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

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        <div xml:id="echoid-div1174" type="section" level="1" n="702">
          <pb o="509" file="0529" n="529" rhead="LIBER VII."/>
        </div>
        <div xml:id="echoid-div1176" type="section" level="1" n="703">
          <head xml:id="echoid-head736" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s13124" xml:space="preserve">_C_Vm verò etiam cylindrici in baſibus dictorum fruſtorum, & </s>
            <s xml:id="echoid-s13125" xml:space="preserve">in
              <lb/>
            æqualibus cum eiſdem altituainibus conſtituti, ſint inter ſe vt
              <lb/>
            baſes, erunt etiam inter ſe vt dicta fruſta, & </s>
            <s xml:id="echoid-s13126" xml:space="preserve">permutando habebunt
              <lb/>
              <note position="right" xlink:label="note-0529-01" xlink:href="note-0529-01a" xml:space="preserve">_5. huius._</note>
            eandem rationem ad dicta fruſta, vnde propoſito quocunq; </s>
            <s xml:id="echoid-s13127" xml:space="preserve">fruſto coni-
              <lb/>
            co, & </s>
            <s xml:id="echoid-s13128" xml:space="preserve">cylindrico in eadem baſi, & </s>
            <s xml:id="echoid-s13129" xml:space="preserve">altitudine, cum eo exiſtente, vt
              <lb/>
            rationem cylindrici ad fruſtum conicum inueniamus, ſufficiet alicuius
              <lb/>
            cylindrici præfatæ altitudinis rationem ad fruſtum conicum in eadem
              <lb/>
            baſi, & </s>
            <s xml:id="echoid-s13130" xml:space="preserve">altitudine cum eo exiſtens inuenire, ex ea enim propoſiti cylin
              <lb/>
            drici, & </s>
            <s xml:id="echoid-s13131" xml:space="preserve">fruſti conici ratio illicò apparebit. </s>
            <s xml:id="echoid-s13132" xml:space="preserve">Per hanc autem Propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s13133" xml:space="preserve">ſatisfit etiam Prop. </s>
            <s xml:id="echoid-s13134" xml:space="preserve">27. </s>
            <s xml:id="echoid-s13135" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s13136" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13137" xml:space="preserve">& </s>
            <s xml:id="echoid-s13138" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s13139" xml:space="preserve">K. </s>
            <s xml:id="echoid-s13140" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s13141" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13142" xml:space="preserve">gen. </s>
            <s xml:id="echoid-s13143" xml:space="preserve">34. </s>
            <s xml:id="echoid-s13144" xml:space="preserve">eiuſdem Lib. </s>
            <s xml:id="echoid-s13145" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13146" xml:space="preserve">
              <lb/>
            vbi contenditur probare, conicorum fruſta in eadem baſi, & </s>
            <s xml:id="echoid-s13147" xml:space="preserve">altitudi-
              <lb/>
            ne exiſtentia, eſſe inuicem æqualia, hoc enim per hanc Prop maniſe-
              <lb/>
            ſtum eſt.</s>
            <s xml:id="echoid-s13148" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1178" type="section" level="1" n="704">
          <head xml:id="echoid-head737" xml:space="preserve">THEOREMA X PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s13149" xml:space="preserve">CYlindri cus ad fruſtum conicum quodcunq; </s>
            <s xml:id="echoid-s13150" xml:space="preserve">in eadem
              <lb/>
            baſi, & </s>
            <s xml:id="echoid-s13151" xml:space="preserve">altitudine cum eo conſtitutum (ſumptis dua-
              <lb/>
              <emph style="bf">bus homologis in oppoſitis baſibus fruſti conici) eam ha-</emph>
              <lb/>
              <emph style="bf">bet rationem, quam quadratum maioris homologarum ad</emph>
              <lb/>
              <emph style="bf">rectangulum ſub ambabus homologis, vna cum tertia</emph>
              <lb/>
            parte quadrati differentiæ earundem. </s>
            <s xml:id="echoid-s13152" xml:space="preserve">Idem verò fruſtum
              <lb/>
            ad conicum in eadem baſi, & </s>
            <s xml:id="echoid-s13153" xml:space="preserve">altitudine, cum eo exiſten-
              <lb/>
            tem, erit vt rectangulum ſub maiori, & </s>
            <s xml:id="echoid-s13154" xml:space="preserve">tripla minoris, vna
              <lb/>
              <emph style="bf">cum quadrato diferentiæ earundem homologarum, ad</emph>
              <lb/>
            maioris quadratum.</s>
            <s xml:id="echoid-s13155" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13156" xml:space="preserve">Sint in quacunque baſi, PRQS, & </s>
            <s xml:id="echoid-s13157" xml:space="preserve">eadem altitudine cylindri-
              <lb/>
            cus, FQ, fi uſtum conici, BPRQS, nempè, LNMISR, in baſi mi-
              <lb/>
            noriquoque, LNMI, & </s>
            <s xml:id="echoid-s13158" xml:space="preserve">conicus, OPRQS, ſecto autem quomodo-
              <lb/>
            cunq; </s>
            <s xml:id="echoid-s13159" xml:space="preserve">conico plano per verticem acto, producatur triangulum, B
              <lb/>
              <note position="right" xlink:label="note-0529-02" xlink:href="note-0529-02a" xml:space="preserve">Coro. 21.
                <lb/>
              l. 1.</note>
            PQ, ſecans oppoſitas baſes fruſti conici in rectis, LM, PQ, quæ
              <lb/>
            erunt homologæ ſimilium ſigurarum, LNMI, PRQS, ſimiliter,
              <lb/>
            codem extenſo plano, ac completo cylindrico in eadem altitudi-
              <lb/>
            ne cum conico, BRS, ſecentur eius oppoſitæ baſes, necnon ſigu-
              <lb/>
            ra, FVHG, ab eodem plano in rectis, AC, FH, PQ. </s>
            <s xml:id="echoid-s13160" xml:space="preserve">Dico </s>
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