Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
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          <pb o="17" file="0045" n="45" rhead="DE IIS QVAE VEH. IN AQVA."/>
          <p>
            <s xml:space="preserve">SIT portio, qualis dicta eſt, & </s>
            <s xml:space="preserve">in humidum demittatur,
              <lb/>
            ſicuti diximus, adeo ut baſis eius in uno puncto contingat
              <lb/>
            humidum. </s>
            <s xml:space="preserve">demonſtrandum eſtnon manere ipſam portio-
              <lb/>
            nem, ſed reuoluiita, ut baſis nullo modo humidi ſuperſicie
              <lb/>
              <anchor type="note" xlink:label="note-0045-01a" xlink:href="note-0045-01"/>
            contingat. </s>
            <s xml:space="preserve">Secta enim ipſa per axem, plano ad ſuper ſiciem
              <lb/>
            humidi recto, ſit ſectio ſuperſiciei portionis a p o l re-
              <lb/>
            ctãguli coni ſe
              <lb/>
              <anchor type="figure" xlink:label="fig-0045-01a" xlink:href="fig-0045-01"/>
            ctio: </s>
            <s xml:space="preserve">ſuperſi-
              <lb/>
            ciei humidi ſe-
              <lb/>
            ctio ſit a s: </s>
            <s xml:space="preserve">axis
              <lb/>
            autem portio-
              <lb/>
            nis, ac ſectio-
              <lb/>
            nis diameter n
              <lb/>
            o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſccetur in
              <lb/>
            f quidẽ ita, ut
              <lb/>
            o f ſit dupla ip
              <lb/>
            ſius ſn; </s>
            <s xml:space="preserve">in ω ue
              <lb/>
            ro, ut n o ad
              <lb/>
            f ω eandem ha
              <lb/>
            beat proportionem, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ipſi
              <lb/>
            n o ad rectos angulos ducatur ω k. </s>
            <s xml:space="preserve">Itaque quoniam n o
              <lb/>
              <anchor type="note" xlink:label="note-0045-02a" xlink:href="note-0045-02"/>
            ad f ω maiorem habet proportionem, quàm ad eam, quæ
              <lb/>
            uſque ad axem; </s>
            <s xml:space="preserve">ſit ei, quæ uſque ad axem æqualis f b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">du
              <lb/>
            catur p c quidem ipſi a s æquidiſtans, cõtingensq; </s>
            <s xml:space="preserve">ſectio-
              <lb/>
            nem a p o l in p; </s>
            <s xml:space="preserve">pi uero æquidiſtans ipſi n o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">primum
              <lb/>
            ſecet pi ipſam κ ω in h. </s>
            <s xml:space="preserve">Quoniã ergo in portione a p o l,
              <lb/>
              <anchor type="note" xlink:label="note-0045-03a" xlink:href="note-0045-03"/>
            quæ continetur recta linea, & </s>
            <s xml:space="preserve">rectanguli coni ſectione, κ ω
              <lb/>
            quidem æ quidiſtans eſtipſi a l; </s>
            <s xml:space="preserve">p i uero diametro æquidi-
              <lb/>
            ſtat: </s>
            <s xml:space="preserve">ſecaturq; </s>
            <s xml:space="preserve">ab ipſa κ ω in h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a s æquidiſtat contingen-
              <lb/>
            ti in p: </s>
            <s xml:space="preserve">neceſſarium eſtipſam p i ad p h uel ean dem pro-
              <lb/>
            portionem habere, quam habet n ω ad ω o, uel maiorem:
              <lb/>
            </s>
            <s xml:space="preserve">hocenim iam demonſtratum eſt. </s>
            <s xml:space="preserve">At uero n ω ſeſquialtera
              <lb/>
            eſt ipſius ω o. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pi igitur uel ſeſquialtera eſt ipſius h p; </s>
            <s xml:space="preserve">
              <lb/>
            uel maior, quàm ſeſquialtera. </s>
            <s xml:space="preserve">Quare ph ipſius h i aut du
              <lb/>
              <anchor type="note" xlink:label="note-0045-04a" xlink:href="note-0045-04"/>
            </s>
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