Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
< >
page |< < (44) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="56">
          <p>
            <s xml:space="preserve">
              <pb o="44" file="0099" n="99" rhead="DE IIS QVAE VEH. IN AQVA."/>
            gura: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia eadem diſponantur demonſtrabimus rurſum
              <lb/>
            n t æqualem eſſe ipſi u i: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portiones a u q, a n z inter
              <lb/>
            ſe ſe æquales.
              <lb/>
            </s>
            <s xml:space="preserve">
              <anchor type="figure" xlink:label="fig-0099-01a" xlink:href="fig-0099-01"/>
            Itaque quoniã
              <lb/>
            ĩ portionibus
              <lb/>
            æqualibus, & </s>
            <s xml:space="preserve">ſi
              <lb/>
            milibus a u q l,
              <lb/>
            a n z g ductæ
              <lb/>
            sũt a q, a z, por
              <lb/>
            tiones æqua-
              <lb/>
            les auferentes;
              <lb/>
            </s>
            <s xml:space="preserve">cum diametris
              <lb/>
            portionum æ-
              <lb/>
            quales angu-
              <lb/>
            los cõtinebũt. </s>
            <s xml:space="preserve">
              <lb/>
            ergo triangulo
              <lb/>
            rum n l s, u ω c
              <lb/>
            anguli, qui cõ-
              <lb/>
            ſiſtũt ad l ω pũ-
              <lb/>
            cta, æquales ſunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b s recta linea æqualis ipſi b c: </s>
            <s xml:space="preserve">ſ r ipſi cr,
              <lb/>
            n χ ipſi u h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">χ tipſi h i. </s>
            <s xml:space="preserve">quòd cum u y dupla ſit ipſius y i,
              <lb/>
            erit n χ maior, quàm dupla χ t. </s>
            <s xml:space="preserve">Sit igitur n m ipſius m t du
              <lb/>
            pla. </s>
            <s xml:space="preserve">Rurſus ex his manifeſtum eſt, non manere ipſam por-
              <lb/>
            tionem; </s>
            <s xml:space="preserve">ſed inclinari ex parte a: </s>
            <s xml:space="preserve">ponebatur autem portio
              <lb/>
            humidi ſuperficiem in uno puncto contingere. </s>
            <s xml:space="preserve">ergo ne-
              <lb/>
            ceſſe eſt, ut eius baſis in humidum magis demergatur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0097-01" xlink:href="fig-0097-01a">
              <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0097-01"/>
            </figure>
            <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a">
              <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0098-01"/>
            </figure>
            <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a">
              <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0099-01"/>
            </figure>
          </div>
        </div>
        <div type="section" level="1" n="57">
          <head xml:space="preserve">DEMONSTRATIO QVINT AE PARTIS.</head>
          <p>
            <s xml:space="preserve">HABEAT denique portio ad humidum in grauitate
              <lb/>
            minorem proportionem, quàm quadratum f p ad quadra-
              <lb/>
            tum b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet portio ad humidũ
              <lb/>
            in grauitate, eandem quadratum, quod fit à linea ψ habeat
              <lb/>
            ad quadratum b d. </s>
            <s xml:space="preserve">erit χ minor ipſa p f. </s>
            <s xml:space="preserve">Rurſus aptetur</s>
          </p>
        </div>
      </text>
    </echo>