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

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            <s xml:id="echoid-s11625" xml:space="preserve">
              <pb o="454" file="0474" n="474" rhead="GEOMETRIÆ"/>
            ergo, ΦΖ, erit æqualis circumferentiæ, IK, & </s>
            <s xml:id="echoid-s11626" xml:space="preserve">eſt altitudo triangu-
              <lb/>
              <note position="left" xlink:label="note-0474-01" xlink:href="note-0474-01a" xml:space="preserve">Corol. 2.
                <lb/>
              3. huius.</note>
            li, LΦ Ζ, ideſt L4, æqualis ipſi, kA, ergo triangulus, LΦΖ, ſectori,
              <lb/>
            KAI, æqualis erit. </s>
            <s xml:id="echoid-s11627" xml:space="preserve">Eodem modo oſtendemus triangulum, LVB,
              <lb/>
              <note position="left" xlink:label="note-0474-02" xlink:href="note-0474-02a" xml:space="preserve">Elici tur
                <lb/>
              ex Cor. 1.
                <lb/>
              3. huius.</note>
            æquari ſectori, AXS, & </s>
            <s xml:id="echoid-s11628" xml:space="preserve">triangulum, LO7, ſectori, ATM, & </s>
            <s xml:id="echoid-s11629" xml:space="preserve">tan-
              <lb/>
            dem triangulum, Ab
              <emph style="sub">9</emph>
            Ω, ſectori, AHG, ergo figura inſcripta trili-
              <lb/>
            neo, LQΩ, æqualis erit inſcriptæ ſpatio, GMSIB, eſt autem illa
              <lb/>
            maior ſpatio, GMSIB, èrgo figura inſcripta ſpatio, GMSIB, erit
              <lb/>
            eodem ſpatio, GMSIB, maior, quod eſt abſurdum, non ergo tri-
              <lb/>
            lineus, LQΩ, maior eſt ſpatio, GMSIB.</s>
            <s xml:id="echoid-s11630" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11631" xml:space="preserve">Sed dico neq; </s>
            <s xml:id="echoid-s11632" xml:space="preserve">eſſe minorem eodem ſpatio, GMSIB, ſi enim eſt
              <lb/>
            ſit adhuc defectus ſpatium, 8, modo autem ſupra adhibito circum-
              <lb/>
            ſcribatur trilineo, ΙΩQ, figura, & </s>
            <s xml:id="echoid-s11633" xml:space="preserve">alia inſcribatur ex triangulis
              <lb/>
            compoſita, ita vt circumſcripta fuperet inſcriptam minori ſpatio,
              <lb/>
            quam ſit, 8, deſeruiant autem nobis iam in prima parte deſcriptæ
              <lb/>
            figuræ, tum intra, & </s>
            <s xml:id="echoid-s11634" xml:space="preserve">extra trilineum, LΩQ, tum intra, vel extra
              <lb/>
            ſpatium, GMSIB. </s>
            <s xml:id="echoid-s11635" xml:space="preserve">Igitur figura circumſcripta trilineo, LΩQ, ſu-
              <lb/>
            perabit eundem trilineum multò minori ſpatio, quam ſit, 8, nem-
              <lb/>
            pè quam ſpatium, GMSIB, excedat trilineum, LΩQ, ergo figura
              <lb/>
            huic trilineo circumſcripta erit minor ſpatio, GMSIB, oſtendemus
              <lb/>
            autem eandem ęquari figurę circumſcriptæ eidem ſpatio, GMSIB,
              <lb/>
            modo ſuprapoſito, ergo figura circumſcripta ſpatio, GMSIB, erit
              <lb/>
            eodem minor, quod eſt abſurdum, igitur trilineus, LΩQ, neq; </s>
            <s xml:id="echoid-s11636" xml:space="preserve">eſt
              <lb/>
            maior, neq; </s>
            <s xml:id="echoid-s11637" xml:space="preserve">minor ſpatio, GMSIB, ergo eſt eidem æqualis, & </s>
            <s xml:id="echoid-s11638" xml:space="preserve">eſt
              <lb/>
            triangulus, LQΣ, æqualis circulo, CDFB, ergo circulus, CDFB,
              <lb/>
              <note position="left" xlink:label="note-0474-03" xlink:href="note-0474-03a" xml:space="preserve">Ex ant.</note>
            ad ſpatium, GMSIB, erit vt triangulus, LQΣ, ad tr lineum, LQΩ,
              <lb/>
            eſt autem triangulus, LQΣ, ad trilineum, LQΩ, vt quadratum, P
              <lb/>
            Lad rectangulum, ΡLβ, vnam {1/3}. </s>
            <s xml:id="echoid-s11639" xml:space="preserve">quadrati, Ρβ, ergo circulus, CD
              <lb/>
            FB, ad ſpatium, GMSIB, erit vt quadratum, PL, ad rectangulum,
              <lb/>
            ΡLβ, vna cum {1/3}. </s>
            <s xml:id="echoid-s11640" xml:space="preserve">quadrati, Ρβ, ideſt vt quadratum, BA, ad rectan-
              <lb/>
            gulum, BAG, vna cum {1/3}. </s>
            <s xml:id="echoid-s11641" xml:space="preserve">quadrati, GB, quod erat nobis oſtendẽ-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s11642" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1068" type="section" level="1" n="640">
          <head xml:id="echoid-head670" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s11643" xml:space="preserve">_P_Oterant autem, vt in Prop. </s>
            <s xml:id="echoid-s11644" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11645" xml:space="preserve">& </s>
            <s xml:id="echoid-s11646" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11647" xml:space="preserve">huius, componi figuræ, quæ
              <lb/>
            circumſcrihuntur, & </s>
            <s xml:id="echoid-s11648" xml:space="preserve">inſcrihuntur, ex trapezijs, in quo caſu,
              <lb/>
            circumſcriptio, & </s>
            <s xml:id="echoid-s11649" xml:space="preserve">inſcriptio intelligi dehuiſſet cir ca trilineum, Q
              <lb/>
            ΩΣ, vel in ſupra demonſtratis propoſitionibus poterant dicta figuræ
              <lb/>
            ex triangulis componi, veluti in hac effectum eſt, & </s>
            <s xml:id="echoid-s11650" xml:space="preserve">tunc circumſcri-
              <lb/>
            ptio, & </s>
            <s xml:id="echoid-s11651" xml:space="preserve">inſcriptio ſectionibus, FLH, in Schem ate poſterioris demõſtra-
              <lb/>
            t ionis Prop. </s>
            <s xml:id="echoid-s11652" xml:space="preserve">9. </s>
            <s xml:id="echoid-s11653" xml:space="preserve">& </s>
            <s xml:id="echoid-s11654" xml:space="preserve">H℟F, in Propoſ. </s>
            <s xml:id="echoid-s11655" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11656" xml:space="preserve">fieridebuiſſet intelligi, banc
              <lb/>
            tamen varietatem proſequutus ſum, vt pateat vtroq; </s>
            <s xml:id="echoid-s11657" xml:space="preserve">modo nos, quod
              <lb/>
            inquirimus, obtinere poſſe.</s>
            <s xml:id="echoid-s11658" xml:space="preserve"/>
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