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

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            <s xml:id="echoid-s11593" xml:space="preserve">
              <pb o="453" file="0473" n="473" rhead="LIBER VI."/>
            AG, & </s>
            <s xml:id="echoid-s11594" xml:space="preserve">per, β, ducatur, βΔ, parallela ipſi, QP, ſecans curuam pa-
              <lb/>
            rabolæ in, Ω, & </s>
            <s xml:id="echoid-s11595" xml:space="preserve">iunctis, LΩ, producatur, LΩ, vſq; </s>
            <s xml:id="echoid-s11596" xml:space="preserve">ad, QP, cui in-
              <lb/>
              <note position="right" xlink:label="note-0473-01" xlink:href="note-0473-01a" xml:space="preserve">‘Corol’ .9.
                <lb/>
              huius, ad
                <lb/>
              poſter de.
                <lb/>
              moaſtr.</note>
            cidat in, Σ. </s>
            <s xml:id="echoid-s11597" xml:space="preserve">Quia igitur eſt, QP, ad, ΡΣ, vt, PL, ad, Lβ, per con-
              <lb/>
            uerſionem rationis, PQ, ad, QΣ, erit vt, LP, ad, Ρβ, quotuplex
              <lb/>
            ergo eſt, LP, ipſius, Ρβ, radio primi circuli æqualis, totuplex erit,
              <lb/>
            QP, ipſius, QΣ, eſt autem etiam totuplex, QP, circumferentiæ, C
              <lb/>
            DFB, ergo, QΣ, erit æqualis circumferentiæ, CDFB, eſt autem, L
              <lb/>
            P, æqualis ipſi, AB, ergo triangulus, LQΣ, circulo, CDFB, æqua-
              <lb/>
            lis erit. </s>
            <s xml:id="echoid-s11598" xml:space="preserve">Dico vlterius trilineum, LQΩ, æquari ſpatio circuli, CD
              <lb/>
              <note position="right" xlink:label="note-0473-02" xlink:href="note-0473-02a" xml:space="preserve">Iuxta 2.
                <lb/>
              huius</note>
            FB, nempè contento ſub ſpirali, GSIB, & </s>
            <s xml:id="echoid-s11599" xml:space="preserve">voluta, GB, ſi enim nõ,
              <lb/>
            erit eo maior, vel minor, ſit primò, maior quantitate ſpatij ſeorſim
              <lb/>
            expoſiti, 8, diuiſa autem bifariam, QΣ, in, ℟, iungatur, L℟, rur-
              <lb/>
            ſus bifariam diuidantur, Q℟, RΣ, in punctis, &</s>
            <s xml:id="echoid-s11600" xml:space="preserve">, Π, & </s>
            <s xml:id="echoid-s11601" xml:space="preserve">iungantur,
              <lb/>
            &</s>
            <s xml:id="echoid-s11602" xml:space="preserve">L, ΠL, & </s>
            <s xml:id="echoid-s11603" xml:space="preserve">ſic ſemper fiat donec deuentum ſit ad triangulum mi-
              <lb/>
            norem ſpatio, 8, ſit is triangulus, LΠΣ, per puncta autem, in qui-
              <lb/>
              <note position="right" xlink:label="note-0473-03" xlink:href="note-0473-03a" xml:space="preserve">Iuxta prè
                <lb/>
              10. Elem.</note>
            bus, LΠ, L℟, L&</s>
            <s xml:id="echoid-s11604" xml:space="preserve">, ſecant curuam, QΩ, ſcilicet per, O, V, Z, du-
              <lb/>
            cantur, QP, parallelæ, 7Γ, 69, Φ+, quæ ſi producantur ſecent, β
              <lb/>
            P, in punctis, 2, 3, 4, quia ergo, Q&</s>
            <s xml:id="echoid-s11605" xml:space="preserve">, &</s>
            <s xml:id="echoid-s11606" xml:space="preserve">℟, ℟Π, ΠΣ, ſunt æqua-
              <lb/>
            les facilè oſtendemus per Coroll. </s>
            <s xml:id="echoid-s11607" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s11608" xml:space="preserve">9. </s>
            <s xml:id="echoid-s11609" xml:space="preserve">huius, etiam, P4, 43, 32,
              <lb/>
              <note position="right" xlink:label="note-0473-04" xlink:href="note-0473-04a" xml:space="preserve">Iux. Cor.
                <lb/>
              1. tertiæ
                <lb/>
              huius.</note>
            2β, eſſe æquales, ſimiliter facilè oſtendemus, trapezia, QZ, ZV, V
              <lb/>
            O, & </s>
            <s xml:id="echoid-s11610" xml:space="preserve">triangulum, LΟΓ, ſimul collecta æquari triangulo, LΠΣ, .</s>
            <s xml:id="echoid-s11611" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s11612" xml:space="preserve">eſſe minora ſpatio, 8, habemus ergo ſpatio, LQΩ, circum ſcriptam
              <lb/>
            figuram ex triangulis, LQ&</s>
            <s xml:id="echoid-s11613" xml:space="preserve">, L+Z, L9V, LΓΟ, & </s>
            <s xml:id="echoid-s11614" xml:space="preserve">aliam eidem in-
              <lb/>
            ſcriptam ex triangulis, LZ+, LV6, LO7, LΩΣ, compoſitam,
              <lb/>
            quam circumſcripta excedit minori ſpatio, quam ſit, 8, ergo tri-
              <lb/>
            lineum, LQΩ, excedet inſcriptam multò minori ſpatio, ergo in-
              <lb/>
            ſcripta erit manior ſpatio, GMSIB, quod eſt abſurdum, nam ſi cen-
              <lb/>
            tro, A, ſemidiametris æqualibus ipſis, L4, L3, L2, deſcribantur ſe-
              <lb/>
            ctores, vel ſectorum reſidua. </s>
            <s xml:id="echoid-s11615" xml:space="preserve">AkIR, XSN, TME, habebimus ſpa-
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            tio, BISMG, inſcriptam figuram ex ſectoribus, vel ſectorum reſi-
              <lb/>
            duis iam dictis compoſitam, & </s>
            <s xml:id="echoid-s11616" xml:space="preserve">aliam circumſcriptam ex ſectori-
              <lb/>
            bus, vel ſectorum reſidius, BAC, IAR, SAN, MAE, compoſitam,
              <lb/>
              <note position="right" xlink:label="note-0473-05" xlink:href="note-0473-05a" xml:space="preserve">Corol. 9.
                <lb/>
              huius, ad
                <lb/>
              poſteric-
                <lb/>
              rem dc-
                <lb/>
              monſt.</note>
            & </s>
            <s xml:id="echoid-s11617" xml:space="preserve">quia, ΣQ, ad, QP, eſt vt, βΡ, ad, PL, &</s>
            <s xml:id="echoid-s11618" xml:space="preserve">, PQ. </s>
            <s xml:id="echoid-s11619" xml:space="preserve">ad, Q&</s>
            <s xml:id="echoid-s11620" xml:space="preserve">, eſt vt, L
              <lb/>
            P, ad, P4, ex æquali, ΣQ, ad, Q&</s>
            <s xml:id="echoid-s11621" xml:space="preserve">, erit vt, βΡ, ad, P4, ideſt vt GB,
              <lb/>
            ad, BK, ideſt vt circumferentia, CDFB, ad circumferentiam, CB,
              <lb/>
            (nam dum punctus, B, deſcribit totam circumferentiam, CDFB,
              <lb/>
            punctus deſcribens ſpiralem percurrit ipſam, GB, & </s>
            <s xml:id="echoid-s11622" xml:space="preserve">dum, B, deſcri-
              <lb/>
            pſit circumferentiam, CB, idem punctus percurrit ipſam, Bκ,) eſt
              <lb/>
              <note position="right" xlink:label="note-0473-06" xlink:href="note-0473-06a" xml:space="preserve">Elicitur
                <lb/>
              ex 4 Sex.
                <lb/>
              ti Elem.</note>
            autem, QΣ, æqualis circumferentiæ, CDFB, ergo, Q&</s>
            <s xml:id="echoid-s11623" xml:space="preserve">, æqualis
              <lb/>
            erit circumfer. </s>
            <s xml:id="echoid-s11624" xml:space="preserve">CB, eſt verò, Q&</s>
            <s xml:id="echoid-s11625" xml:space="preserve">, ad, ΦΖ, vt, PL, ad, L4, ideſt vt,
              <lb/>
            BA, ad, Ak, ideſt vt circumferentia, CB, ad circumferentiam, </s>
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