Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div485" type="section" level="1" n="292">
          <head xml:id="echoid-head308" xml:space="preserve">THEOREMA XL. PROPOS. XL.</head>
          <p>
            <s xml:id="echoid-s4746" xml:space="preserve">SI recta linea bifariam ſecta fuerit, & </s>
            <s xml:id="echoid-s4747" xml:space="preserve">illi in directum ad-
              <lb/>
            iuncta quæuis recta linea; </s>
            <s xml:id="echoid-s4748" xml:space="preserve">parallelepipedum ſub com-
              <lb/>
            poſita ex dimidia propoſitæ, & </s>
            <s xml:id="echoid-s4749" xml:space="preserve">ex adiuncta linea, & </s>
            <s xml:id="echoid-s4750" xml:space="preserve">ſub re-
              <lb/>
            ctangulo ſub compoſita ex tota, & </s>
            <s xml:id="echoid-s4751" xml:space="preserve">adiuncta, & </s>
            <s xml:id="echoid-s4752" xml:space="preserve">ſub adiun-
              <lb/>
            cta, vna cum parallelepipedo ſub compoſito ex eadem pro-
              <lb/>
            poſitæ medietate, & </s>
            <s xml:id="echoid-s4753" xml:space="preserve">ex adiuncta, & </s>
            <s xml:id="echoid-s4754" xml:space="preserve">ſub quadrato eiuſdem
              <lb/>
            medietatis, æquabitur cubo compoſitæ ex dicta medietate,
              <lb/>
            & </s>
            <s xml:id="echoid-s4755" xml:space="preserve">adiuncta.</s>
            <s xml:id="echoid-s4756" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4757" xml:space="preserve">Sit recta linea propoſita, AC, bifariam in, B, diuiſa, cui in dire-
              <lb/>
            ctum ſit adiuncta vtcumq; </s>
            <s xml:id="echoid-s4758" xml:space="preserve">CE. </s>
            <s xml:id="echoid-s4759" xml:space="preserve">Dico parallelepipedum ſub, BE,
              <lb/>
            & </s>
            <s xml:id="echoid-s4760" xml:space="preserve">rectangulo, AEC, vna cum parallelepipedo ſub, BE, & </s>
            <s xml:id="echoid-s4761" xml:space="preserve">qua-
              <lb/>
            drato, BC, æquari cubo ipſius, BE. </s>
            <s xml:id="echoid-s4762" xml:space="preserve">Nam rectangulum, AEC, cum
              <lb/>
            quadrato, CB, æquatur quadrato, BE, igitur (ſumpta communi
              <lb/>
              <note position="left" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">6. Secũdi
                <lb/>
              Elem.</note>
            altitudine, BE,) parallelepipedum ſub, BE, & </s>
            <s xml:id="echoid-s4763" xml:space="preserve">rectangulo, AEC,
              <lb/>
            vna cum parallelepipedo ſub, BE, & </s>
            <s xml:id="echoid-s4764" xml:space="preserve">quadrato, BC, æquabitur pa-
              <lb/>
            rallelepipedo ſub, BE, & </s>
            <s xml:id="echoid-s4765" xml:space="preserve">quadrato, BE, ideſt cubo, BE, quod eran
              <unsure/>
              <lb/>
              <note position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">5. huius.</note>
            oſtendendum.</s>
            <s xml:id="echoid-s4766" xml:space="preserve"/>
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        <div xml:id="echoid-div487" type="section" level="1" n="293">
          <head xml:id="echoid-head309" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4767" xml:space="preserve">_E_X methodo in ſuperioribus demonſtrationibus adhibita manifeſtum
              <lb/>
            eſt nos ſimiliter cęteras Propoſitiones ſecundi Elementorum de-
              <lb/>
            monſtrare poſſe, in quibus linea ſecta in vno, vel pluribus punctis con-
              <lb/>
            ſideratur, ad parallelepipeda eadem traducentes, nam ſi ſuper ſpatia
              <lb/>
            in illis conſiderata intelligantur conſtitui æquè alta parallelepipeda,
              <lb/>
            erunt illa, vt ipſę baſes, propterea quę ibi de baſibus demonſtrantur,
              <lb/>
            de parallelepipedis æquè altis eiſdem baſibus inſiſtentibus rectè colligi
              <lb/>
            poſſunt, quæ ob claritatem, & </s>
            <s xml:id="echoid-s4768" xml:space="preserve">facilitatem à me relinquuntur.</s>
            <s xml:id="echoid-s4769" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div488" type="section" level="1" n="294">
          <head xml:id="echoid-head310" xml:space="preserve">THEOREMA XLI. PROPOS. XLI.</head>
          <p>
            <s xml:id="echoid-s4770" xml:space="preserve">PArallelepipedum, quod ſub tribus rectis lineis propor-
              <lb/>
            tionalibus continetur, æquale eſt cubo mediæ.</s>
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