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

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        <div xml:id="echoid-div397" type="section" level="1" n="241">
          <pb o="158" file="0178" n="178" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div398" type="section" level="1" n="242">
          <head xml:id="echoid-head257" xml:space="preserve">H. SECTIO VIII.</head>
          <p style="it">
            <s xml:id="echoid-s3743" xml:space="preserve">_I_V xta octauam, ſi ſupponamus figuram, ABCD, vtcunque ſectam
              <lb/>
            per lineam, AC, (quæ tamen ſecet omnes ipſi, BD, æquidiſtantes
              <lb/>
            in figura, ABCD, ductas, & </s>
            <s xml:id="echoid-s3744" xml:space="preserve">in vno tantum puncto vti dictum eſt) col-
              <lb/>
            ligemus rectangula quater ſub figuris, ABCD, ABC, cum omnibus
              <lb/>
            quadratis, ACD, aquari omnibus quadratis figuræ compoſitæ ex figu-
              <lb/>
            ra, ABCD, &</s>
            <s xml:id="echoid-s3745" xml:space="preserve">, ABC, ita vt omnium linearum figuræ, ABCD ſin-
              <lb/>
            gulis intelligatur adiecta, quænunc in figura, ABC, eſicum illa in ea-
              <lb/>
            dem rectitudine.</s>
            <s xml:id="echoid-s3746" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div399" type="section" level="1" n="243">
          <head xml:id="echoid-head258" xml:space="preserve">I. SECTIO IX.</head>
          <p style="it">
            <s xml:id="echoid-s3747" xml:space="preserve">_I_V xta nonam, ſi ſupponamus lineam, AI, ſecare omnes æquidiſtan-
              <lb/>
            tes ipſi, BD, in figura, ABID, ductas bifariam, & </s>
            <s xml:id="echoid-s3748" xml:space="preserve">lineam, AC,
              <lb/>
            eaſdem bifariam non ſecare, colligemus omnia quadr ata figuræ, ACD,
              <lb/>
            cum omnibus quadratis figuræ, ABC, dupla eſſe omnium quadratorum
              <lb/>
            figuræ, AID, cum omnibus quadratis figuræ, ACI, intermediæ.</s>
            <s xml:id="echoid-s3749" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div400" type="section" level="1" n="244">
          <head xml:id="echoid-head259" xml:space="preserve">K. SECTIO X.</head>
          <p style="it">
            <s xml:id="echoid-s3750" xml:space="preserve">_I_V xta decimam, ſi ſupponamus, AC, lineam bifariam ſecare omnes
              <lb/>
            æquidiſtantes ipſi, BD, in figura, ABI, ductas, & </s>
            <s xml:id="echoid-s3751" xml:space="preserve">illis addi, quæ
              <lb/>
            in directum illas iacent in figura, AID; </s>
            <s xml:id="echoid-s3752" xml:space="preserve">colligemus omnia quadrata fi-
              <lb/>
            guræ, ABCD, cum omnibus quadratis figuræ, ADI, dupla eſſe om-
              <lb/>
            nium quadratorum figuræ, ABC, cum omnibus quadratis figuræ, ACD.</s>
            <s xml:id="echoid-s3753" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div401" type="section" level="1" n="245">
          <head xml:id="echoid-head260" xml:space="preserve">L. SECTIO XI.</head>
          <p style="it">
            <s xml:id="echoid-s3754" xml:space="preserve">_I_V xta vndecimam, ſi ſupponamus, BD, in, E, itaſectam eſſe, vtre-
              <lb/>
            ctangulum, DBE, ſit æquate quadrato, ED, quælibet autem æqui-
              <lb/>
            diſtantium ipſi, BD, in figura, ABCD, tali modo, & </s>
            <s xml:id="echoid-s3755" xml:space="preserve">ad eandem par-
              <lb/>
            tem diuid itur per lineam, AEC, patet, quod etiam rectangula ſub fi-
              <lb/>
            guris, ABCD, ABC, æquabuntur omnibus quadratis figuræ, ACD,
              <lb/>
            regula, BD, igitur linea, AC, diuidet ſuperſiciem planam, ABCD,
              <lb/>
            (ſic dicere liceat) ſecundum extremam, ac mediam rationem, hæc au-
              <lb/>
            tempro ſequentibus accuratè memoriæ commendetur.</s>
            <s xml:id="echoid-s3756" xml:space="preserve"/>
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