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

Table of figures

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            <p type="main">
              <s>
                <pb xlink:href="040/01/990.jpg" pagenum="296"/>
              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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                <figure id="id.040.01.990.1.jpg" xlink:href="040/01/990/1.jpg" number="201"/>
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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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                <figure id="id.040.01.990.2.jpg" xlink:href="040/01/990/2.jpg" number="202"/>
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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>
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