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

Table of figures

< >
[Figure 241]
Page: 1046
[Figure 242]
Page: 1046
[Figure 243]
Page: 1046
[Figure 244]
Page: 1047
[Figure 245]
Page: 1048
[Figure 246]
Page: 1049
[Figure 247]
Page: 1050
[Figure 248]
Page: 1051
[Figure 249]
Page: 1051
[Figure 250]
Page: 1052
[Figure 251]
Page: 1052
[Figure 252]
Page: 1053
[Figure 253]
Page: 1054
[Figure 254]
Page: 1055
[Figure 255]
Page: 1057
[Figure 256]
Page: 1058
[Figure 257]
Page: 1059
[Figure 258]
Page: 1060
[Figure 259]
Page: 1060
[Figure 260]
Page: 1061
[Figure 261]
Page: 1061
[Figure 262]
Page: 1062
[Figure 263]
Page: 1063
[Figure 264]
Page: 1064
[Figure 265]
Page: 1065
[Figure 266]
Page: 1066
[Figure 267]
Page: 1066
[Figure 268]
Page: 1067
[Figure 269]
Page: 1067
[Figure 270]
Page: 1069
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/1067.jpg" pagenum="373"/>
              did ſuppoſe that it made an Angle greater than the Angle B, the
                <lb/>
              Poriton did not reſt then neither; It is manifeſt that it ſhall ſtay
                <lb/>
                <arrow.to.target n="marg1253"/>
                <lb/>
              or reſt when it ſhall make an Angle eqnall to B. </s>
              <s>For ſo ſhall I O
                <lb/>
              be equall to
                <foreign lang="grc">Ψ</foreign>
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ; and
                <foreign lang="grc">ω</foreign>
              I equall to
                <lb/>
                <figure id="id.040.01.1067.1.jpg" xlink:href="040/01/1067/1.jpg" number="268"/>
                <lb/>
                <foreign lang="grc">Ψ</foreign>
              R; and P H equall to F: There­
                <lb/>
              fore
                <emph type="italics"/>
              M P
                <emph.end type="italics"/>
              ſhall be ſeſquialter of
                <emph type="italics"/>
              P H,
                <emph.end type="italics"/>
                <lb/>
              and
                <emph type="italics"/>
              P H
                <emph.end type="italics"/>
              double of H M: And there­
                <lb/>
              fore ſince H is the Centre of Gravity
                <lb/>
              of that part of it which is within the
                <lb/>
              Liquid, it ſhall move upwards along
                <lb/>
              the ſame
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicular according to
                <lb/>
              which the whole
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              ortion moveth;
                <lb/>
              and along the ſame alſo ſhall the part
                <lb/>
              which is above move downwards:
                <lb/>
              The
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              ortion therefore ſhall reſt; for­
                <lb/>
              aſmuch as the parts are not repulſed by each other.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1238"/>
              A</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1239"/>
              B</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1240"/>
              C</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1241"/>
              D</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1242"/>
              E</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1243"/>
              F</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1244"/>
              G</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1245"/>
              (a)
                <emph type="italics"/>
              By 13. of the
                <lb/>
              fifth.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1246"/>
              H</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1247"/>
              K</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1248"/>
              L</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1249"/>
              M</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1250"/>
              N</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1251"/>
              O</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1252"/>
              P</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1253"/>
              Q</s>
            </p>
            <p type="head">
              <s>COMMANDINE.</s>
            </p>
            <p type="main">
              <s>And let
                <emph type="italics"/>
              C B
                <emph.end type="italics"/>
              be ſeſquialter of
                <emph type="italics"/>
              B R
                <emph.end type="italics"/>
              : C D ſhall alſo be ſeſquialter
                <lb/>
                <arrow.to.target n="marg1254"/>
                <lb/>
              of K R.]
                <emph type="italics"/>
              In the Tranſlation it is read thus:
                <emph.end type="italics"/>
              Sit autem & CB quidem hemeolia
                <lb/>
              ipſius B R: C D autem ipſius K R.
                <emph type="italics"/>
              But we at the reading of this paſſage have thought
                <lb/>
              fit thus to correctit; for it is not ſuppoſed ſo to be, but from the things ſuppoſed is proved to
                <lb/>
              be ſo. </s>
              <s>For if B
                <emph.end type="italics"/>
                <foreign lang="grc">ψ</foreign>
                <emph type="italics"/>
              be double of
                <emph.end type="italics"/>
                <foreign lang="grc">ψ</foreign>
                <emph type="italics"/>
              D, D B ſhall be ſeſquialter of B
                <emph.end type="italics"/>
                <foreign lang="grc">ψ.</foreign>
                <emph type="italics"/>
              And becauſe E B is
                <lb/>
              ſeſquialter of B R, it followeth that the
                <emph.end type="italics"/>
              (a)
                <emph type="italics"/>
              Remainder C D is ſeſquialter of
                <emph.end type="italics"/>
                <foreign lang="grc">ψ</foreign>
                <emph type="italics"/>
              R; that is, of
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1255"/>
                <lb/>
                <emph type="italics"/>
              the Semi-parameter: Wherefore B C ſhall be the Exceſſe by which the Axis is greater than
                <lb/>
              ſeſquialter of the Semi-parameter.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1254"/>
              A</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1255"/>
              (a)
                <emph type="italics"/>
              By 19. of the
                <lb/>
              fifth.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>And therefore F Q is leſſe than
                <emph type="italics"/>
              B C.] For in regard that the Portion hath
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1256"/>
                <lb/>
                <emph type="italics"/>
              the ſame proportion in Gravity unto the Liquid, as the Square F Q hath to the Square D B;
                <lb/>
              and hath leſſer proportion than the Square made of the Exceſſe by which the Axis
                <lb/>
              is greater than Seſquialter of the Semi parameter, hath to the Square made of the Axis; that
                <lb/>
              is, leßer than the Square C B hath to the Square B D; for the Line B D was ſuppoſed to be
                <lb/>
              equall unto the Axis: Therefore the Square F Q ſhall have to the Square D B leſſer proporti­
                <lb/>
              on than the Sqnare C B to the ſame Square B D: And therefore the Square
                <emph.end type="italics"/>
              (b)
                <emph type="italics"/>
              F Q ſhall be
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1257"/>
                <lb/>
                <emph type="italics"/>
              leße than the Square C B: And, for that reaſon, the Line F Q ſhall be leße than B C.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1256"/>
              B</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1257"/>
              (b)
                <emph type="italics"/>
              By 8 of the
                <lb/>
              fifth.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>And, for the ſame reaſon, F is leſſe than
                <emph type="italics"/>
              B R.] For C B being ſeſqui-
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1258"/>
                <lb/>
                <emph type="italics"/>
              alter of B R, and F Q ſeſquialter of F
                <emph.end type="italics"/>
              : (c) F
                <emph type="italics"/>
              Q ſhall be likewiſe leſſe than B C; and F
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1259"/>
                <lb/>
                <emph type="italics"/>
              leße than B R.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1258"/>
              C</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1259"/>
              (c)
                <emph type="italics"/>
              By 14 of the
                <lb/>
              fifth.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Now becauſe it hath been ſuppoſed that the Axis of the
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              ortion
                <lb/>
                <arrow.to.target n="marg1260"/>
                <lb/>
              doth make an Angle with the Surface of the Liquid greater than
                <lb/>
              the Angle
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              the Angle
                <emph type="italics"/>
              P Y I
                <emph.end type="italics"/>
              ſhall be greater than the Angle
                <emph type="italics"/>
              B.]
                <lb/>
              For the Line P Y being parallel to the Surface of the Liquid, that is, to XS
                <emph.end type="italics"/>
              ; (d)
                <emph type="italics"/>
              the Angle
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1261"/>
                <lb/>
                <emph type="italics"/>
              P Y I ſhall be equall to the Angle contained betwixt the Diameter of the Portion N O, and the
                <lb/>
              Line X S: And therefore ſhall be greater than the Angle B.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1260"/>
              D</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1261"/>
              (d)
                <emph type="italics"/>
              By 29 of the
                <lb/>
              firſt.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Therefore the Square
                <emph type="italics"/>
              P I
                <emph.end type="italics"/>
              hath greater proportion to the Square
                <lb/>
                <arrow.to.target n="marg1262"/>
                <lb/>
              Y I, than the Square E
                <foreign lang="grc">Ψ</foreign>
              hath to the Square
                <foreign lang="grc">Ψ</foreign>
                <emph type="italics"/>
              B] Let the Triangles P I Y
                <lb/>
              and E
                <emph.end type="italics"/>
                <foreign lang="grc">ψ</foreign>
                <emph type="italics"/>
              B, be deſcribed apart: And ſeeing that the Angle P Y I is greater
                <lb/>
              than the Angle E B
                <emph.end type="italics"/>
                <foreign lang="grc">ψ,</foreign>
                <emph type="italics"/>
              unto the Line I Y, and at the Point Y aſſigned in
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.1067.2.jpg" xlink:href="040/01/1067/2.jpg" number="269"/>
                <lb/>
                <emph type="italics"/>
              the ſame, make the Angle V Y I equall to the Angle E B
                <emph.end type="italics"/>
                <foreign lang="grc">ψ</foreign>
              ;
                <emph type="italics"/>
              But
                <lb/>
              the Right Angle at I, is equall unto the Right Angle at
                <emph.end type="italics"/>
                <foreign lang="grc">ψ;</foreign>
                <emph type="italics"/>
              therefore the
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum