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

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          <pb o="463" file="0483" n="483" rhead="LIBER VI."/>
          <p>
            <s xml:id="echoid-s11860" xml:space="preserve">Series ſpatiorum 1. </s>
            <s xml:id="echoid-s11861" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11862" xml:space="preserve">3. </s>
            <s xml:id="echoid-s11863" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11864" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11865" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11866" xml:space="preserve">7.</s>
            <s xml:id="echoid-s11867" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11868" xml:space="preserve">Series numerorum 1. </s>
            <s xml:id="echoid-s11869" xml:space="preserve">7. </s>
            <s xml:id="echoid-s11870" xml:space="preserve">19. </s>
            <s xml:id="echoid-s11871" xml:space="preserve">37. </s>
            <s xml:id="echoid-s11872" xml:space="preserve">61. </s>
            <s xml:id="echoid-s11873" xml:space="preserve">91. </s>
            <s xml:id="echoid-s11874" xml:space="preserve">127.</s>
            <s xml:id="echoid-s11875" xml:space="preserve"/>
          </p>
          <figure number="328">
            <image file="0483-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0483-01"/>
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          <p>
            <s xml:id="echoid-s11876" xml:space="preserve">cum {1/3}. </s>
            <s xml:id="echoid-s11877" xml:space="preserve">quadrati, CB, ſi ergo, AB, ſtatuatur 3. </s>
            <s xml:id="echoid-s11878" xml:space="preserve">erit, AC, 6. </s>
            <s xml:id="echoid-s11879" xml:space="preserve">rectan-
              <lb/>
            gulum, CAB, 18. </s>
            <s xml:id="echoid-s11880" xml:space="preserve">tertia pars quadrati, BC, erit 3. </s>
            <s xml:id="echoid-s11881" xml:space="preserve">quæ iuncta ipſi
              <lb/>
            18. </s>
            <s xml:id="echoid-s11882" xml:space="preserve">efficit 21. </s>
            <s xml:id="echoid-s11883" xml:space="preserve">erit ergo qualium partium quadratum, AB, eſt 9. </s>
            <s xml:id="echoid-s11884" xml:space="preserve">re-
              <lb/>
            ctangulum, CAB, cum tertia parte quadrati, BC, 21. </s>
            <s xml:id="echoid-s11885" xml:space="preserve">& </s>
            <s xml:id="echoid-s11886" xml:space="preserve">tertia pars
              <lb/>
            quadrati, AB, eſt 3. </s>
            <s xml:id="echoid-s11887" xml:space="preserve">eſt igitur ſpatium, AIN, ad trilineum, AMN,
              <lb/>
            vt 3. </s>
            <s xml:id="echoid-s11888" xml:space="preserve">ad 21. </s>
            <s xml:id="echoid-s11889" xml:space="preserve">ideſt vt 1. </s>
            <s xml:id="echoid-s11890" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s11891" xml:space="preserve">Eodem modo reperiemus trilineum, A
              <lb/>
            NM, ad, AMH, eſſe vt 7. </s>
            <s xml:id="echoid-s11892" xml:space="preserve">ad 19. </s>
            <s xml:id="echoid-s11893" xml:space="preserve">& </s>
            <s xml:id="echoid-s11894" xml:space="preserve">hoc ad trilineum, AHF, vt 19.
              <lb/>
            </s>
            <s xml:id="echoid-s11895" xml:space="preserve">ad 37. </s>
            <s xml:id="echoid-s11896" xml:space="preserve">& </s>
            <s xml:id="echoid-s11897" xml:space="preserve">ſic deinceps, prout indicat ſeries numerorum ſupra poſi-
              <lb/>
            ta, quod demonſtrandum erat.</s>
            <s xml:id="echoid-s11898" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1081" type="section" level="1" n="648">
          <head xml:id="echoid-head678" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s11899" xml:space="preserve">_H_Inc patet ſi expoſita ſint ſpirales in quotcunque reuolutionibus
              <lb/>
            genitæ, initio circulationis exiſtente in, K, ſint autem volutæ
              <lb/>
            ipſæ, KL, LO, OP, PG, & </s>
            <s xml:id="echoid-s11900" xml:space="preserve">ſpirales eodem ordine procedentes, KRL, L
              <lb/>
            SO, OTP, PVG, quod ſi, KG, fuerit æqualis ipſi AE, & </s>
            <s xml:id="echoid-s11901" xml:space="preserve">diuiſa in pun-
              <lb/>
            ctis, L, O, P, prout diuiditur, AE, in punctis, B, C, D, ſpatium, KRL,
              <lb/>
              <note position="right" xlink:label="note-0483-01" xlink:href="note-0483-01a" xml:space="preserve">_Elicitur e@_
                <lb/>
              _9. huius._
                <lb/>
              _Elicitur_
                <lb/>
              _15. huiur._</note>
            erit æquale ſpatio, AIN, &</s>
            <s xml:id="echoid-s11902" xml:space="preserve">, LSO, trilineo, AMN, &</s>
            <s xml:id="echoid-s11903" xml:space="preserve">, OTP, trili-
              <lb/>
            neo, AMH, & </s>
            <s xml:id="echoid-s11904" xml:space="preserve">tãdem, PVG, trilineo, AHF, & </s>
            <s xml:id="echoid-s11905" xml:space="preserve">ſic deinceps, vnde
              <lb/>
            etiam hæc ſpatia ſe habebunt, prout indicat ſuprapoſita ſeries nume-</s>
          </p>
          <p>
            <s xml:id="echoid-s11906" xml:space="preserve">Secunda ſeries num. </s>
            <s xml:id="echoid-s11907" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11908" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11909" xml:space="preserve">12. </s>
            <s xml:id="echoid-s11910" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11911" xml:space="preserve">24. </s>
            <s xml:id="echoid-s11912" xml:space="preserve">30. </s>
            <s xml:id="echoid-s11913" xml:space="preserve">36.</s>
            <s xml:id="echoid-s11914" xml:space="preserve"/>
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