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

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            <s xml:id="echoid-s10730" xml:space="preserve">
              <pb o="411" file="0431" n="431" rhead="LIBER V."/>
            pipedo ſub, SO, & </s>
            <s xml:id="echoid-s10731" xml:space="preserve">quadrato, OY, cum {1/3}. </s>
            <s xml:id="echoid-s10732" xml:space="preserve">cubi, OY, ad parallele.
              <lb/>
            </s>
            <s xml:id="echoid-s10733" xml:space="preserve">pipedum ſub, ΛΩ, & </s>
            <s xml:id="echoid-s10734" xml:space="preserve">quadrato, Ω4, vna cum parallelepipedo ſub,
              <lb/>
            Λ4, & </s>
            <s xml:id="echoid-s10735" xml:space="preserve">compoſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s10736" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10737" xml:space="preserve">quadrati, Λ4, ab his dẽ-
              <lb/>
            pto parallelepipedo ſub, SO, & </s>
            <s xml:id="echoid-s10738" xml:space="preserve">quadrato, Ο6, cum {1/3}. </s>
            <s xml:id="echoid-s10739" xml:space="preserve">cubi, Ο6,
              <lb/>
            quod oſtendere opus erat.</s>
            <s xml:id="echoid-s10740" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div961" type="section" level="1" n="572">
          <head xml:id="echoid-head597" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s10741" xml:space="preserve">_H_Inc patet, quod eadem methodo oſtendemus omnia quadrátá fi-
              <lb/>
            guræ parallelogrammi, TV, nibil ab eis dempto, ad omnia
              <lb/>
            quadrata figuræ parallelogrammi βΩ, nibil pariter ab eis dempto, eſſe
              <lb/>
            Vt parallelepipeda primò dicta ad parallelepipeda ſecundò dicta.</s>
            <s xml:id="echoid-s10742" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div962" type="section" level="1" n="573">
          <head xml:id="echoid-head598" xml:space="preserve">THEOREMA XXIX. PROPOS. XXX.</head>
          <p>
            <s xml:id="echoid-s10743" xml:space="preserve">IN omnibus huius Lib. </s>
            <s xml:id="echoid-s10744" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10745" xml:space="preserve">Propoſitionibus, in quibus
              <lb/>
            duarum quarumcunq; </s>
            <s xml:id="echoid-s10746" xml:space="preserve">figurarum notificata fuit ratio
              <lb/>
            omn ium quadratorum, iuxta regulas in eiſdem aſſumptas,
              <lb/>
            nota etiam euadit ratio ſimiliarium ſolidorum, quæ exillis
              <lb/>
            gignuntur figuris, iuxta eaſdem regulas.</s>
            <s xml:id="echoid-s10747" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10748" xml:space="preserve">Quoniam enim oſtenſum eſt Lib. </s>
            <s xml:id="echoid-s10749" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10750" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s10751" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10752" xml:space="preserve">vt omnia qua-
              <lb/>
            drata duarum figurarum inter ſe ſumpta cum datis regulis, ita eſſe
              <lb/>
            ſolida ſimilaria genita ex ijſdem figuris iuxta eaſdem regulas, ideò
              <lb/>
            cum in huius Libri Propoſitionibus inuẽta eſt ratio omnium qua-
              <lb/>
            dratorum duarum figurarum cum talibus regulis, colligemus etiã
              <lb/>
            nunc eandem eſſe rationem duorum ſimilarium ſolidorum, quæ
              <lb/>
            ex illis figuris iuxta eaſdem regulas genita dicuntur, quæ amplius
              <lb/>
            in ſequentibus dilucidabimus ſingulas Propoſitiones, quæ oppor-
              <lb/>
            tunæ fuerint, denuò aſſumentes.</s>
            <s xml:id="echoid-s10753" xml:space="preserve"/>
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            <s xml:id="echoid-s10754" xml:space="preserve">Vnde cum in prima Propoſ. </s>
            <s xml:id="echoid-s10755" xml:space="preserve">exempli gratia oſtenſum eſt (con-
              <lb/>
            ſpecta denuò eiuſdem figura) omnia quadrata hyperbolæ, DBF,
              <lb/>
            regula, DF, ad omnia quadrata, AF, eſſe vt compoſitam ex, NB,
              <lb/>
            & </s>
            <s xml:id="echoid-s10756" xml:space="preserve">{1/3}, BE, ad, OE, eandem comperiemus habere rationem ſolidum
              <lb/>
            ſimilare genitum ex hyperbola, DBF, ad ſolidum ſimilare genitũ
              <lb/>
            ex, AF, iuxta communem regulam, DF; </s>
            <s xml:id="echoid-s10757" xml:space="preserve">& </s>
            <s xml:id="echoid-s10758" xml:space="preserve">eodem pacto collige-
              <lb/>
            mus, veluti omnia quadrata hyperbolæ, DBF, ad omnia quadra-
              <lb/>
            ta trianguli, DBF, ſunt vt compoſita ex ſexquialtera, OB, & </s>
            <s xml:id="echoid-s10759" xml:space="preserve">ex,
              <lb/>
            BE, ad, OE, ita eſſe ſolidum ſimilare genitum ex hyperbola, </s>
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