Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
161 25
162
163 26
164
165 27
166
167 28
168
169 29
170
< >
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>