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

Table of figures

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              <s>
                <pb xlink:href="040/01/1084.jpg" pagenum="390"/>
                <figure id="id.040.01.1084.1.jpg" xlink:href="040/01/1084/1.jpg" number="285"/>
                <lb/>
                <emph type="italics"/>
              B D in
                <emph.end type="italics"/>
                <foreign lang="grc">λ</foreign>
                <emph type="italics"/>
              ; and from the Point O, and parallel to
                <lb/>
              A
                <emph.end type="italics"/>
                <foreign lang="grc">λ,</foreign>
                <emph type="italics"/>
              draw O X; and let it touch the Section in O,
                <lb/>
              as in the first Figure: And the
                <emph.end type="italics"/>
              (d)
                <emph type="italics"/>
              Angle at X,
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1372"/>
                <lb/>
                <emph type="italics"/>
              ſhall be equall alſo to the angle
                <emph.end type="italics"/>
                <foreign lang="grc">λ</foreign>
                <emph type="italics"/>
              : But the angle at Y
                <lb/>
              is equall to the Angle at
                <emph.end type="italics"/>
                <foreign lang="grc">γ;</foreign>
                <emph type="italics"/>
              and the
                <emph.end type="italics"/>
              (e)
                <emph type="italics"/>
              Angle
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1373"/>
                <lb/>
              A
                <foreign lang="grc">Γ</foreign>
              D
                <emph type="italics"/>
              greater than the Angle A
                <emph.end type="italics"/>
                <foreign lang="grc">λ</foreign>
                <emph type="italics"/>
              D, which falleth
                <lb/>
              without it: Therefore the Angle at Y ſhall be great­
                <lb/>
              er than that at X. </s>
              <s>And becauſe now the Portion
                <lb/>
              turneth about, ſo, as that the Baſe doth not touch
                <lb/>
              the Liquid, the Axis ſhall make an Angle with its
                <lb/>
              Surface greater than the Angle G; that is, than the
                <lb/>
              Angle Y: And, for that reaſon, much greater than
                <lb/>
              the Angle X.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1372"/>
              (d)
                <emph type="italics"/>
              By 29 of the
                <lb/>
              firſt.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1373"/>
              (e)
                <emph type="italics"/>
              By 16. of the
                <lb/>
              firſt.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>CONCLUSION III.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              If the Portion have the ſame proportion in Gravity to the
                <lb/>
              Liquid, that the Square X O hath to the Square
                <emph.end type="italics"/>
                <lb/>
              BD,
                <emph type="italics"/>
              being demitted into the Liquid, ſo inclined, as that
                <lb/>
              its Baſe touch not the Liquid, it ſhall ſtand and
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              continue inclined, ſo, as that its Baſe touch the Sur­
                <lb/>
              face of the Liquid, in one Point only, and its Axis ſhall
                <lb/>
              make an Angle with the Liquids Surface equall to the
                <lb/>
              Angle X. And, if the Portion have the ſame proportion
                <lb/>
              in Gravity to the Liquid, that the Square P F hath
                <lb/>
              to the Square B D, being demitted into the Liquid,
                <lb/>
              & ſet ſo inclined, as that its Baſe touch not the Liquid,
                <lb/>
              it ſhall ſtand inclined, ſo, as that its Baſe touch the
                <lb/>
              Surface of the Liquid in one Point only, & its Axis ſhall
                <lb/>
              make an Angle with it, equall to the Angle
                <emph.end type="italics"/>
                <foreign lang="grc">Φ.</foreign>
              </s>
            </p>
            <p type="main">
              <s>Let the Portion have the ſame proportion in Gravity to tho
                <lb/>
              Liquid that the Square
                <emph type="italics"/>
              X
                <emph.end type="italics"/>
              O hath to the Square B D; and let
                <lb/>
              it be demitted into the Liquid ſo inclined, as that its Baſe touch
                <lb/>
                <figure id="id.040.01.1084.2.jpg" xlink:href="040/01/1084/2.jpg" number="286"/>
                <lb/>
              not the Liquid. </s>
              <s>And cutting it by
                <lb/>
              a Plane thorow the Axis, erect unto
                <lb/>
              the Surface of the Liquid, let the
                <lb/>
              Section of the Solid, be the Section
                <lb/>
              of a Right-angled Cone, A P M L;
                <lb/>
              let the Section of the Surface of the
                <lb/>
              Liquid be I M; and the Axis of the
                <lb/>
              Portion and Diameter of the Section
                <lb/>
              B D; and let B D be divided as be­
                <lb/>
              fore; and draw PN parallel to IM </s>
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