Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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              <pb o="12" file="0035" n="35" rhead="DE IIS QVAE VEH. IN AQVA."/>
            m productam per pendicularem eſſe ad ipſam e f, quam
              <lb/>
            quidem ſecet in n.</s>
            <s xml:id="echoid-s681" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s682" xml:space="preserve">
              <emph style="sc">D_vcatvr_</emph>
            enim à puncto g linea g o ad rectos angulos ipſi
              <lb/>
            e f, diametrum in o ſecans: </s>
            <s xml:id="echoid-s683" xml:space="preserve">& </s>
            <s xml:id="echoid-s684" xml:space="preserve">rurſus ab eodem puncto ducatur g p
              <lb/>
            ad diametrum perpendicularis: </s>
            <s xml:id="echoid-s685" xml:space="preserve">ſecet autem ipſa diameter producta
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            lineã e f in q. </s>
            <s xml:id="echoid-s686" xml:space="preserve">erit p b ipſi b q æqualis, ex trigeſimaquinta primi co
              <lb/>
            nicorum: </s>
            <s xml:id="echoid-s687" xml:space="preserve">& </s>
            <s xml:id="echoid-s688" xml:space="preserve">g p pro-
              <lb/>
              <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">cor. 8. ſe-
                <lb/>
              xti.</note>
              <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a" number="21">
                <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0035-01"/>
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            portionalis ĩter q p, p o
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            quare quadratũ g p re-
              <lb/>
              <note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">17. ſextĩ.</note>
            ctangulo o p q æquale
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            erit: </s>
            <s xml:id="echoid-s689" xml:space="preserve">ſed etiã æquale est
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            rectangulo cõtento ipſa
              <lb/>
            p b, & </s>
            <s xml:id="echoid-s690" xml:space="preserve">linea, iuxta quã
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            poſſunt, quæ à ſectione
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            ad diametrũ ordinatim
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            ducuntur, ex undecima
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            primi conicorum. </s>
            <s xml:id="echoid-s691" xml:space="preserve">ergo
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              <note position="right" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve">14. ſexti.</note>
            quæ est proportio q p
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            ad p b eadem est lineæ,
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            iuxta quã poſſunt, quæ
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            à ſectione ducũtur ad ip
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            ſam p o: </s>
            <s xml:id="echoid-s692" xml:space="preserve">est autem q p
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            dupla p b: </s>
            <s xml:id="echoid-s693" xml:space="preserve">cũ ſint p b,
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            b q æquales, ut dictum
              <lb/>
            est. </s>
            <s xml:id="echoid-s694" xml:space="preserve">Linea igitur iuxta
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            quam poſſunt, quæ à ſe-
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            ctione ducuntur ipſi-
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            us p o dupla erit: </s>
            <s xml:id="echoid-s695" xml:space="preserve">& </s>
            <s xml:id="echoid-s696" xml:space="preserve">
              <lb/>
            propterea p o æqualis
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            ei, quæ uſque ad axem,
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            uidelicet ipſi k h: </s>
            <s xml:id="echoid-s697" xml:space="preserve">ſed eſt p g æqualis k m; </s>
            <s xml:id="echoid-s698" xml:space="preserve">& </s>
            <s xml:id="echoid-s699" xml:space="preserve">angulus o p g angu-
              <lb/>
              <note position="right" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">32. primi</note>
            lo h k m; </s>
            <s xml:id="echoid-s700" xml:space="preserve">quòd uterque rectus. </s>
            <s xml:id="echoid-s701" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s702" xml:space="preserve">o g ipſi h m est œqualis:
              <lb/>
            </s>
            <s xml:id="echoid-s703" xml:space="preserve">
              <note position="right" xlink:label="note-0035-05" xlink:href="note-0035-05a" xml:space="preserve">4. primi.</note>
            & </s>
            <s xml:id="echoid-s704" xml:space="preserve">angulus p o g angulo _k_ h m. </s>
            <s xml:id="echoid-s705" xml:space="preserve">æquidistantes igitur ſunt o g, h n:
              <lb/>
            </s>
            <s xml:id="echoid-s706" xml:space="preserve">
              <note position="right" xlink:label="note-0035-06" xlink:href="note-0035-06a" xml:space="preserve">28</note>
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