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

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            <s xml:id="echoid-s11245" xml:space="preserve">
              <pb o="432" file="0452" n="452" rhead="GEOMETRIÆ"/>
            XEZ, ducta, HN, quæ abſcindat, NM, æqualem circumferentię,
              <lb/>
            CD, facilè oſtendemus, hæc autem erant demonſtranda.</s>
            <s xml:id="echoid-s11246" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1035" type="section" level="1" n="623">
          <head xml:id="echoid-head653" xml:space="preserve">THEOREMA V. PROPOS. V.</head>
          <p>
            <s xml:id="echoid-s11247" xml:space="preserve">QVicumque ſectores inter ſe comparati, ſeu quæcum-
              <lb/>
            que figuræ ex ſectoribus compoſitæ ad ſectores, vel
              <lb/>
            ad figuras ex ſectoribus compoſitas comparatæ, habent
              <lb/>
            eandem rationem, quam omnes ipſarum circumferentiæ
              <lb/>
            ad omnes illarum circumferentias.</s>
            <s xml:id="echoid-s11248" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11249" xml:space="preserve">Sint quicunque circuli ſuper centro, A, nempè, ECD, maior, &</s>
            <s xml:id="echoid-s11250" xml:space="preserve">,
              <lb/>
            VIO, minor, & </s>
            <s xml:id="echoid-s11251" xml:space="preserve">in, ECD, fit ſector quicunque, CAD, & </s>
            <s xml:id="echoid-s11252" xml:space="preserve">ſimiliter
              <lb/>
            in, VIO, quilibet ſector, OAB. </s>
            <s xml:id="echoid-s11253" xml:space="preserve">Dico ſectorem, CAD, ad ſectorẽ,
              <lb/>
            OAB, eſſe vt omnes circumferentias, CAD, ad omnes circumfe-
              <lb/>
            rentias, OAB. </s>
            <s xml:id="echoid-s11254" xml:space="preserve">Secent radij, CA, AD, circumferentiam, VIO, in
              <lb/>
              <figure xlink:label="fig-0452-01" xlink:href="fig-0452-01a" number="311">
                <image file="0452-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0452-01"/>
              </figure>
            punctis, I, O; </s>
            <s xml:id="echoid-s11255" xml:space="preserve">Eſt ergo ſector, CAD, ſi-
              <lb/>
            milis ſectori, IAO, & </s>
            <s xml:id="echoid-s11256" xml:space="preserve">ideo eſt ad illum,
              <lb/>
            vt omnes circumferentiæ ad omnes
              <lb/>
              <note position="left" xlink:label="note-0452-01" xlink:href="note-0452-01a" xml:space="preserve">Exantec.</note>
            circumferentias, ſed & </s>
            <s xml:id="echoid-s11257" xml:space="preserve">vt ſector, IAO,
              <lb/>
            ad ſectorem, OAB, ita omnes cir-
              <lb/>
            cumferentiæ ad omnes circumferen-
              <lb/>
            tias, nam ſector, IAO, ad, OAB,
              <lb/>
            eſt vt circumferentia, IO, ad, OB,
              <lb/>
            vt verò, IO, ab, OB, ſic, deſcripta cir-
              <lb/>
            cumferentia, STR, vtcumque, ipſa, ST,
              <lb/>
            ad, TR, eſt enim, IO, ad, ST, vt OA, ad,
              <lb/>
              <note position="left" xlink:label="note-0452-02" xlink:href="note-0452-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              3 huius.</note>
            AT, ideſt vt, OB, ad, TR, vnde, permu-
              <lb/>
            tando, vt, IO, 3d, OB, ſic, ST, ad, SR, & </s>
            <s xml:id="echoid-s11258" xml:space="preserve">vt vnum ad vnum, ita
              <lb/>
            omnia ad omnia, ideſt vt, IO, ad, OB, ita omnes circumferentiæ,
              <lb/>
            IAO, ſectoris ad omnes circumferentias ſectoris, OAB, ſed vt, IO,
              <lb/>
            ad, OB, ſic, vt dectũ eſt, ſe habet ſector, IAO, ad, OAB, ergo, IAO,
              <lb/>
            ad, OAB, eſt vt omnes circum ferentiæ, IAO, ad omnes circumfe-
              <lb/>
            rentias, OAB, ſed & </s>
            <s xml:id="echoid-s11259" xml:space="preserve">ſectorem, CAD, ad, IAO, eſſe oſtenſum eſt,
              <lb/>
            vt omnes circumferentiæ, CAD, ad omnes circumferentias, IAO,
              <lb/>
            ergo ex æquali ſector, CAD, ad ſectorem OAB, eſt vt omnes cir-
              <lb/>
            cumferentiæ, CAD, ad omnes circumferentias, OAB. </s>
            <s xml:id="echoid-s11260" xml:space="preserve">Et com-
              <lb/>
            ponendo figura compoſita ex ſectoribus, CAD, OAB, ad ſectorẽ,
              <lb/>
            OAB, erit vt omnes circumferentiæ figuę eiuſdem, ad omnes cir-
              <lb/>
            cumferentias ſectoris, OAB, veiuti etiam ſi prædicta figura </s>
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