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

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            <s xml:id="echoid-s11300" xml:space="preserve">
              <pb o="435" file="0455" n="455" rhead="LIBER VI."/>
            FN, ergo omnes circumferentiæ figuræ circumſcriptæ minores
              <lb/>
              <note position="right" xlink:label="note-0455-01" xlink:href="note-0455-01a" xml:space="preserve">Exantec.</note>
            erunt omnibus circumferentijs ſectoris, QAR, cum verò figura ex
              <lb/>
            ſectoribus compoſita ad ſectorem, ſit vt omnes circumferentiæ ad
              <lb/>
            omnes circumferentias, ideò etiam figura circumſcripta minor erit
              <lb/>
            ſectore, QAR, & </s>
            <s xml:id="echoid-s11301" xml:space="preserve">multò minor eri
              <unsure/>
            t fig ira, AFN, ſectore, QAR, ſed
              <lb/>
            & </s>
            <s xml:id="echoid-s11302" xml:space="preserve">æqualis illi oſtenſa fuit, quod eſt abſurdum, igitur abſurdum etiã
              <lb/>
            eſt dicere omnes circumferentias ſectoris, QAR, maiores eſſe om-
              <lb/>
            nibus circumferentijs ſpatij, AFN. </s>
            <s xml:id="echoid-s11303" xml:space="preserve">Dico nunc neque eſſe mino-
              <lb/>
            res, ſi hoc verum eſt, ſint minores omnibus circumferentijs ſecto-
              <lb/>
            ris, SAT, & </s>
            <s xml:id="echoid-s11304" xml:space="preserve">repetita eadem conſtructione, ſit ſpatio, AFN, circũ-
              <lb/>
            ſcripta figura ex ſectoribus compoſita, & </s>
            <s xml:id="echoid-s11305" xml:space="preserve">alia inſcripta, ita vt cir-
              <lb/>
            cumſcriptæ figurę omnes circumferentiæ ſuperent omnes circum-
              <lb/>
            ferentias inſcriptæ minori quantitate, quam ſint omnes circum-
              <lb/>
            ferentiæ ſectoris, SAT, ergo omnes circumferentiæ figuræ, AFN,
              <lb/>
            ſuperabunt omnes circumferentias figuræ inſcriptæ multò minori
              <lb/>
            quantitate, quam eædem ſuperent omnes circumferentias, QAR,
              <lb/>
            ergo omnes circumferentię inſcriptæ figuræ maiores erunt omni-
              <lb/>
            bus circumferentijs ſectoris, QAR, ergo figura inſcripta maior e-
              <lb/>
            tiam erit ſectore, QAR, & </s>
            <s xml:id="echoid-s11306" xml:space="preserve">eodem multò maior erit figura, AFN,
              <lb/>
            contra hypoteſim, eſt enim illi æ qualis, quod eſt obſurdum, igitur
              <lb/>
            abſurdum etiam eſt omnes circumferentias ſectoris, QAR, mino-
              <lb/>
            res eſſe omnibus circumferentijs figuræ, AFN, ſed neq; </s>
            <s xml:id="echoid-s11307" xml:space="preserve">ſunt illis
              <lb/>
            maiores, vt oſtenſum eſt, ergo ſunt eiſdem æquales, ſed omnes cir-
              <lb/>
            cumferentiæ ſectoris, AQR, ad circulum, OQSN, vel quemcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s11308" xml:space="preserve">ſectorem comparatæ ſunt, vt ſpatium ad ſpatium, ergo ſpatium
              <lb/>
              <note position="right" xlink:label="note-0455-02" xlink:href="note-0455-02a" xml:space="preserve">Exantec,</note>
            quoque, AFN, ad circulum, OQSN, vel ad quemcunque ſectorem,
              <lb/>
            erit, vt omnes illius circumfer. </s>
            <s xml:id="echoid-s11309" xml:space="preserve">ad omnes iſtius circumferentias,
              <lb/>
            quod, &</s>
            <s xml:id="echoid-s11310" xml:space="preserve">c.</s>
            <s xml:id="echoid-s11311" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1040" type="section" level="1" n="626">
          <head xml:id="echoid-head656" xml:space="preserve">THEOREMA VII. PROPOS. VII.</head>
          <p>
            <s xml:id="echoid-s11312" xml:space="preserve">SI in ſpiralem ex prima reuolutione ortam incidant duę
              <lb/>
            lineæ à puncto, quod eſt initium ſpiralis, & </s>
            <s xml:id="echoid-s11313" xml:space="preserve">producã-
              <lb/>
            tur vſq; </s>
            <s xml:id="echoid-s11314" xml:space="preserve">ad circumferentiam primi circuli, eandem rationẽ
              <lb/>
            inter ſe habebunt iſtæ in ſpiralem incidentes, quam arcus
              <lb/>
            circuli, medij inter terminum ſpiralis, & </s>
            <s xml:id="echoid-s11315" xml:space="preserve">limites linearum
              <lb/>
            productarum in citcumferentia factos, ſumptis in conſe-
              <lb/>
            quentia arcubus à fine ſpiralis.</s>
            <s xml:id="echoid-s11316" xml:space="preserve"/>
          </p>
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