Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
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
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div182" type="section" level="1" n="56">
          <p>
            <s xml:id="echoid-s2582" xml:space="preserve">
              <pb file="0098" n="98" rhead="ARCHIMEDIS"/>
            ſuperficiem recto, ſit portionis ſectio anzg; </s>
            <s xml:id="echoid-s2583" xml:space="preserve">ſuperficiei
              <lb/>
            humidi ez: </s>
            <s xml:id="echoid-s2584" xml:space="preserve">a-
              <lb/>
              <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a" number="64">
                <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0098-01"/>
              </figure>
            xis portionis,
              <lb/>
            & </s>
            <s xml:id="echoid-s2585" xml:space="preserve">ſectionis dia-
              <lb/>
            meter b d: </s>
            <s xml:id="echoid-s2586" xml:space="preserve">ſece-
              <lb/>
            turq, b d in pũ-
              <lb/>
            ctis _K_r, ſicuti
              <lb/>
            prius; </s>
            <s xml:id="echoid-s2587" xml:space="preserve">& </s>
            <s xml:id="echoid-s2588" xml:space="preserve">duca-
              <lb/>
            tur n l quidem
              <lb/>
            ipſi e z æquidi-
              <lb/>
            ſtans, quæ con-
              <lb/>
            tingat ſectionẽ
              <lb/>
            a n z g in n; </s>
            <s xml:id="echoid-s2589" xml:space="preserve">& </s>
            <s xml:id="echoid-s2590" xml:space="preserve">
              <lb/>
            n t æquidiſtans
              <lb/>
            ipſi b d; </s>
            <s xml:id="echoid-s2591" xml:space="preserve">n s ue-
              <lb/>
            ro ad b d perpẽ
              <lb/>
            dicularis. </s>
            <s xml:id="echoid-s2592" xml:space="preserve">Itaq;
              <lb/>
            </s>
            <s xml:id="echoid-s2593" xml:space="preserve">quoniam portio ad humidum in grauitate eam proportio
              <lb/>
            nem habet, quam quadratum, quod fit à linea ψ ad quadra
              <lb/>
            tum b d: </s>
            <s xml:id="echoid-s2594" xml:space="preserve">erit ψ ipſi n t æqualis: </s>
            <s xml:id="echoid-s2595" xml:space="preserve">quod ſimiliter demonſtrabi
              <lb/>
            tur, ut ſuperius. </s>
            <s xml:id="echoid-s2596" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s2597" xml:space="preserve">n t eſt æqualis ipſi u i. </s>
            <s xml:id="echoid-s2598" xml:space="preserve">portiones
              <lb/>
            igitur a u q, e n z inter ſe ſunt æquales. </s>
            <s xml:id="echoid-s2599" xml:space="preserve">Et cum in æquali-
              <lb/>
            bus, & </s>
            <s xml:id="echoid-s2600" xml:space="preserve">ſimilibus portionibus a u q l, a n z g ductæ ſint a q
              <lb/>
            e z, quæ æquales portiones auferunt; </s>
            <s xml:id="echoid-s2601" xml:space="preserve">illa quidem ab extre
              <lb/>
            mitate baſis; </s>
            <s xml:id="echoid-s2602" xml:space="preserve">hæc autem non ab extremitate: </s>
            <s xml:id="echoid-s2603" xml:space="preserve">minorem fa-
              <lb/>
            ciet acutum angulum cum portionis diametro, quæ ab ex-
              <lb/>
            tremitate baſis ducitur. </s>
            <s xml:id="echoid-s2604" xml:space="preserve">At triangulorum n l s, u ω c angu
              <lb/>
            lus ad l angulo ad ω maior eſt. </s>
            <s xml:id="echoid-s2605" xml:space="preserve">ergo b s minor erit, quam
              <lb/>
            b c: </s>
            <s xml:id="echoid-s2606" xml:space="preserve">& </s>
            <s xml:id="echoid-s2607" xml:space="preserve">ſ r maior, quàm c r: </s>
            <s xml:id="echoid-s2608" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s2609" xml:space="preserve">n χ maior, quam u h; </s>
            <s xml:id="echoid-s2610" xml:space="preserve">& </s>
            <s xml:id="echoid-s2611" xml:space="preserve">
              <lb/>
            χ t minor, quàm h i. </s>
            <s xml:id="echoid-s2612" xml:space="preserve">Quoniam igitur u y dupla eſt ipſius
              <lb/>
            y i; </s>
            <s xml:id="echoid-s2613" xml:space="preserve">conſtat n χ maiorem eſſe, quàm duplã χ t. </s>
            <s xml:id="echoid-s2614" xml:space="preserve">Sit n m dupla
              <lb/>
            ipſius m t. </s>
            <s xml:id="echoid-s2615" xml:space="preserve">perſpicuũ eſt ex iis, quæ dicta ſunt, non manere
              <lb/>
            portionẽ; </s>
            <s xml:id="echoid-s2616" xml:space="preserve">ſed in clinari, donec eius baſis contingat ſuperfi-
              <lb/>
            ciem humidi: </s>
            <s xml:id="echoid-s2617" xml:space="preserve">contingat autem in puncto uno, ut patet in </s>
          </p>
        </div>
      </text>
    </echo>
Impressum