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

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          <figure number="319">
            <image file="0464-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0464-01"/>
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          <p>
            <s xml:id="echoid-s11456" xml:space="preserve">Sit ſpiralis ex prima reuolutione orta, AOVE, primus circulus,
              <lb/>
            EYG, ſumptum in ſpirali vtcumq; </s>
            <s xml:id="echoid-s11457" xml:space="preserve">punctum, V, & </s>
            <s xml:id="echoid-s11458" xml:space="preserve">centro, A, in-
              <lb/>
            teruallo autem, AV, circulus deſcriptus, VHX. </s>
            <s xml:id="echoid-s11459" xml:space="preserve">Dico portionẽ,
              <lb/>
            AOVA, comprehenſam ſpiralis portione, AOV, & </s>
            <s xml:id="echoid-s11460" xml:space="preserve">recta, AV, eſ-
              <lb/>
            ſe {1/3}. </s>
            <s xml:id="echoid-s11461" xml:space="preserve">portionis eiuſdem circuli comprehenſæ rectis, AV, AC, & </s>
            <s xml:id="echoid-s11462" xml:space="preserve">
              <lb/>
            circumferentia, VHXC. </s>
            <s xml:id="echoid-s11463" xml:space="preserve">Exponatur triangulus rectangulus, HkF,
              <lb/>
            rectum habens angulum, FKH, cuius latus, HK, æquale ſit ipſi,
              <lb/>
            AC, & </s>
            <s xml:id="echoid-s11464" xml:space="preserve">kF, circumferentiæ, CXHV, erit ergo triangulus, HFk,
              <lb/>
            æqualis portioni circuli, cuius baſis eſt circumferentia, CXHV;
              <lb/>
            </s>
            <s xml:id="echoid-s11465" xml:space="preserve">
              <note position="left" xlink:label="note-0464-01" xlink:href="note-0464-01a" xml:space="preserve">2. huius.
                <lb/>
              10. l. 4.</note>
            deſcripta deinde intelligatur parabola, F℟H, cuius vertex, H,
              <lb/>
            quam tangat, KH, in, H, &</s>
            <s xml:id="echoid-s11466" xml:space="preserve">, FK, ſit axi eiuſdem æquidiſtans.
              <lb/>
            </s>
            <s xml:id="echoid-s11467" xml:space="preserve">Dico trilineum, H℟Fk, eſſe æqualem ſpatio circumferentia, VHX
              <lb/>
            C, ſpirali, VOA, & </s>
            <s xml:id="echoid-s11468" xml:space="preserve">recta, AC, contento (quod ſpatium breuitatis
              <lb/>
            cauſa dicatur reſiduum portionis circuli, VHC,) ſi enim non, erit
              <lb/>
            co maius, vel minus, ſit primò maius, & </s>
            <s xml:id="echoid-s11469" xml:space="preserve">vt in antecedenti trilineo,
              <lb/>
            H℟Fk, figura circumſcripta intelligatur ex triangulo, HM3, & </s>
            <s xml:id="echoid-s11470" xml:space="preserve">
              <lb/>
            ex trapexijs, P3, ℟4, F6, compoſita, & </s>
            <s xml:id="echoid-s11471" xml:space="preserve">alia inſcripta ex </s>
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