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

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            <s xml:id="echoid-s11782" xml:space="preserve">
              <pb o="461" file="0481" n="481" rhead="LIBER VI."/>
            ſub, YT, & </s>
            <s xml:id="echoid-s11783" xml:space="preserve">quadrato, TE, cum cubo, TY, vel vt horum ſub tri-
              <lb/>
            pla .</s>
            <s xml:id="echoid-s11784" xml:space="preserve">i. </s>
            <s xml:id="echoid-s11785" xml:space="preserve">vt parallelepipedum ſub, ZY, & </s>
            <s xml:id="echoid-s11786" xml:space="preserve">quadrato, YE, ſub, EY, & </s>
            <s xml:id="echoid-s11787" xml:space="preserve">
              <lb/>
            quadrato, YZ; </s>
            <s xml:id="echoid-s11788" xml:space="preserve">.</s>
            <s xml:id="echoid-s11789" xml:space="preserve">i. </s>
            <s xml:id="echoid-s11790" xml:space="preserve">ſub, ZY, & </s>
            <s xml:id="echoid-s11791" xml:space="preserve">rectangulo, ZYE, cum tertia parte
              <lb/>
            cubi, ZY, quæ conficiunt parallelepipedum ſub, ZY, & </s>
            <s xml:id="echoid-s11792" xml:space="preserve">his iunctis
              <lb/>
              <note position="right" xlink:label="note-0481-01" xlink:href="note-0481-01a" xml:space="preserve">35 l. 2.
                <lb/>
              33. l. 2.</note>
            ideſt rectangulo, ZYE, quadrato, YE, cum tertia parte quadrati,
              <lb/>
            ZY, ideſt ſub, ZY, & </s>
            <s xml:id="echoid-s11793" xml:space="preserve">rectangulo, ZEY, cum tertia parte quadrati,
              <lb/>
            ZY, ad parallelepipedum ſub, YT, & </s>
            <s xml:id="echoid-s11794" xml:space="preserve">quadrato, TE, ſub, ET, & </s>
            <s xml:id="echoid-s11795" xml:space="preserve">
              <lb/>
            quadrato, TY, cum tertia parte cubi, TY, quæ eſſe æqualia oſtẽ-
              <lb/>
            demus parallelepipedo ſub, YT, & </s>
            <s xml:id="echoid-s11796" xml:space="preserve">rectangulo YET, cum tertia
              <lb/>
            parte quadrati, YT, igitur trilineum, EQX, ad trilineum, EXI,
              <lb/>
            erit vt parallelepipedum ſub, ZY, & </s>
            <s xml:id="echoid-s11797" xml:space="preserve">rectangulo, ZEY, cum tertia
              <lb/>
            @arte quadrati, ZY, ad parallelepipedum ſub, YT, ideſt ſub, ZY,
              <lb/>
              <note position="right" xlink:label="note-0481-02" xlink:href="note-0481-02a" xml:space="preserve">B. G. Cor.
                <lb/>
              4. gener.
                <lb/>
              34. l. 2.</note>
            & </s>
            <s xml:id="echoid-s11798" xml:space="preserve">ſub rectangulo, YET, cum tertia parte quadrati, TY, & </s>
            <s xml:id="echoid-s11799" xml:space="preserve">quia
              <lb/>
            hæc parallelepipeda ſunt in eadem altitudine, ideo ſunt vt baſes,
              <lb/>
            igitur trilineum, EQX, ad trilineum, EXI, erit vt rectangulum, ZE
              <lb/>
              <note position="right" xlink:label="note-0481-03" xlink:href="note-0481-03a" xml:space="preserve">Blicitur ex
                <lb/>
              9. huius.
                <lb/>
              Elicitur
                <lb/>
              ex 15. hui
                <lb/>
              us.</note>
            Y, cum tertia parte quadrati, YZ, ad rectangulum, YET, cum ter-
              <lb/>
            tia parte quadrati, YT, eſt autem ſectio, E℟I, æqualis ſpatio, AG
              <lb/>
            H, & </s>
            <s xml:id="echoid-s11800" xml:space="preserve">trilineum, EXI, ſpatio, HPMH, & </s>
            <s xml:id="echoid-s11801" xml:space="preserve">trilineum, EQX, ſpatio,
              <lb/>
            MZSBM, ergo ſpatium, AGH, ad ſpatium, HPMH, erit vt ter-
              <lb/>
            tia pars quadrati, TE, ad rectangulum, TEY, cum tertia parte
              <lb/>
            quadrati, TY, ideſt vt tertia pars quadrati, HA, ad rectangulum,
              <lb/>
            HAM, cum tertia parte quadrati, HM. </s>
            <s xml:id="echoid-s11802" xml:space="preserve">Similiter concludemus
              <lb/>
            ſpatium, HPMH, ad ſpatium, MZSBM, eſſe vt rectangulum, HA
              <lb/>
            M, cum tertia parte quadrati, HM, ad rectangulum, MAB, cum
              <lb/>
            tertia parte quadrati, MB, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s11803" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1078" type="section" level="1" n="646">
          <head xml:id="echoid-head676" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s11804" xml:space="preserve">_H_Inc patet ſi ducatur quædam tangens parabolam, quæ in partes
              <lb/>
            quotcunq; </s>
            <s xml:id="echoid-s11805" xml:space="preserve">æquales diuidatur, & </s>
            <s xml:id="echoid-s11806" xml:space="preserve">per puncta diuiſionum du-
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            cantur recta linea diametro parallelæ, quouſq; </s>
            <s xml:id="echoid-s11807" xml:space="preserve">incidant in curuam
              <lb/>
            parabolæ, his incidentiæ punctis cum contactus puncto iunctis, ſpa-
              <lb/>
            tium ſub prima iungente, & </s>
            <s xml:id="echoid-s11808" xml:space="preserve">ſubtenſa curua parabola ad trilineum
              <lb/>
            ſub prima, & </s>
            <s xml:id="echoid-s11809" xml:space="preserve">ſecunda iungente, & </s>
            <s xml:id="echoid-s11810" xml:space="preserve">ab illis appræhenſa curua, eſſe vt
              <lb/>
            tertia pars quadrati primæ partis tangentis eſt ad rectangulum ſub
              <lb/>
            prima parte, & </s>
            <s xml:id="echoid-s11811" xml:space="preserve">compoſito ex prima, & </s>
            <s xml:id="echoid-s11812" xml:space="preserve">ſecunda cum tertia parte qua-
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            dratis ſecundæ. </s>
            <s xml:id="echoid-s11813" xml:space="preserve">Similiter hoc trilineum ad trilineum ſub ſecunda,
              <lb/>
            & </s>
            <s xml:id="echoid-s11814" xml:space="preserve">tertia iungente, & </s>
            <s xml:id="echoid-s11815" xml:space="preserve">ab illis appræhenſa curua parabolæ, eſſe vt re-
              <lb/>
            ctangulum ſub prima, & </s>
            <s xml:id="echoid-s11816" xml:space="preserve">ſub compoſito ex prima, & </s>
            <s xml:id="echoid-s11817" xml:space="preserve">ſecunda parte
              <lb/>
            tangentis (enumeratione ſemper à puncto contactus incepta) vna cum
              <lb/>
            tertia parte quadrati ſecunda ad rectangulum ſub compoſita ex </s>
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