Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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<archimedes>
<text>
<body>
<chap>
<p type="main">
<s>
able hath upon the inclined Plane C A hath to its total Moment
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wherewith it gravitates in the Perpendicular to the Horizon C P the
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ſame proportion that the ſaid Line P C hath to C A. </s>
<s>And if thus it
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be, it is manifeſt, that like as the Force that ſuſtai­
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neth the Weight in the Perpendiculation P C ought
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to be equal to the ſame, ſo for ſuſtaining it in the
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inclined Plane C A, it will ſuffice that it be ſo much
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leſſer, by how much the ſaid Perpendicular C P wan­
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teth of the Line C A: and becauſe, as ſometimes we
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ſce, it ſufficeth, that the Force for moving of the
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Weight do inſenſibly ſuperate that which ſuſtaineth it, therefore
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we will infer this univerſal Propoſition, [That upon an Elevated
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Plane the Force hath to the Weight the ſame proportion, as the
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Perpendicular let fall from the Plane unto the Horizon hath to the
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Length of the ſaid Plane.]</s>
</p>
<p type="margin">
<s>
<margin.target id="marg1117"/>
* Or along</s>
</p>
<p type="main">
<s>Returning now to our firſt Intention, which was to inveſtigate
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the Nature of the Screw, we will conſider the Triangle A B C, of
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which the Line A B is Horizontal, B C perpendicular to the ſaid
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Horizon, and A C a Plane elevated; upon which the Moveable D
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ſhall be drawn by a Force ſo much leſs than it, by how much the
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Line B C is ſhorter than C A: But to elevate or raiſe the ſaid
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Weight along the ſaid Plane A C, is as much as if the Triangle
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C A B ſtanding ſtill, the Weight
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D be moved towards C, which is
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the ſame, as if the ſame Weight
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never removing from the Perpen­
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dicular A E, the Triangle did
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preſs forwards towards H. </s>
<s>For if
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it were in the Site F H G, the
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Moveable would be found to
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have mounted the height A I.
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Now, in fine, the primary Form and Eſſence of the Screw is no­
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thing elſe but ſuch a Triangle A C B, which being forced for­
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wards, ſhall work it ſelf under the Grave Body to be raiſed, and
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lifteth it up, as we ſay, by the ^{*} head and ſhoulders. </s>
<s>And this was
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<arrow.to.target n="marg1118"/>
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its firſt Original: For its firſt Inventor (whoever he was) conſi­
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dering how that the Triangle A B C going forwards raiſeth the
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Weight D, he might have framed an Inſtrument like to the ſaid
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Triangle, of a very ſolid Matter, which being thruſt forwards did
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raiſe up the propoſed Weight: But afterwards conſidering better,
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how that that ſame Machine might be reduced into a much leſſer
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and more commodious Form, taking the ſame Triangle he twined
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and wound it about the Cylinder A B C D in ſuch a faſhion, that
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the height of the ſaid Triangle, that is the Line C B, did make the
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Height of the Cylinder, and the Aſcending Plane did beget upon </s>
</p>
</chap>
</body>
</text>
</archimedes>