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

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        <div xml:id="echoid-div1040" type="section" level="1" n="626">
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        </div>
        <div xml:id="echoid-div1041" type="section" level="1" n="627">
          <head xml:id="echoid-head657" xml:space="preserve">THEOREMA VIII. PROPOS. VIII.</head>
          <p>
            <s xml:id="echoid-s11317" xml:space="preserve">SI in ſpirales in alijs reuolutionibus genitas, quam in
              <lb/>
              <figure xlink:label="fig-0456-01" xlink:href="fig-0456-01a" number="314">
                <image file="0456-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0456-01"/>
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            prima incidant duę
              <lb/>
            lineæ ab initio ſpira-
              <lb/>
            lis, habebunt illæ in-
              <lb/>
            ter ſe eandem rationẽ,
              <lb/>
            quam arcus circuli pri-
              <lb/>
            mi, intercepti, veluti
              <lb/>
            dicitur in anteceden-
              <lb/>
            te, cum integra circũ-
              <lb/>
            ferentia toties aſſum-
              <lb/>
            pta, quotus eſt vnitate
              <lb/>
            minor reuolut ionum
              <lb/>
            numerus.</s>
            <s xml:id="echoid-s11318" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11319" xml:space="preserve">Hę duę Propoſitiones oſtenduntur ab Archimede lib. </s>
            <s xml:id="echoid-s11320" xml:space="preserve">de pir.
              <lb/>
            </s>
            <s xml:id="echoid-s11321" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s11322" xml:space="preserve">14. </s>
            <s xml:id="echoid-s11323" xml:space="preserve">& </s>
            <s xml:id="echoid-s11324" xml:space="preserve">15.</s>
            <s xml:id="echoid-s11325" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1043" type="section" level="1" n="628">
          <head xml:id="echoid-head658" xml:space="preserve">SCOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s11326" xml:space="preserve">_I_N prima reuolutione orta ſit ſpiralis, ACER, & </s>
            <s xml:id="echoid-s11327" xml:space="preserve">RTV MG, in ſe-
              <lb/>
            cunda, &</s>
            <s xml:id="echoid-s11328" xml:space="preserve">, AC, AE, pertingant ad primam, AV, AM, ad ſecun-
              <lb/>
            dam, erit, AC, ad, AE, vt circumferentia, RSO, ad, RSN, AV, verò
              <lb/>
            ad, AM, erit vt circumferentia tota, RNOS, cum, RSO, ad, RNOS,
              <lb/>
            totam, cum, RSON, &</s>
            <s xml:id="echoid-s11329" xml:space="preserve">, ſic in cæteris.</s>
            <s xml:id="echoid-s11330" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1044" type="section" level="1" n="629">
          <head xml:id="echoid-head659" xml:space="preserve">THEOREMA IX. PROPOS. IX.</head>
          <p>
            <s xml:id="echoid-s11331" xml:space="preserve">SPatium compręhenſum à ſpirali ex prima reuolutione
              <lb/>
            orta, & </s>
            <s xml:id="echoid-s11332" xml:space="preserve">prima linea, quæ initium eſt reuolutionis, eſt
              <lb/>
            tertia pars primi circuli.</s>
            <s xml:id="echoid-s11333" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11334" xml:space="preserve">Sit ſpiralis in prima reuolutione genita ipſa, AIE, AE, verò re-
              <lb/>
            uolutionis initium, & </s>
            <s xml:id="echoid-s11335" xml:space="preserve">centro, A, interuallo, AE, ſit primus circu-
              <lb/>
            lus deſcriptus, ESM. </s>
            <s xml:id="echoid-s11336" xml:space="preserve">Dico ſpatium, AIE, tertiam partem eſſe cir-
              <lb/>
            culi, EMS. </s>
            <s xml:id="echoid-s11337" xml:space="preserve">Sumpto itaq; </s>
            <s xml:id="echoid-s11338" xml:space="preserve">vtcunq; </s>
            <s xml:id="echoid-s11339" xml:space="preserve">puncto, vt, V, in, AE, centro,
              <lb/>
            A, interuallo, AV, circulus deſcribatur, VIT, & </s>
            <s xml:id="echoid-s11340" xml:space="preserve">iuncta, AI, </s>
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