Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb file="0040" n="40" rhead="ARCHIMEDIS"/>
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        <div xml:id="echoid-div57" type="section" level="1" n="26">
          <head xml:id="echoid-head31" xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:id="echoid-s821" xml:space="preserve">_Sit ei, quæ uſque ad axem æqualis r h.</s>
            <s xml:id="echoid-s822" xml:space="preserve">]_ Ita legendum eſt,
              <lb/>
              <note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">A</note>
            non r m, ut tranſlatio habet, quod ex ijs, quæ ſequuntur, manifeſte
              <lb/>
            conſtare poteſt.</s>
            <s xml:id="echoid-s823" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s824" xml:space="preserve">_Et oh dupla ipſius h m.</s>
            <s xml:id="echoid-s825" xml:space="preserve">]_ In tranſlatione mendoſe legeba-
              <lb/>
              <note position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve">B</note>
            tur, on dupla ipſius rm.</s>
            <s xml:id="echoid-s826" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s827" xml:space="preserve">Hoc enim ſupra demonſtratum eſt.</s>
            <s xml:id="echoid-s828" xml:space="preserve">] _In prima huius_.</s>
            <s xml:id="echoid-s829" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">C</note>
          <p>
            <s xml:id="echoid-s830" xml:space="preserve">Et quam proportionem habet demerſa portio ad totã,
              <lb/>
              <note position="left" xlink:label="note-0040-04" xlink:href="note-0040-04a" xml:space="preserve">D</note>
            eam quadratum p f habet ad n o quadratum.</s>
            <s xml:id="echoid-s831" xml:space="preserve">] _Hoc loco in_
              <lb/>
            _tranſlatione non nulli deſider abantur, quænos reſtituimus. </s>
            <s xml:id="echoid-s832" xml:space="preserve">Illud au_
              <lb/>
            _tem ab Archimede demonſtratum eſt in libro de conoidibus & </s>
            <s xml:id="echoid-s833" xml:space="preserve">ſphæ_
              <lb/>
            _roidibus propoſitione_ 26.</s>
            <s xml:id="echoid-s834" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s835" xml:space="preserve">_Quare p f non eſt minor ipſa m o.</s>
            <s xml:id="echoid-s836" xml:space="preserve">]_ Nam ex decima quinti
              <lb/>
              <note position="left" xlink:label="note-0040-05" xlink:href="note-0040-05a" xml:space="preserve">E</note>
            ſequitur, quadratum p f non eſſe minus quadrato m o. </s>
            <s xml:id="echoid-s837" xml:space="preserve">quare neque
              <lb/>
            linea p f minor erit linea m o ex 22 ſexti.</s>
            <s xml:id="echoid-s838" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s839" xml:space="preserve">_Nec b p item minor h o.</s>
            <s xml:id="echoid-s840" xml:space="preserve">]_ Eſt enim ut p f ad p b, ita m o,
              <lb/>
              <note position="left" xlink:label="note-0040-06" xlink:href="note-0040-06a" xml:space="preserve">F</note>
            ad h o & </s>
            <s xml:id="echoid-s841" xml:space="preserve">permutando, ut p f ad mo, ita b p, ad b o. </s>
            <s xml:id="echoid-s842" xml:space="preserve">ſed p f non
              <lb/>
            est minor m o, ut oſtenſiim cst. </s>
            <s xml:id="echoid-s843" xml:space="preserve">ergo neque b p ipſa h o minor erit.</s>
            <s xml:id="echoid-s844" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">14. quinti</note>
          <p>
            <s xml:id="echoid-s845" xml:space="preserve">Si igitur ab h
              <lb/>
              <note position="left" xlink:label="note-0040-08" xlink:href="note-0040-08a" xml:space="preserve">G</note>
              <figure xlink:label="fig-0040-01" xlink:href="fig-0040-01a" number="24">
                <image file="0040-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0040-01"/>
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            ducatur linea ad
              <lb/>
            rectos angulos ip
              <lb/>
            ſi n o, coibit cum
              <lb/>
            b p, atque inter
              <lb/>
            b & </s>
            <s xml:id="echoid-s846" xml:space="preserve">p cadet.</s>
            <s xml:id="echoid-s847" xml:space="preserve">]
              <lb/>
            _Corruptus erat hic_
              <lb/>
            _locus in tranſlatio-_
              <lb/>
            _ne. </s>
            <s xml:id="echoid-s848" xml:space="preserve">Illud uero ita de-_
              <lb/>
            _monſtr abitur. </s>
            <s xml:id="echoid-s849" xml:space="preserve">Quo-_
              <lb/>
            _niam p f non eſt mi-_
              <lb/>
            _nor o m, nec p b ip-_
              <lb/>
            _ſa h o; </s>
            <s xml:id="echoid-s850" xml:space="preserve">ſi ponatur p f_
              <lb/>
            _æqualis o m; </s>
            <s xml:id="echoid-s851" xml:space="preserve">& </s>
            <s xml:id="echoid-s852" xml:space="preserve">p b,_
              <lb/>
            _ipſi h o æqualis erit._</s>
            <s xml:id="echoid-s853" xml:space="preserve"/>
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