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

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        <div xml:id="echoid-div737" type="section" level="1" n="432">
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              <pb o="309" file="0329" n="329" rhead="LIBER IV."/>
            ditiones reperiuntur etiam in lateribus circumſcriptorum illis paral-
              <lb/>
            lelogrammorum, vel in altitudine, & </s>
            <s xml:id="echoid-s7452" xml:space="preserve">baſi eorundem, quia baſis eſt
              <lb/>
            communis, & </s>
            <s xml:id="echoid-s7453" xml:space="preserve">reliquum latus axi, vel diametro parabola æquidiſtans,
              <lb/>
            ideò ſequuntur illicò oſtenſæ concluſiones pro parallelogrammis; </s>
            <s xml:id="echoid-s7454" xml:space="preserve">& </s>
            <s xml:id="echoid-s7455" xml:space="preserve">
              <lb/>
            conſequenter etiam pro ipſis parabolis, quarum ipſa parallelogramma
              <lb/>
            ſunt ſexquialtera, recipi poſſunt.</s>
            <s xml:id="echoid-s7456" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div738" type="section" level="1" n="433">
          <head xml:id="echoid-head453" xml:space="preserve">B. SECTIO II.</head>
          <note position="right" xml:space="preserve">B</note>
          <p style="it">
            <s xml:id="echoid-s7457" xml:space="preserve">_Q_Via ergo oſtenſum eſt pàrallelogramma, quæ ſunt in eadem altitu-
              <lb/>
            dine, eſſe inter ſe, vt baſes, & </s>
            <s xml:id="echoid-s7458" xml:space="preserve">quæ in eadem baſi, vel æqualibus
              <lb/>
            baſibus, eſſe interſe, vt altitudines, vel vtlinea à verticibus ad baſes
              <lb/>
            cum æquali inclinatione ad eaſdem ductæ: </s>
            <s xml:id="echoid-s7459" xml:space="preserve">ideò colligemus etiam para-
              <lb/>
            bolas, quæ ſunt circa eundem axem, vel diametrum, eſſe inter ſe, vt ba-
              <lb/>
            ſes; </s>
            <s xml:id="echoid-s7460" xml:space="preserve">& </s>
            <s xml:id="echoid-s7461" xml:space="preserve">quæ ſunt in eadem, vel æqualibus baſibus, eſſe inter ſe, vt alti,
              <lb/>
            tudines, vel vt lineæ, quæ à verticibus eorundem ad baſes cumæquali
              <lb/>
            inclinatione ducuntur, ſiue illa ſint axes, ſiue diametri.</s>
            <s xml:id="echoid-s7462" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div739" type="section" level="1" n="434">
          <head xml:id="echoid-head454" xml:space="preserve">C. SECTIO III.</head>
          <note position="right" xml:space="preserve">C</note>
          <p style="it">
            <s xml:id="echoid-s7463" xml:space="preserve">_S_Imiliter colligemus parabolas habere rationem compoſitam ex ra-
              <lb/>
            tione baſium, & </s>
            <s xml:id="echoid-s7464" xml:space="preserve">altitudinum, vel linearum, quæ à verticibus du-
              <lb/>
            cuntur, æqualiter baſibus inclinatarum, ſiue ſint axes, ſiue diametri.</s>
            <s xml:id="echoid-s7465" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div740" type="section" level="1" n="435">
          <head xml:id="echoid-head455" xml:space="preserve">D. SECTIO IV.</head>
          <note position="right" xml:space="preserve">D</note>
          <p style="it">
            <s xml:id="echoid-s7466" xml:space="preserve">_I_Tem parabolæ habentes baſes altitudinibus, vel lineis à verticibus
              <lb/>
            ductis æqualiter inclinatis reciprocas erunt æquales; </s>
            <s xml:id="echoid-s7467" xml:space="preserve">& </s>
            <s xml:id="echoid-s7468" xml:space="preserve">parabolæ
              <lb/>
            æquales, quarum diametri æqualiter ab baſes ſint inclinatæ, habebunt
              <lb/>
            baſes altitudinibus, vel lineis ductis à verticibus ad baſes æquali@er in-
              <lb/>
            clinatis reciprocas.</s>
            <s xml:id="echoid-s7469" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div741" type="section" level="1" n="436">
          <head xml:id="echoid-head456" xml:space="preserve">E. SECTIO V.</head>
          <note position="right" xml:space="preserve">E</note>
          <p style="it">
            <s xml:id="echoid-s7470" xml:space="preserve">_D_Eniq; </s>
            <s xml:id="echoid-s7471" xml:space="preserve">parabolæ, quarum axes, vel diametri, ad haſes ęqualiter in-
              <lb/>
            clinati, ad eaſdem baſes habent eandem rationem, ſunt in dupla
              <lb/>
            ratione baſium, ſiue axium, vel diametrorum, vel vt quadrata eorun-
              <lb/>
            dem: </s>
            <s xml:id="echoid-s7472" xml:space="preserve">N am parallelogramma his parabolis circumſcripta ſunt ſimilia,
              <lb/>
            & </s>
            <s xml:id="echoid-s7473" xml:space="preserve">ideò ſunt, vt quadrata laterum homologorum, quæ vel ſunt axes, aut
              <lb/>
            diametri, vel baſes dictarum parabolarum, & </s>
            <s xml:id="echoid-s7474" xml:space="preserve">ideò etiam ipſæ parabolæ
              <lb/>
            ſunt, vt quadrata axium, vel diametrorum æqualiter baſibus inclina-
              <lb/>
            tarum, vel vt quadrata baſium, quæ omnia facilè patent.</s>
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