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

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          <p>
            <s xml:id="echoid-s11491" xml:space="preserve">
              <pb o="446" file="0466" n="466" rhead="GEOMETRIÆ"/>
            producta, AC, vſq; </s>
            <s xml:id="echoid-s11492" xml:space="preserve">ad circumferentiam circuli, DG, cui incidat
              <lb/>
              <figure xlink:label="fig-0466-01" xlink:href="fig-0466-01a" number="320">
                <image file="0466-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0466-01"/>
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            in, O, portio igi-
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            tur circuli, CAV
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            N, ad portionem
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            circuli, DAEGO,
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            habet rationem
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            compoſitá ex ea,
              <lb/>
            quam habet por-
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              <note position="left" xlink:label="note-0466-01" xlink:href="note-0466-01a" xml:space="preserve">Deſin. 12.
                <lb/>
              1. 1.</note>
            tio, CAVN, ad
              <lb/>
            portionem, OAE
              <lb/>
              <note position="left" xlink:label="note-0466-02" xlink:href="note-0466-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              3. huius.</note>
            G, ideſt ex ratio-
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            ne quadrati, VA,
              <lb/>
              <note position="left" xlink:label="note-0466-03" xlink:href="note-0466-03a" xml:space="preserve">33. Sexti.
                <lb/>
              Elem.
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              7. huius.</note>
            ad quadratum, A
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            E, & </s>
            <s xml:id="echoid-s11493" xml:space="preserve">ex ratione
              <lb/>
            portionis, OAEG, ad portionem, DAEGO, ideſt ex r@tione cir-
              <lb/>
            cumferentiæ, EGO, ad circumferentiam, EGD, ideſt ex ratione,
              <lb/>
            VA, ad, AE, duæ autem rationes quadrati, VA, ad qua lratum, A
              <lb/>
            E, & </s>
            <s xml:id="echoid-s11494" xml:space="preserve">ipſius, VA, ad, AE, componunt rationem cubi, VA, ad cu-
              <lb/>
            bum, AE, ergo portio, CAVN, ad portionem, DAEGO, erit vt
              <lb/>
            cubus, VA, ad cubum, AE, ſunt autem ſpatia, AXC, AXCD, ter-
              <lb/>
            tiæ partes dictarum portionum, ergo ſpacium, AXC, ad ſpatium,
              <lb/>
            AXCD, erit vt cubus, VA, ad cubum, AE, quoderat oſtenden-
              <lb/>
              <note position="left" xlink:label="note-0466-04" xlink:href="note-0466-04a" xml:space="preserve">Exantec.</note>
            dum.</s>
            <s xml:id="echoid-s11495" xml:space="preserve"/>
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        <div xml:id="echoid-div1058" type="section" level="1" n="636">
          <head xml:id="echoid-head666" xml:space="preserve">THEOREMA XII. PROPOS. XII.</head>
          <p>
            <s xml:id="echoid-s11496" xml:space="preserve">COmpræhenſum ſpatium ſub ſpirali, q æ eſt minor
              <lb/>
            ea, quæ ſub prima reuolutione fit, nec abet termi-
              <lb/>
            num initium ſpiralis, & </s>
            <s xml:id="echoid-s11497" xml:space="preserve">rectis, quæ à terminis ipſius in ſpi-
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            ralis initium ducuntur, ad ſectorem habentem radium æ-
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            qualem maiori earum, quæ à termino ad initium ſpiralis
              <lb/>
            ducuntur, arcum verò, qui intercipitur inter duas rectas
              <lb/>
            ſecundum eaſdem partes ſpiralis, habet eandem rationem,
              <lb/>
            quam rectangulum compræhenſum ſub rectis à terminis
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            in principium ſpiralis ductis, vna cum. </s>
            <s xml:id="echoid-s11498" xml:space="preserve">quadrati exceſſus,
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            quo maior dictarum linearum ſuperat minotẽ, ad quadra-
              <lb/>
            tum maioris linearum à terminis ad initium ſpiralis coniũ-
              <lb/>
            ctarum.</s>
            <s xml:id="echoid-s11499" xml:space="preserve"/>
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