Archimedes, Natation of bodies, 1662

Page concordance

< >
Scan Original
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
< >
page |< < of 68 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="073/01/064.jpg" pagenum="398"/>
                <figure id="id.073.01.064.1.jpg" xlink:href="073/01/064/1.jpg" number="67"/>
                <lb/>
                <emph type="italics"/>
              ſhall be equall to the Angle at
                <emph.end type="italics"/>
                <foreign lang="grc">φ;</foreign>
                <emph type="italics"/>
              and the Line B S
                <lb/>
              equall to the Line B C; and S R to C R: Where­
                <lb/>
              fore, M H ſhall be likewiſe equall to P Y. There­
                <lb/>
              fore, having drawn HK and prolonged it; the
                <lb/>
              Centre of Gravity of the whole Portion ſhall be
                <lb/>
              K; of that which is in the Liquid H; and of
                <lb/>
              that which is above it, the Centre ſhall be in
                <lb/>
              the Line prolonged: let it be in
                <emph.end type="italics"/>
                <foreign lang="grc">ω.</foreign>
                <emph type="italics"/>
              There­
                <lb/>
              fore, along that ſame Line K H, which is per­
                <lb/>
              pendicular to the Surface of the Liquid, ſhall
                <lb/>
              the part which is within the Liquid move up­
                <lb/>
              wards, and that which is above the Liquld
                <lb/>
              downwards: And, for this cauſe, the Portion,
                <lb/>
              ſhall be no longer moved, but ſhall ſtay, and
                <lb/>
              reſt, ſo, as that its Baſe do touch the Liquids Surface in but one Point; and its Axis
                <lb/>
              maketh an Angle therewith equall to the Angle
                <emph.end type="italics"/>
                <foreign lang="grc">φ</foreign>
                <emph type="italics"/>
              ; And, this is that which we were to
                <lb/>
              demonſtrate.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1391"/>
              F</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1392"/>
              (g)
                <emph type="italics"/>
              By 9 of t
                <lb/>
              fifth.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>CONCLVSION IV.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              If the Portion have greater proportion in Gravity
                <lb/>
              to the Liquid, than the Square F P to the Square
                <lb/>
              B D, but leſſer than that of the Square X O to the
                <lb/>
              Square B D, being demitted into the Liquid,
                <lb/>
              and inclined, ſo, as that its Baſe touch not the
                <lb/>
              Liquid, it ſhall ſtand and reſt, ſo, as that its Baſe
                <lb/>
              ſhall be more ſubmerged in the Liquid.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Again, let the Portion have greater proportion in
                <lb/>
              Gravity to the Liquid, than the Square F P to the
                <lb/>
              Square B D, but leſſer than that of the Square X O to
                <lb/>
              the Square B D; and as the Portion is in Gravity to the Liquid,
                <lb/>
              ſo let the Square made of the Line
                <foreign lang="grc">ψ</foreign>
              be to the Square B D.
                <foreign lang="grc">Ψ</foreign>
                <lb/>
              ſhall be greater than F P, and leſſer than X O. Apply, therefore,
                <lb/>
              the right Line I V to fall betwixt the Portions A V Q L and A X D;
                <lb/>
              and let it be equall to
                <foreign lang="grc">ψ,</foreign>
              and parallel to B D; and let it meet
                <lb/>
              the Remaining Section in Y: V Y ſhall alſo be proved double
                <lb/>
              to Y I, like as it hath been demonſtrated, that O G is double off
                <lb/>
              G X. And, draw from V, the Line V
                <foreign lang="grc">ω,</foreign>
              touching the Section
                <lb/>
              A V Q L in V; and drawing a Line from A to I, prolong it unto
                <lb/>
                <expan abbr="q.">que</expan>
              We prove in the ſame manner, that the Line A I is equall
                <lb/>
              to I
                <expan abbr="q;">que</expan>
              and that A Q is parallel to V
                <foreign lang="grc">ω.</foreign>
              It is to be demonſtrated,
                <lb/>
              that the Portion being demitted into the Liquid, and ſo inclined,
                <lb/>
              as that its Baſe touch not the Liquid, ſhall ſtand, ſo, that its Baſe
                <lb/>
              ſhall be more ſubmerged in the Liquid, than to touch it Surface in </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum