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

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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/210.jpg" pagenum="192"/>
                <arrow.to.target n="marg388"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg388"/>
                <emph type="italics"/>
              The greater
                <lb/>
              city exactly
                <lb/>
              penſates thegreater
                <lb/>
              gravity.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>But do you think that the velocity doth fully make
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              good the gravity? </s>
              <s>that is, that the moment and force of a
                <lb/>
              able of
                <emph type="italics"/>
              v. </s>
              <s>g.
                <emph.end type="italics"/>
              four pounds weight, is as great as that of one of an
                <lb/>
              hundred weight, whenſoever that the firſt hath an hundred degrees
                <lb/>
              of velocity, and the later but four onely?</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Yes doubtleſs, as I am able by many experiments to
                <lb/>
              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. </s>
              <s>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
                <lb/>
              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. </s>
              <s>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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              </s>
              <s>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. </s>
              <s>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. </s>
              <s>Let two unequal
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              wheels be deſcribed about this centre A, [
                <emph type="italics"/>
              in Fig.
                <emph.end type="italics"/>
              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 </s>
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          </chap>
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