Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo
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          <pb file="0034" n="34" rhead="ARCHIMEDIS"/>
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            <s xml:id="echoid-s655" xml:space="preserve">_Erit r o minor, quàm, quæ uſque ad axem]_ Ex decima
              <lb/>
              <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">E</note>
            propoſitione quinti libri elementorum. </s>
            <s xml:id="echoid-s656" xml:space="preserve">Linea, quæ uſque ad axem
              <lb/>
            apud Archimedem, eſt dimidia eius, iuxta quam poſſunt, quæ à ſe-
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            ctione ducuntur; </s>
            <s xml:id="echoid-s657" xml:space="preserve">ut ex quarta propoſitione libri de conoidibus, & </s>
            <s xml:id="echoid-s658" xml:space="preserve">
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            ſphæroidibus apparet. </s>
            <s xml:id="echoid-s659" xml:space="preserve">cur uero ita appellata ſit, nos in commentarijs
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            in eam editis tradidimus.</s>
            <s xml:id="echoid-s660" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s661" xml:space="preserve">_Quare angulus r p ω acutus erit]_ producatur linea n o ad
              <lb/>
              <note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">F</note>
            h, ut ſit r h æqualis ei, quæ uſque ad axem. </s>
            <s xml:id="echoid-s662" xml:space="preserve">ſi igitur à puncto h du-
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            catur linea ad rectos angulos ipſi n h, conueniet cum f p extra ſe-
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            ctionem: </s>
            <s xml:id="echoid-s663" xml:space="preserve">ducta enim per o ipſi a l æquidiſtans, extra ſectionem ca
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            dit ex decima ſepti-
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              <figure xlink:label="fig-0034-01" xlink:href="fig-0034-01a" number="20">
                <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0034-01"/>
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            ma primi libri coni-
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            corum. </s>
            <s xml:id="echoid-s664" xml:space="preserve">Itaque con-
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            ueniat in u. </s>
            <s xml:id="echoid-s665" xml:space="preserve">& </s>
            <s xml:id="echoid-s666" xml:space="preserve">quo
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            niam f p est æqui-
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            distans diametro;
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            </s>
            <s xml:id="echoid-s667" xml:space="preserve">h u uero ad diame-
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            trum perpendicula-
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            ris; </s>
            <s xml:id="echoid-s668" xml:space="preserve">& </s>
            <s xml:id="echoid-s669" xml:space="preserve">r h æqualis
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            ei, quæ uſq; </s>
            <s xml:id="echoid-s670" xml:space="preserve">ad axẽ,
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            linea à puncto r ad
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            u ducta angulos re-
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            ctos faciet cum ea, quæ ſectionem in puncto p contingit, hoc eſt cum
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            k ω, ut mox demonstrabitur. </s>
            <s xml:id="echoid-s671" xml:space="preserve">quare perpendicularis r t inter p & </s>
            <s xml:id="echoid-s672" xml:space="preserve">
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            ω cadet; </s>
            <s xml:id="echoid-s673" xml:space="preserve">erítque r p ω angulus acutus.</s>
            <s xml:id="echoid-s674" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s675" xml:space="preserve">Sit rectanguli coni ſectio, ſeu parabole a b c, cuius
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            diameter b d: </s>
            <s xml:id="echoid-s676" xml:space="preserve">atque ipſam contingat linea e f in pun-
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            cto g: </s>
            <s xml:id="echoid-s677" xml:space="preserve">ſumatur autem in diametro b d linea h k æqua-
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            lis ei, quæ uſque ad axem: </s>
            <s xml:id="echoid-s678" xml:space="preserve">& </s>
            <s xml:id="echoid-s679" xml:space="preserve">per g ducta g l, diame-
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            tro æquidistante, à puncto _k_ ad rectos angulos ipſi b d
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            ducatur _k_ m, ſecans g l in m. </s>
            <s xml:id="echoid-s680" xml:space="preserve">Dico lineam ab h </s>
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