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

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        <div xml:id="echoid-div1084" type="section" level="1" n="650">
          <pb o="468" file="0486" n="486" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div1086" type="section" level="1" n="651">
          <head xml:id="echoid-head681" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s11957" xml:space="preserve">_E_T quia in ſuprápoſitis Propoſitionibus baſium prædictorum ſoli-
              <lb/>
            dorum ratio fuit adinuenta, ideò eandem pro dictis ſolidis ratio-
              <lb/>
            nem inde colligemus.</s>
            <s xml:id="echoid-s11958" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1087" type="section" level="1" n="652">
          <head xml:id="echoid-head682" xml:space="preserve">THEOREMA XXII. PROPOS. XXII.</head>
          <p>
            <s xml:id="echoid-s11959" xml:space="preserve">PRimus cylindrus nonuplus eſt primi conici.</s>
            <s xml:id="echoid-s11960" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11961" xml:space="preserve">Hæc Propoſitio pariter manifeſta eſt, nam primus cylindrus ad
              <lb/>
            primum cylindricum eſt, vt primus circulus ad ſuum ſpatium
              <lb/>
            ideſt in ratione tripla, primus verò cylindricus ad primum conicũ
              <lb/>
            eſt in ratione tripla, quia ſunt in eadem baſi, quod eſt ſpatium pri-
              <lb/>
              <note position="left" xlink:label="note-0486-01" xlink:href="note-0486-01a" xml:space="preserve">1. Cor. 4.
                <lb/>
              gener. 34.
                <lb/>
              l. 2.</note>
            mi circuli, & </s>
            <s xml:id="echoid-s11962" xml:space="preserve">in eadem altitudine, & </s>
            <s xml:id="echoid-s11963" xml:space="preserve">ideò primus cylindrus ad
              <lb/>
            primum conicum eſt in ratione nonupla, quæ ex duabus triplis
              <lb/>
            conflatur.</s>
            <s xml:id="echoid-s11964" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1089" type="section" level="1" n="653">
          <head xml:id="echoid-head683" xml:space="preserve">THEOREMA XXIII. PROPOS. XXIII.</head>
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            <s xml:id="echoid-s11965" xml:space="preserve">SEcundus cylindrus ad ſecundum conicum eſt, vt tri-
              <lb/>
            plum quadrati radij ſecundi circuli, ad rectangulum
              <lb/>
            ſub radio eiuſdem ſecundi, & </s>
            <s xml:id="echoid-s11966" xml:space="preserve">radio primi circuli, vna cũ
              <lb/>
            tertia parte quadrati differentiæ eorundem radiorum.</s>
            <s xml:id="echoid-s11967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11968" xml:space="preserve">Secundus enim cylindrus ad ſecundum cylindricum eſt, vt ſecũ-
              <lb/>
              <note position="left" xlink:label="note-0486-02" xlink:href="note-0486-02a" xml:space="preserve">15, huius.</note>
            dus circulus ad ſuum ſpatium ideſt vt quadratum radij ſecundi cir-
              <lb/>
            culi ad rectangulum ſub radio eiuſdem, & </s>
            <s xml:id="echoid-s11969" xml:space="preserve">ſub radio primi vna cũ
              <lb/>
            tertia parce quadrati differentiæ eorundem radiorum, ſecundus ve-
              <lb/>
              <note position="left" xlink:label="note-0486-03" xlink:href="note-0486-03a" xml:space="preserve">1. Coro. 4.
                <lb/>
              gener. 14.
                <lb/>
              l. 2.</note>
            rò cylindricus triplus eſt conici ſecundi, quoniam in eadem baſi,
              <lb/>
            & </s>
            <s xml:id="echoid-s11970" xml:space="preserve">altitudine cum eo conſtituitur, ergo eſt ad illum, vt dictum re-
              <lb/>
            ctangulum ſub radijs primi, & </s>
            <s xml:id="echoid-s11971" xml:space="preserve">ſecundi circuli, vna cum tertia par-
              <lb/>
            te quadrati differentiæ eorundem ad horum coniunctorum tertiã
              <lb/>
            partem, & </s>
            <s xml:id="echoid-s11972" xml:space="preserve">ex æquali ſecundus cylindrus ad ſecundum conicum
              <lb/>
            erit, vt quadratum radij primi circuli ad tertiam partem rectangu-
              <lb/>
            li ſub radijs primi, & </s>
            <s xml:id="echoid-s11973" xml:space="preserve">ſecundi circuli, cum nona parte quadrati dif-
              <lb/>
            ferentiæ eorundem radiorum, ideſt, vt triplum quadrati radij ſe-
              <lb/>
            cundi circuli ad rectangulum ſub radijs primi, & </s>
            <s xml:id="echoid-s11974" xml:space="preserve">ſecundi circuli,
              <lb/>
            vna cum tertia parte quadrati differentiæ eorundem radiorum.</s>
            <s xml:id="echoid-s11975" xml:space="preserve"/>
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