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

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            <s xml:id="echoid-s11437" xml:space="preserve">
              <pb o="443" file="0463" n="463" rhead="LIBER VI."/>
              <figure xlink:label="fig-0463-01" xlink:href="fig-0463-01a" number="318">
                <image file="0463-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0463-01"/>
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            etiam parallela, ΚΣ,
              <lb/>
            abſcinditab, LA, ver
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            ſus, A, {4/5}. </s>
            <s xml:id="echoid-s11438" xml:space="preserve">ipſius, LA,
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            ſic ergo puncta notata
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            erunt, Q, γ Ζ, &</s>
            <s xml:id="echoid-s11439" xml:space="preserve">, Φ,
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            Δ, Γ, Π, ℟, Χ, per
              <lb/>
            quæ ſi extend itur cur-
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            ua linea, dico propin-
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            quiſſimè ſic Parabolã
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            delineari, prædictanẽ-
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            pè puncta eſſe in Pa-
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            rabola, cuius diame-
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            ter, A2, & </s>
            <s xml:id="echoid-s11440" xml:space="preserve">baſis, QX,
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            etenim babet bæc pro-
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            prietatem in præbabito Corollario declaratam, vel, vt clarius loquar,
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            XF, ad, E℟, exempligratia babetrationem compoſitam ex ratione, X
              <lb/>
            F, ad, FV, ideſt, propter conſtructionem, ex ratione, FA, ad, AE, & </s>
            <s xml:id="echoid-s11441" xml:space="preserve">ex
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            ratione, VF, ad, E℟, boc eſt adbuc ex ratione, FA, ad, AE, duæ autẽ
              <lb/>
            rationes, F A, ad, AE, componunt ratione quadrati, FA, ad quadra-
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            tum, AE, ergo, XF, ad, E℟, eſt Vt quadratum, FA, ad quadratum, A
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              <note position="right" xlink:label="note-0463-01" xlink:href="note-0463-01a" xml:space="preserve">Corol. 1.
                <lb/>
              1. 4.</note>
            E, ſedſic etiam eſt, FX, ad parallelam ipſi, A2, interiectam inter, A
              <lb/>
            F, & </s>
            <s xml:id="echoid-s11442" xml:space="preserve">Parabolam circa diametrum, A2, in baſi, QX, ergo punctum,
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            ℟, eſt in tali parabola: </s>
            <s xml:id="echoid-s11443" xml:space="preserve">Hoc idem oſtendemus eodem modo de cęteris
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            punctis, Π Γ, Δ, Φ, &</s>
            <s xml:id="echoid-s11444" xml:space="preserve">, Z γ, ergo dicta puncta ſunt omnia in dicta pa-
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            rabola. </s>
            <s xml:id="echoid-s11445" xml:space="preserve">Hic quidẽ modus debuiſſet poni Lib. </s>
            <s xml:id="echoid-s11446" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11447" xml:space="preserve">ſiue in meo Tractatu de
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            Specuio V ſtorio iam in lucem edito, ſed quia oritur bic ex proprietate
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            proximè demonſtrata, nec illud prius menti ſubuenit, propterea idip.
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            </s>
            <s xml:id="echoid-s11448" xml:space="preserve">ſum bic ſubiungere libuit.</s>
            <s xml:id="echoid-s11449" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1053" type="section" level="1" n="634">
          <head xml:id="echoid-head664" xml:space="preserve">THEOREMA X. PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s11450" xml:space="preserve">SI in ſpirali ex prima reuolutione orta ſumatur punctũ,
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            quod non ſit initium, nec terminus eiuſdem ſpiralis,
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            ab initio autem ſpiralis ad dictum punctum agatur recta
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            linea, & </s>
            <s xml:id="echoid-s11451" xml:space="preserve">ſuper initio ſpiralis centro ad diſtantiam dicti pũ-
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            cti deſctibatur circulus, eiuſdem portio comprehenſa du-
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            cta linea, & </s>
            <s xml:id="echoid-s11452" xml:space="preserve">portione eius, quæ dicitur reuolutionis initia-
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            tiua, quam abſcindit circumferentia dicti circuli, & </s>
            <s xml:id="echoid-s11453" xml:space="preserve">circũ-
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            ferentia eiuſdem, quæ eſt ad conſequentia, tripla eſt figu-
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            ræ comprehenſæ ducta linea, & </s>
            <s xml:id="echoid-s11454" xml:space="preserve">portione ſpiralis, quæ eſt
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            ad conſequentia vſquc ad initium ſpiralis.</s>
            <s xml:id="echoid-s11455" xml:space="preserve"/>
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