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

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        <div xml:id="echoid-div770" type="section" level="1" n="454">
          <p style="it">
            <s xml:id="echoid-s7736" xml:space="preserve">
              <pb o="322" file="0342" n="342" rhead="GEOMETRIÆ"/>
            colliguntur pro omnibus quadratis dictorum parallelogrammorum, pro
              <lb/>
            omnibus quadratis etiam parabolarum eiſdem inſcriptiarum, tamquam
              <lb/>
            pro earundem partibus proportionalibus, ſcilicet dimidijs, pariter vt
              <lb/>
            vera recipi poſſunt.</s>
            <s xml:id="echoid-s7737" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div771" type="section" level="1" n="455">
          <head xml:id="echoid-head475" xml:space="preserve">B. SECTIO II.</head>
          <note position="left" xml:space="preserve">B</note>
          <p style="it">
            <s xml:id="echoid-s7738" xml:space="preserve">_E_T quia oſtenſum eſt omnia quadrata parallelogrammorum in ea-
              <lb/>
              <note position="left" xlink:label="note-0342-02" xlink:href="note-0342-02a" xml:space="preserve">_9. l. 2._</note>
            dem altitudine ſtantium, regulis baſibus, eſſe interſe, vt qua-
              <lb/>
            drata baſium; </s>
            <s xml:id="echoid-s7739" xml:space="preserve">& </s>
            <s xml:id="echoid-s7740" xml:space="preserve">exiſtentium in eadem baſi eſſe, vt altitudines, vel
              <lb/>
            etiam, vt latera eorundem æqualiter baſibus inclinata, ideò pariter hic
              <lb/>
            colligemus omnia quadrata parabolarum in eadam altitudine exiſten-
              <lb/>
            tium, regulis baſibus, eſſe vt quadrata baſium, & </s>
            <s xml:id="echoid-s7741" xml:space="preserve">exiſtentium in ea-
              <lb/>
            dem baſis eſſe interſe, vt altitudines, vel vt diametros æqualiter ba-
              <lb/>
            ſibus inclinatas.</s>
            <s xml:id="echoid-s7742" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div773" type="section" level="1" n="456">
          <head xml:id="echoid-head476" xml:space="preserve">C. SECTIO III.</head>
          <note position="left" xml:space="preserve">C</note>
          <p style="it">
            <s xml:id="echoid-s7743" xml:space="preserve">_S_Imiliter quia oſtenſum eſt omnia quadrata parallelogrammorum, re-
              <lb/>
              <note position="left" xlink:label="note-0342-04" xlink:href="note-0342-04a" xml:space="preserve">_10. l. 2._</note>
            gulis baſibus, babere inter ſe rationem compoſitam ex ratione qua-
              <lb/>
            dratorum baſium, & </s>
            <s xml:id="echoid-s7744" xml:space="preserve">altitudinum, vel laterum æqualiter baſibus in-
              <lb/>
            clinatorum; </s>
            <s xml:id="echoid-s7745" xml:space="preserve">ideò colligemus, hic, omnia quadrata parabolarum regu-
              <lb/>
            lis baſibus, babere inter ſe rationem compoſitam ex ratione quadrato-
              <lb/>
            rum baſium, & </s>
            <s xml:id="echoid-s7746" xml:space="preserve">altitudinum, vel diametrorum æqualiter baſibus in-
              <lb/>
            clinatorum.</s>
            <s xml:id="echoid-s7747" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div775" type="section" level="1" n="457">
          <head xml:id="echoid-head477" xml:space="preserve">D. SECTIO IV.</head>
          <note position="left" xml:space="preserve">D</note>
          <p style="it">
            <s xml:id="echoid-s7748" xml:space="preserve">_C_Onſimili metbodo colligemus, omnia quadrata parabolarum, regu-
              <lb/>
            lis baſibus, quarum baſium quadrata alt itudinibus, vel diametris
              <lb/>
            æqualiter baſibus inclinatis reciprocantur, eſſe æqualia, & </s>
            <s xml:id="echoid-s7749" xml:space="preserve">quæ ſunt
              <lb/>
            æqualia, eſſe parabolarum, quarum altitudines, vel diametri æquali-
              <lb/>
            ter baſibus inclinatæ, baſium quadratis reciprocantur.</s>
            <s xml:id="echoid-s7750" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div776" type="section" level="1" n="458">
          <head xml:id="echoid-head478" xml:space="preserve">E. SECTIO V.</head>
          <note position="left" xml:space="preserve">E</note>
          <p style="it">
            <s xml:id="echoid-s7751" xml:space="preserve">_D_Eniq; </s>
            <s xml:id="echoid-s7752" xml:space="preserve">& </s>
            <s xml:id="echoid-s7753" xml:space="preserve">hoc obtinemus. </s>
            <s xml:id="echoid-s7754" xml:space="preserve">nempè omnia quadrata parabolarum,
              <lb/>
            regulis baſibus, quarum altitudines, veldiametri, baſibus æ-
              <lb/>
            qualiter inclinatæ, ad eaſdem baſes eandem rationem habeant, eſſe in-
              <lb/>
            ter ſe in tripla ratione baſium, vel altitudinum, vel diametrorum
              <lb/>
            æqualiter baſibus inclinatarum; </s>
            <s xml:id="echoid-s7755" xml:space="preserve">quæ omnia clarè, & </s>
            <s xml:id="echoid-s7756" xml:space="preserve">facilè patent.</s>
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