Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb o="7" file="0025" n="25" rhead="DE IIS QVAE VEH. IN AQVA."/>
        </div>
        <div xml:id="echoid-div27" type="section" level="1" n="18">
          <head xml:id="echoid-head21" xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:id="echoid-s399" xml:space="preserve">H_
              <emph style="sc">VIVS</emph>
            _ propoſitionis demonſtratio iniuria temporum deſidera-
              <lb/>
            tur, quam nos ita reſtituimus, ut ex figuris, quæ remanſerunt Archi
              <lb/>
            medem ſcripſiſſe colligi potuit: </s>
            <s xml:id="echoid-s400" xml:space="preserve">neque enim eas immutare uiſum est,
              <lb/>
            quæ uero ad declarationem, explicationémque addenda fuerant, in
              <lb/>
            commentarijs ſuppleuimus, id quod etiam præstitimus in ſecunda
              <lb/>
            propoſitione ſecundi libri.</s>
            <s xml:id="echoid-s401" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s402" xml:space="preserve">_SI aliqua magnitudo ſolida leuior humido.</s>
            <s xml:id="echoid-s403" xml:space="preserve">]_ Ea uerba,
              <lb/>
              <note position="right" xlink:label="note-0025-01" xlink:href="note-0025-01a" xml:space="preserve">A</note>
            leuior bumido, nos addidimus, quæ in translatione non erant; </s>
            <s xml:id="echoid-s404" xml:space="preserve">quo-
              <lb/>
            niam de eiuſmodi magnitudinibus in bac propoſitione agitur.</s>
            <s xml:id="echoid-s405" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s406" xml:space="preserve">In humidũ demittatur, ita ut baſis portionis nõ tangat hu
              <lb/>
              <note position="right" xlink:label="note-0025-02" xlink:href="note-0025-02a" xml:space="preserve">B</note>
            midum.</s>
            <s xml:id="echoid-s407" xml:space="preserve">] _Hoc est in humidum ita demitt atur, ut baſis ſurſum ſpe_
              <lb/>
            _ctet; </s>
            <s xml:id="echoid-s408" xml:space="preserve">uertex autem deorſum. </s>
            <s xml:id="echoid-s409" xml:space="preserve">quod quidem opponitur ei, quod in ſe-_
              <lb/>
            _quenti dixit._ </s>
            <s xml:id="echoid-s410" xml:space="preserve">In humidum demittatur, ita ut baſis tota ſit in
              <lb/>
            humido. </s>
            <s xml:id="echoid-s411" xml:space="preserve">_His enim uerbis ſignificat portionem oppoſito modo in_
              <lb/>
            _humidum demitti, ut ſcilicet uertex ſurſum; </s>
            <s xml:id="echoid-s412" xml:space="preserve">baſis autem deorſum_
              <lb/>
            _uergat. </s>
            <s xml:id="echoid-s413" xml:space="preserve">eodem dicendi modo frequenter uſus est in ſecundo libro; </s>
            <s xml:id="echoid-s414" xml:space="preserve">in_
              <lb/>
            _quo de portionibus conoidis rectangulitractatur._</s>
            <s xml:id="echoid-s415" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s416" xml:space="preserve">_Quoniã igitur unaquæq; </s>
            <s xml:id="echoid-s417" xml:space="preserve">ſphæræ portio axẽ habet in linea,_
              <lb/>
              <note position="right" xlink:label="note-0025-03" xlink:href="note-0025-03a" xml:space="preserve">C</note>
            _quæ à cẽtro ſphæræ ad eius baſim perpẽdicularis ducitur.</s>
            <s xml:id="echoid-s418" xml:space="preserve">]_
              <lb/>
            Iungatur enim b c, & </s>
            <s xml:id="echoid-s419" xml:space="preserve">k l ſecet circunferentiam a b c d in puncto g;
              <lb/>
            </s>
            <s xml:id="echoid-s420" xml:space="preserve">lineam uero rectam b c in m. </s>
            <s xml:id="echoid-s421" xml:space="preserve">& </s>
            <s xml:id="echoid-s422" xml:space="preserve">quoniam duo circuli a b c d, e f b
              <lb/>
            ſecant ſe ſe in punctis b c; </s>
            <s xml:id="echoid-s423" xml:space="preserve">recta linea, quæ ipſorum centra coniun-
              <lb/>
            git, uidelicet k l lineam b c bifariam, & </s>
            <s xml:id="echoid-s424" xml:space="preserve">ad angulos rectos ſecat: </s>
            <s xml:id="echoid-s425" xml:space="preserve">
              <lb/>
            ut in commentarij s in Ptolemæi planiſpbærium oſtendimus. </s>
            <s xml:id="echoid-s426" xml:space="preserve">quare
              <lb/>
            portionis circuli b n c diameter eſt m n; </s>
            <s xml:id="echoid-s427" xml:space="preserve">& </s>
            <s xml:id="echoid-s428" xml:space="preserve">portionis b g c diame-
              <lb/>
              <note position="right" xlink:label="note-0025-04" xlink:href="note-0025-04a" xml:space="preserve">29. primi</note>
            ter m g: </s>
            <s xml:id="echoid-s429" xml:space="preserve">nam rectæ lineæ, quæ ipſi b c æquidistantes ex utraque
              <lb/>
            parte ducuntur, cum linea n g rectos angulos faciunt; </s>
            <s xml:id="echoid-s430" xml:space="preserve">& </s>
            <s xml:id="echoid-s431" xml:space="preserve">idcirco ab
              <lb/>
              <note position="right" xlink:label="note-0025-05" xlink:href="note-0025-05a" xml:space="preserve">3. tertii.</note>
            ipſa bifariam ſecantur. </s>
            <s xml:id="echoid-s432" xml:space="preserve">portionis igitur ſpbæræ b n c axis eſt n m;
              <lb/>
            </s>
            <s xml:id="echoid-s433" xml:space="preserve">& </s>
            <s xml:id="echoid-s434" xml:space="preserve">portionis b g c axis m g. </s>
            <s xml:id="echoid-s435" xml:space="preserve">ex quo ſequitur, portionis in bumido
              <lb/>
            demerſæ axem eſſe in linea k l; </s>
            <s xml:id="echoid-s436" xml:space="preserve">ipſam ſcilicet n g. </s>
            <s xml:id="echoid-s437" xml:space="preserve">& </s>
            <s xml:id="echoid-s438" xml:space="preserve">cum grauita-
              <lb/>
            tis centrum cuius libet ſpbæræ portionis ſit in axe; </s>
            <s xml:id="echoid-s439" xml:space="preserve">quod nos in </s>
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