the Force E, by
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the ſame firſt
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A
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xiom, the Force D upon the Arm
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A
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B ſhall make an
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Equilibrium
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with the Force E upon the Arm
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A
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C.</s>
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<s>Now, in the following Figure, let the Center of the Balance be
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A,
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the Arms A B and A C, the Lines of Direction B D and C E
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which are not Perpendicular to the Arms, and the Forces D and E
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drawing likewiſe by the Lines of Direction, upon which Perpen­
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diculars are erected unto the Center A, that is A F upon B D, and
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A G upon E C, and that as A F is to A G, ſo is the Force E to the
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Force D: which Forces draw one
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againſt the other: I ſay, that they will
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make an
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Equilibrium
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upon the Balance
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C A B: For let the Lines A F and A G
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be underſtood to be the two Arms of
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a Balance G A F, upon which the For­
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ces D and E do draw by the Lines of
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Direction F D and G E: Theſe Forces
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ſhall make an
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Equilibrium,
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by the firſt
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part of this ſecond Propoſition; but, by the ſecond Axiom, the Force
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D upon the Arm A F hath the ſame Effect as upon the Arm A B:
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Therefore the Force D upon the Arm A B maketh an
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Equilibrium
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with the Force E upon the Arm A C.</s>
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<s>There are many Caſes, according to the Series of Perpendicu­
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lars, but it will be eaſie for you to ſee that they have all but one
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and the ſame Demonſtration.</s>
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<s>It is alſo eaſie to demonſtrate, that if the Forces draw both on
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one ſide they ſhall make the ſame Effect one as another, and that
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the Effect of two together ſhall be double to that of one alone.</s>
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<s>OF THE
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GEOSTATICKS.</s>
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<s>The Principle which you demand for the
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Geoſtaticks
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is,
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That if two equal Weights are conjoyned by a right
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Line fixed and void of Gravity, and that being ſo di­
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ſpoſed they may deſcend freely, they will never reſt till
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that the middle of the Line, that is the Center of Gravitation of
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the Ancients, unites it ſelf to the common Center of Grave Bodies.</s>
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