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

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            <s xml:id="echoid-s11260" xml:space="preserve">
              <pb o="433" file="0453" n="453" rhead="LIBER VI."/>
            ad ſectorem, ſed ad aliam quamcunq; </s>
            <s xml:id="echoid-s11261" xml:space="preserve">figuram ex ſectoribus com-
              <lb/>
            poſitam compararetur, oſtenderemus, eaſdem figuras eſſe inter ſe,
              <lb/>
            vt omnes earundem circumferentiæ, quod demonſtrare opus
              <lb/>
            erat.</s>
            <s xml:id="echoid-s11262" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1037" type="section" level="1" n="624">
          <head xml:id="echoid-head654" xml:space="preserve">COROLL ARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s11263" xml:space="preserve">_P_Atet aùtem, veluti oſtenſum eſt ſectores, AIO, AOB, eſſe vt om-
              <lb/>
            nes eorum circumferentiæ eodem modo demonſtrari poſſe, circu-
              <lb/>
            lum, VOB, & </s>
            <s xml:id="echoid-s11264" xml:space="preserve">ſectorem, AOB, & </s>
            <s xml:id="echoid-s11265" xml:space="preserve">in uniuerſam circulos, & </s>
            <s xml:id="echoid-s11266" xml:space="preserve">ſuos ſe-
              <lb/>
            ctores inter ſe eſſe, vt omnes eorum circumferentiæ.</s>
            <s xml:id="echoid-s11267" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1038" type="section" level="1" n="625">
          <head xml:id="echoid-head655" xml:space="preserve">THEOREMA VI. PROPOS. VI.</head>
          <p>
            <s xml:id="echoid-s11268" xml:space="preserve">SI in circulo ab eiuſdem centro ad circumferentiam
              <lb/>
            curuam quædam linea illius conditionis producatur,
              <lb/>
            vt quæcunq; </s>
            <s xml:id="echoid-s11269" xml:space="preserve">rectæ lineæ à centro ad ipſam pertingentes
              <lb/>
            (præter illius extrema iungentem) intra illud ſpatium ca-
              <lb/>
            dant, quod comprehenditur ducta curua, & </s>
            <s xml:id="echoid-s11270" xml:space="preserve">illius extrema
              <lb/>
            iungente: </s>
            <s xml:id="echoid-s11271" xml:space="preserve">Erit dictum ſpatium ad propoſitum circulum,
              <lb/>
            vel quemcunq; </s>
            <s xml:id="echoid-s11272" xml:space="preserve">ſectorem, vt omnes eiuſdem circumferen-
              <lb/>
            tiæ ad omnes illius circumferentias.</s>
            <s xml:id="echoid-s11273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11274" xml:space="preserve">Sit quicunque circulus, NOQT, & </s>
            <s xml:id="echoid-s11275" xml:space="preserve">centrum, A, curua, AFN,
              <lb/>
            ducta à centro, A, ad periphæriam, cui incidat in, N, & </s>
            <s xml:id="echoid-s11276" xml:space="preserve">fit eius
              <lb/>
            conditionis, qualis ſuppoſitum eſt, ſitq; </s>
            <s xml:id="echoid-s11277" xml:space="preserve">iuncta, AN, Dico igitur
              <lb/>
              <figure xlink:label="fig-0453-01" xlink:href="fig-0453-01a" number="312">
                <image file="0453-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0453-01"/>
              </figure>
            ſpatium, ſeu figuram, AFN, ad
              <lb/>
            circulum, NOQT, vel ad quem-
              <lb/>
            cunque ſectorem, eſſe vt omnes
              <lb/>
            eiuſdem circumferentiæ ad om-
              <lb/>
            nes illius circumferentias. </s>
            <s xml:id="echoid-s11278" xml:space="preserve">Fiat
              <lb/>
            vt circulus, NOQT, ad figuram,
              <lb/>
            NFA, ita circumferentia, NOQ
              <lb/>
            T, ad circumferentiam, QR, ita
              <lb/>
            enim erit, & </s>
            <s xml:id="echoid-s11279" xml:space="preserve">circulus, NOQT,
              <lb/>
            ad ſectorem, QAR, iunctis, QA,
              <lb/>
            AR, vnde ſector, QAR, erit æ-
              <lb/>
            qualis figuræ, AFN, vel ergo
              <lb/>
            omnes circumferentiæ, QAR, æquantur etiam omnibus circum-
              <lb/>
            ferentijs figuræ, AFN, & </s>
            <s xml:id="echoid-s11280" xml:space="preserve">ſic quia fector, QAR, ad circulum, </s>
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