Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[Figure 151]
Page: 208
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            <s xml:id="echoid-s1668" xml:space="preserve">
              <pb o="29" file="0069" n="69" rhead="DE IIS QVAE VEH. IN AQVA."/>
            interdũ quidem ita, ut baſis in humidum magis
              <lb/>
              <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">C</note>
            demergatur: </s>
            <s xml:id="echoid-s1669" xml:space="preserve">interdum uero ita, ut ſuperficiem
              <lb/>
              <note position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">D</note>
            humidi nullo modo contingat; </s>
            <s xml:id="echoid-s1670" xml:space="preserve">ſecundum pro-
              <lb/>
              <note position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve">E</note>
            portionem, quam habet ad humidum in grauita-
              <lb/>
            te. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">Eorum quæ dicta ſunt, ſingula inferius de-
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            monſtrabuntur.</s>
            <s xml:id="echoid-s1672" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1673" xml:space="preserve">SIT portio qualis dicta eſt: </s>
            <s xml:id="echoid-s1674" xml:space="preserve">& </s>
            <s xml:id="echoid-s1675" xml:space="preserve">ſecta ipſa plano per axẽ.
              <lb/>
            </s>
            <s xml:id="echoid-s1676" xml:space="preserve">recto ad ſuperficiem humidi, ſectio ſit a p o l rectanguli co
              <lb/>
            ni ſeccio: </s>
            <s xml:id="echoid-s1677" xml:space="preserve">axis portionis, & </s>
            <s xml:id="echoid-s1678" xml:space="preserve">ſectionis diameter b d: </s>
            <s xml:id="echoid-s1679" xml:space="preserve">ſece-
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            turq; </s>
            <s xml:id="echoid-s1680" xml:space="preserve">b d in puncto quidem _k_ ita, ut b k dupla ſitipſius
              <lb/>
            _k_ d: </s>
            <s xml:id="echoid-s1681" xml:space="preserve">in c uero ita, ut b d ad
              <emph style="sc">K C</emph>
            proportionẽ habeat ean-
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            dem, quam quindecim ad quatuor. </s>
            <s xml:id="echoid-s1682" xml:space="preserve">conſtat igitur k c ma-
              <lb/>
              <note position="right" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve">F</note>
            iorem eſſe, quàm quæ uſque ad axem. </s>
            <s xml:id="echoid-s1683" xml:space="preserve">Sit ei quæ uſque ad
              <lb/>
              <note position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve">G</note>
            axem æqualis k r: </s>
            <s xml:id="echoid-s1684" xml:space="preserve">& </s>
            <s xml:id="echoid-s1685" xml:space="preserve">ipſius k r ſeſquialtera d s. </s>
            <s xml:id="echoid-s1686" xml:space="preserve">Eſt autem
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              <note position="right" xlink:label="note-0069-06" xlink:href="note-0069-06a" xml:space="preserve">H</note>
            & </s>
            <s xml:id="echoid-s1687" xml:space="preserve">s b ſeſquial-
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              <figure xlink:label="fig-0069-01" xlink:href="fig-0069-01a" number="43">
                <image file="0069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0069-01"/>
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            tera ipſius b r.
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            </s>
            <s xml:id="echoid-s1688" xml:space="preserve">Itaque iũgatur
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            a b, & </s>
            <s xml:id="echoid-s1689" xml:space="preserve">per c du
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            catur c e per-
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            pẽdicularis ad
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            b d, quæ lineã
              <lb/>
            a b in puncto
              <lb/>
            e ſecet: </s>
            <s xml:id="echoid-s1690" xml:space="preserve">& </s>
            <s xml:id="echoid-s1691" xml:space="preserve">per
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            e ducatur e z
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            æquidiſtãs b d. </s>
            <s xml:id="echoid-s1692" xml:space="preserve">
              <lb/>
            Rurſus ipſa a b
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            bifariã in t di-
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            uiſa, ducatur t
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            h eidem b d æ-
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            quidiſtans: </s>
            <s xml:id="echoid-s1693" xml:space="preserve">& </s>
            <s xml:id="echoid-s1694" xml:space="preserve">
              <lb/>
            intelligantur rectanguli coni ſectiones deſcriptæ a e i </s>
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