Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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            <s xml:id="echoid-s13187" xml:space="preserve">
              <pb o="511" file="0531" n="531" rhead="LIBER VII."/>
            H, ad parallelepipedum ſub, FX, & </s>
            <s xml:id="echoid-s13188" xml:space="preserve">quadrato, XH, ſub, HX, & </s>
            <s xml:id="echoid-s13189" xml:space="preserve">
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            quadrato, XF, cum {1/5}. </s>
            <s xml:id="echoid-s13190" xml:space="preserve">cubi, XF, hæc tria verò æquantur paralle-
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            lepipedo ſub, FX, & </s>
            <s xml:id="echoid-s13191" xml:space="preserve">rectangulo, FHX, cum {3/3}. </s>
            <s xml:id="echoid-s13192" xml:space="preserve">quadrati, FX, nam
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            parallelepipedum ſub, HX, & </s>
            <s xml:id="echoid-s13193" xml:space="preserve">quadrato, XF, idem eſt cum paral-
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            lelepipedo ſub, FX, & </s>
            <s xml:id="echoid-s13194" xml:space="preserve">rectangulo, FXH, quod ſi ipſum iunxeris
              <lb/>
            pcrallelepipedo ſub, FX, & </s>
            <s xml:id="echoid-s13195" xml:space="preserve">quadrato, XH, ſimul cum {1/3}. </s>
            <s xml:id="echoid-s13196" xml:space="preserve">cubi, FX,
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            ideſt vna cum parallelepipedo ſub, FX, & </s>
            <s xml:id="echoid-s13197" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s13198" xml:space="preserve">quadrati, FX, (cum
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            ſit communis altitudo) fiet parallelepipedum ſub, FX, & </s>
            <s xml:id="echoid-s13199" xml:space="preserve">rectan-
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            gulo, FXH, cum quadrato, XH, ideſt ſub, FX, & </s>
            <s xml:id="echoid-s13200" xml:space="preserve">rectangulo, FHX,
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            & </s>
            <s xml:id="echoid-s13201" xml:space="preserve">ſub {1/3}. </s>
            <s xml:id="echoid-s13202" xml:space="preserve">quadrati, FX, igitur cylindricus, FQ, ad fruſtum, ISRN,
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            erit vt parallelepipedum ſub, XF, & </s>
            <s xml:id="echoid-s13203" xml:space="preserve">quadrato, FH, ad parallelepi-
              <lb/>
            pedum ſub, XF, & </s>
            <s xml:id="echoid-s13204" xml:space="preserve">rectangulo, FHX, cum {1/3}. </s>
            <s xml:id="echoid-s13205" xml:space="preserve">quadrati, FX, ideſt vt
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            quadratum, FH, vel quadratum, PQ, ad rectangulum ſub, FH, HX,
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            vel ſub, PQ, LM, vna cum {1/3}. </s>
            <s xml:id="echoid-s13206" xml:space="preserve">quadrati, FX, differentiæ ipſarum
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            homologarum, PQ, LM. </s>
            <s xml:id="echoid-s13207" xml:space="preserve">Quoniam verò conicus, OSR, eſt {1/3}. </s>
            <s xml:id="echoid-s13208" xml:space="preserve">cy-
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              <note position="right" xlink:label="note-0531-01" xlink:href="note-0531-01a" xml:space="preserve">8. huius.</note>
            lindrici, FQ, idcircò adidem fruſtum, ISRN, conicus, OSR, erit
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            vt {1/3}. </s>
            <s xml:id="echoid-s13209" xml:space="preserve">quadrati, PQ, ad rectangulum ſub, PQ, LM, cum {1/3}. </s>
            <s xml:id="echoid-s13210" xml:space="preserve">quadra-
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            ti, FX, vel vt quadratum, PQ, ad rectangulum ſub, PQ, & </s>
            <s xml:id="echoid-s13211" xml:space="preserve">tripla,
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            LM, cum quadrato, FX, & </s>
            <s xml:id="echoid-s13212" xml:space="preserve">conuertendo fruſtum, ISRN, ad coni-
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            cum, OSR, erit vt rectangulum ſub, PQ, & </s>
            <s xml:id="echoid-s13213" xml:space="preserve">tripla, LM, cum {1/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s13214" xml:space="preserve">quadrati, FX, differentiæ earundem homologarum, ad quadra-
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            tum, PQ quæ oſtendere opus erat.</s>
            <s xml:id="echoid-s13215" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1180" type="section" level="1" n="705">
          <head xml:id="echoid-head738" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13216" xml:space="preserve">PEr ſuperiorem autem demonſtrationem ſuppletur prop. </s>
            <s xml:id="echoid-s13217" xml:space="preserve">28.
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            </s>
            <s xml:id="echoid-s13218" xml:space="preserve">1, 2. </s>
            <s xml:id="echoid-s13219" xml:space="preserve">necnon ei, quod colligitur in ſec. </s>
            <s xml:id="echoid-s13220" xml:space="preserve">L. </s>
            <s xml:id="echoid-s13221" xml:space="preserve">& </s>
            <s xml:id="echoid-s13222" xml:space="preserve">M. </s>
            <s xml:id="echoid-s13223" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s13224" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13225" xml:space="preserve">gen. </s>
            <s xml:id="echoid-s13226" xml:space="preserve">24. </s>
            <s xml:id="echoid-s13227" xml:space="preserve">
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            eiuſdem 1. </s>
            <s xml:id="echoid-s13228" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13229" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s13230" xml:space="preserve">autem prop. </s>
            <s xml:id="echoid-s13231" xml:space="preserve">28. </s>
            <s xml:id="echoid-s13232" xml:space="preserve">eſt in gratiam methodi indiui-
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            ſibilium. </s>
            <s xml:id="echoid-s13233" xml:space="preserve">Quod prop. </s>
            <s xml:id="echoid-s13234" xml:space="preserve">29. </s>
            <s xml:id="echoid-s13235" xml:space="preserve">eiuſdem 1. </s>
            <s xml:id="echoid-s13236" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13237" xml:space="preserve">ſi intelligamus in eius figu-
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            ra latera, CD, DB, deſcribere ſimiles figuras planas, in quibus tã-
              <lb/>
            quam in baſibus cylindrici conſiſtant, quorum latera ſint, CD,
              <lb/>
            pro figura, DB, & </s>
            <s xml:id="echoid-s13238" xml:space="preserve">DB, pro figura, CD, oſtendemus conſimili ibi
              <lb/>
            traditæ demonſtrationi cylindricum ſublateræ, DB, baſi figura, D
              <lb/>
            C, ad cylindricum ſub latere, DC, baſi figura, BD, prædictæ ſimili
              <lb/>
            eſſe vt, DC, ad, DB, & </s>
            <s xml:id="echoid-s13239" xml:space="preserve">ſic etiam eſſe conicum ſub lateribus, CB, B
              <lb/>
            D, baſi figura, CD, ad conicum ſub lateribus, BC, CD, baſi figura
              <lb/>
            ipſius, DB, habent enim cylindrici inter ſe, necnon & </s>
            <s xml:id="echoid-s13240" xml:space="preserve">conici, ra-
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            tionem, compoſitam ex ratione baſium, & </s>
            <s xml:id="echoid-s13241" xml:space="preserve">altitudinum, leu late-
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            rum æqualiter baſibus inclinatorum, vt ſuperius denuò animadu-
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              <note position="right" xlink:label="note-0531-02" xlink:href="note-0531-02a" xml:space="preserve">Annot. p-
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              5. & 8. hu.
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              ius.</note>
            crſum eſt: </s>
            <s xml:id="echoid-s13242" xml:space="preserve">Per hæc autem ſatisfit ctiam Sec. </s>
            <s xml:id="echoid-s13243" xml:space="preserve">N. </s>
            <s xml:id="echoid-s13244" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s13245" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13246" xml:space="preserve">gen. </s>
            <s xml:id="echoid-s13247" xml:space="preserve">34.</s>
            <s xml:id="echoid-s13248" xml:space="preserve"/>
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