Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
191 40
192
193 41
194
195 42
196
197 43
198
199 44
200
201 45
202
203 46
204
205 47
206
207
208
209
210
211
212
< >
page |< < (10) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div39" type="section" level="1" n="21">
          <p>
            <s xml:id="echoid-s555" xml:space="preserve">
              <pb o="10" file="0031" n="31" rhead="DE IIS QVAE VEH. IN AQVA."/>
            æqualis magnitudini f a; </s>
            <s xml:id="echoid-s556" xml:space="preserve">ſitq, ipſi f æqualis n: </s>
            <s xml:id="echoid-s557" xml:space="preserve">& </s>
            <s xml:id="echoid-s558" xml:space="preserve">ipſi a æ-
              <lb/>
            qualis i. </s>
            <s xml:id="echoid-s559" xml:space="preserve">magnitudinis autem f a grauitas ſit b: </s>
            <s xml:id="echoid-s560" xml:space="preserve">& </s>
            <s xml:id="echoid-s561" xml:space="preserve">magni-
              <lb/>
            tudinis n i grauitas o r; </s>
            <s xml:id="echoid-s562" xml:space="preserve">& </s>
            <s xml:id="echoid-s563" xml:space="preserve">ipſius i ſit r. </s>
            <s xml:id="echoid-s564" xml:space="preserve">magnitudo igi-
              <lb/>
            tur f a ad n i eam proportionem habet, quam grauitas b
              <lb/>
            ad grauitatem or. </s>
            <s xml:id="echoid-s565" xml:space="preserve">Sed quoniam magnitudo f a in humi-
              <lb/>
            dum demiſſa leuior eſt humido; </s>
            <s xml:id="echoid-s566" xml:space="preserve">patet tantam humidi mo-
              <lb/>
            lem, quanta eſt pars magnitudin_i_s demerſa, eandem quam
              <lb/>
            magnitudo f a habere grauitatem. </s>
            <s xml:id="echoid-s567" xml:space="preserve">hoc enim ſuperius de-
              <lb/>
              <note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">5. priml
                <lb/>
              huius.</note>
            monſtratum eſt. </s>
            <s xml:id="echoid-s568" xml:space="preserve">Atipſi a reſpondet humidum i, cuius qui
              <lb/>
            dem grauitas eſt r; </s>
            <s xml:id="echoid-s569" xml:space="preserve">& </s>
            <s xml:id="echoid-s570" xml:space="preserve">ipſius f a grauitas b. </s>
            <s xml:id="echoid-s571" xml:space="preserve">ergo b graui-
              <lb/>
            tas eius, quod habet molem æqualem toti magnitudini
              <lb/>
            f a, æqualis erit grauitati humidi i, uidelicetipſi r. </s>
            <s xml:id="echoid-s572" xml:space="preserve">Et quo
              <lb/>
            niam ut magnitudo f a ad humidum n i ſibi reſpondens,
              <lb/>
            ita eſt b ad o r: </s>
            <s xml:id="echoid-s573" xml:space="preserve">eſt autem b æqualis ipſi r: </s>
            <s xml:id="echoid-s574" xml:space="preserve">& </s>
            <s xml:id="echoid-s575" xml:space="preserve">utr ad o r, ita
              <lb/>
            i ad n i; </s>
            <s xml:id="echoid-s576" xml:space="preserve">& </s>
            <s xml:id="echoid-s577" xml:space="preserve">a ad f a. </s>
            <s xml:id="echoid-s578" xml:space="preserve">Sequitur ut f a ad humidum æqualis
              <lb/>
              <note position="right" xlink:label="note-0031-02" xlink:href="note-0031-02a" xml:space="preserve">11. quinta
                <unsure/>
              </note>
            molis eam in grauitate proportionem habeat, quam ma-
              <lb/>
            gnitudo a habet ad f a. </s>
            <s xml:id="echoid-s579" xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s580" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div41" type="section" level="1" n="22">
          <head xml:id="echoid-head27" xml:space="preserve">PROPOSITIO II.</head>
          <p>
            <s xml:id="echoid-s581" xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
              <note position="right" xlink:label="note-0031-03" xlink:href="note-0031-03a" xml:space="preserve">A</note>
            axem habuerit minorem, quam ſeſquialterum
              <lb/>
            eius, quæ uſque ad axem, quamcunque propor-
              <lb/>
            tionem habens ad humidum in grauitate; </s>
            <s xml:id="echoid-s582" xml:space="preserve">demiſ
              <lb/>
            ſa in humidum, ita ut baſis ipſius humidum non
              <lb/>
            contingat; </s>
            <s xml:id="echoid-s583" xml:space="preserve">& </s>
            <s xml:id="echoid-s584" xml:space="preserve">poſita inelinata, non manebit incli
              <lb/>
            nata; </s>
            <s xml:id="echoid-s585" xml:space="preserve">ſed recta reſtituetur. </s>
            <s xml:id="echoid-s586" xml:space="preserve">Rectam dico conſi-
              <lb/>
            ſtere talem portionem, quando planum quod ip
              <lb/>
            ſam ſecuit, ſuperficiei humidi fuerit æquidiſtans.</s>
            <s xml:id="echoid-s587" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s588" xml:space="preserve">SIT portio rectanguli conoidis, qualis dicta eſt; </s>
            <s xml:id="echoid-s589" xml:space="preserve">& </s>
            <s xml:id="echoid-s590" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum