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

Table of figures

< >
[Figure 231]
Page: 1035
[Figure 232]
Page: 1036
[Figure 233]
Page: 1038
[Figure 234]
Page: 1039
[Figure 235]
Page: 1040
[Figure 236]
Page: 1042
[Figure 237]
Page: 1042
[Figure 238]
Page: 1043
[Figure 239]
Page: 1044
[Figure 240]
Page: 1046
[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
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/1039.jpg" pagenum="344"/>
              for that B G is the Gravity of the Liquid equal in Maſs unto it:
                <lb/>
              Therefore the Solid compounded of thoſe two Solids A and D
                <lb/>
              being dimerged, it ſhall, by the precedent, ſo much of it ſubmerge,
                <lb/>
              as that a quantity of the Liquid equal to the ſaid ſubmerged part
                <lb/>
              ſhall have equal Gravity with the ſaid compounded Solid. </s>
              <s>And
                <lb/>
                <figure id="id.040.01.1039.1.jpg" xlink:href="040/01/1039/1.jpg" number="234"/>
                <lb/>
              for an example of that
                <emph type="italics"/>
              Propoſition
                <emph.end type="italics"/>
              let the Su­
                <lb/>
              perficies of any Liquid be that which pro­
                <lb/>
              ceedeth according to the Circumference
                <lb/>
              A B G D: Becauſe now a Maſs or quantity
                <lb/>
              of Liquor as big as the Maſs A hath equal
                <lb/>
              Gravity with the whole compounded Solid
                <lb/>
              A D: It is manifeſt that the ſubmerged part
                <lb/>
              thereof ſhall be the Maſs A: and the remain­
                <lb/>
              der, namely, the part D, ſhall be wholly a­
                <lb/>
              top, that is, above the Surface of the Liquid.
                <lb/>
              </s>
              <s>It is therefore evident, that the part A hath ſo much virtue or
                <lb/>
              Force to return upwards, that is, to riſe from below above the Li­
                <lb/>
              quid, as that which is upon it, to wit, the part D, hath to preſs it
                <lb/>
              downwards, for that neither part is repulſed by the other: But D
                <lb/>
              preſſeth downwards with a Gravity equal to G, it having been ſup­
                <lb/>
              poſed that the Gravity of that part D was equal to G: Therefore
                <lb/>
              that is manifeſt which was to be demonſtrated.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>This was a fine Demonſtration, and from this I perceive that you colle­
                <lb/>
              cted your
                <emph type="italics"/>
              Induſtrious Invention
                <emph.end type="italics"/>
              ; and eſpecially that part of it which you inſert in
                <lb/>
              the firſt Book for the recovering of a Ship ſunk: and, indeed, I have many Que­
                <lb/>
              ſtions to ask you about that, but I will not now interrupt the Diſcourſe in hand, but
                <lb/>
              deſire that we may go on to the ſeventh
                <emph type="italics"/>
              Propoſition,
                <emph.end type="italics"/>
              the purport whereof is this.</s>
            </p>
            <p type="head">
              <s>PROP. VII. THEOR. VII.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Solid Magnitudes beavier than the Liquid, being de­
                <lb/>
              mitted into the [ſetled] Liquid, are boren down­
                <lb/>
              wards as far as they can deſcend: and ſhall be lighter
                <lb/>
              in the Liquid by the Gravity of a Liquid Maſs of
                <lb/>
              the ſame bigneſs with the Solid Magnitude.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>This ſeventh
                <emph type="italics"/>
              Propoſition
                <emph.end type="italics"/>
              hath two parts to be demonſtrated.</s>
            </p>
            <p type="main">
              <s>The firſt is, That all Solids heavier than the Liquid, being demit­
                <lb/>
              ted into the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, are boren by their Gravities downwards as far
                <lb/>
              as they can deſcend, that is untill they arrive at the Bottom. </s>
              <s>Which
                <lb/>
              firſt part is manifeſt, becauſe the Parts of the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, which ſtill lie
                <lb/>
              under that Solid, are more preſſed than the others equijacent,
                <lb/>
              becauſe that that Solid is ſuppoſed more grave than the Liquid. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum