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

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          <p>
            <s xml:id="echoid-s12682" xml:space="preserve">
              <pb o="498" file="0518" n="518" rhead="GEOMETRIÆ"/>
              <figure xlink:label="fig-0518-01" xlink:href="fig-0518-01a" number="348">
                <image file="0518-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0518-01"/>
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            ca tantum, & </s>
            <s xml:id="echoid-s12683" xml:space="preserve">per omnium terminos ex parte, 2, tranſeat linea, C
              <lb/>
            P2, ſimiliter in alia figura, Β&</s>
            <s xml:id="echoid-s12684" xml:space="preserve">Δ, ſumantur quotcumq; </s>
            <s xml:id="echoid-s12685" xml:space="preserve">in ipſa, Δ&</s>
            <s xml:id="echoid-s12686" xml:space="preserve">,
              <lb/>
            producta verſus, &</s>
            <s xml:id="echoid-s12687" xml:space="preserve">, æquales ipſis, &</s>
            <s xml:id="echoid-s12688" xml:space="preserve">℟ΓΔ, fimul ſumptis, & </s>
            <s xml:id="echoid-s12689" xml:space="preserve">pro-
              <lb/>
            ductis reliquis in fig. </s>
            <s xml:id="echoid-s12690" xml:space="preserve">Β&</s>
            <s xml:id="echoid-s12691" xml:space="preserve">Δ, ipſi, &</s>
            <s xml:id="echoid-s12692" xml:space="preserve">Δ, parallelis, aliæ tot æquales
              <lb/>
            ſuis productis in directum capiantur, per quorum omnium termi-
              <lb/>
            nos tranſeant lineæ, BGZ, BFY. </s>
            <s xml:id="echoid-s12693" xml:space="preserve">Quoniam ergo figurę, BFYZG,
              <lb/>
            BGZ&</s>
            <s xml:id="echoid-s12694" xml:space="preserve">H, Β&</s>
            <s xml:id="echoid-s12695" xml:space="preserve">℟κΓΔ, ſunt in eiſdem parallelis, AD, ΧΩ; </s>
            <s xml:id="echoid-s12696" xml:space="preserve">& </s>
            <s xml:id="echoid-s12697" xml:space="preserve">ductis
              <lb/>
            in eiſdem quomodocumq; </s>
            <s xml:id="echoid-s12698" xml:space="preserve">ipſis, AD, ΧΩ, parallelis, interceptæ in
              <lb/>
            figuris portiones ſunt æquales, ideò ip@æ figuræ, BYZ, BZ&</s>
            <s xml:id="echoid-s12699" xml:space="preserve">, Β& </s>
            <s xml:id="echoid-s12700" xml:space="preserve">
              <lb/>
            ℟κΓΔ, æqualiter analogæ, & </s>
            <s xml:id="echoid-s12701" xml:space="preserve">ſubinde æquales, erunt: </s>
            <s xml:id="echoid-s12702" xml:space="preserve">Quo pa-
              <lb/>
              <note position="left" xlink:label="note-0518-01" xlink:href="note-0518-01a" xml:space="preserve">Per ant.</note>
            cto etiam oſtendemus figuras, Φ λ, λC2, æquales eſſe: </s>
            <s xml:id="echoid-s12703" xml:space="preserve">Quotu-
              <lb/>
            plex ergo eſt aggregatum ex, Υ℟, ΓΔ, aggregati ex, &</s>
            <s xml:id="echoid-s12704" xml:space="preserve">℟, ΓΔ, to-
              <lb/>
            tuplex erit aggregatum ex figuris, BYZ, BZ&</s>
            <s xml:id="echoid-s12705" xml:space="preserve">, Β&</s>
            <s xml:id="echoid-s12706" xml:space="preserve">℟κΓΔ, ſeu figu-
              <lb/>
            ra, ΒΥ℟κ @Δ, figuræ, Β&</s>
            <s xml:id="echoid-s12707" xml:space="preserve">℟κΓΔ; </s>
            <s xml:id="echoid-s12708" xml:space="preserve">ſimiliter quotuplex erit, Φ2, ipſi-
              <lb/>
            us, φλ, totuplex erit aggregatum ex figuris, Cφλ, Cλ2, hoc eſt figu-
              <lb/>
            ra, CΦ2, ipſius figuræ, CΦλ, habemus ergo æquè multiplices pri-
              <lb/>
            mæ, & </s>
            <s xml:id="echoid-s12709" xml:space="preserve">tertiæ vtcumq; </s>
            <s xml:id="echoid-s12710" xml:space="preserve">aſſumptas, ſimiliter & </s>
            <s xml:id="echoid-s12711" xml:space="preserve">æquè multiplices ſe-
              <lb/>
            cundæ, & </s>
            <s xml:id="echoid-s12712" xml:space="preserve">quartæ. </s>
            <s xml:id="echoid-s12713" xml:space="preserve">Quoniam verò ex. </s>
            <s xml:id="echoid-s12714" xml:space="preserve">g. </s>
            <s xml:id="echoid-s12715" xml:space="preserve">Υ℟, ΓΔ; </s>
            <s xml:id="echoid-s12716" xml:space="preserve">FI, LM, ſunt
              <lb/>
            æquè multiplices ipſarum, &</s>
            <s xml:id="echoid-s12717" xml:space="preserve">℟, ΓΔ; </s>
            <s xml:id="echoid-s12718" xml:space="preserve">HI, LM, ſimiliter, 2Φ, PN,
              <lb/>
            ſunt æquè multiplices ipſarum, Φλ, NO, ipſę verò, &</s>
            <s xml:id="echoid-s12719" xml:space="preserve">℟, ΓΔ, HI,
              <lb/>
            LM, φλ, NO, ſunt proportionales, ideò ſi aggregatum ex, Υ℟, ΓΔ,
              <lb/>
            adæquabitur ipſi, φ2, etiam aggregatum ex, FI, LM, adæquabitur
              <lb/>
            ipſi, NP, vt & </s>
            <s xml:id="echoid-s12720" xml:space="preserve">reliquæ omnes ſimiliter ſumptæ, & </s>
            <s xml:id="echoid-s12721" xml:space="preserve">conſequenter
              <lb/>
              <note position="left" xlink:label="note-0518-02" xlink:href="note-0518-02a" xml:space="preserve">Ex ant.</note>
            etiam figura, ΒΥ℟κΓΔ, adæquabitur figuræ, Cφ2, ſi verò aggre-
              <lb/>
            gutum ex, Υ℟, ΓΔ; </s>
            <s xml:id="echoid-s12722" xml:space="preserve">ſuperet, φ2, eodem modo patebit figuram, ΒΥ
              <lb/>
            ℟κΓΔ, ſuperare figuram, Cφ2, vel ſuperari ab eadem, ſi, Υ℟, ΓΔ;</s>
            <s xml:id="echoid-s12723" xml:space="preserve"/>
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