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

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        <div xml:id="echoid-div625" type="section" level="1" n="362">
          <pb o="263" file="0283" n="283" rhead="LIBER III."/>
        </div>
        <div xml:id="echoid-div626" type="section" level="1" n="363">
          <head xml:id="echoid-head380" xml:space="preserve">COROLLARIVM V.</head>
          <p>
            <s xml:id="echoid-s6570" xml:space="preserve">IN Corollario Propof. </s>
            <s xml:id="echoid-s6571" xml:space="preserve">quintæ, ſi ſupponamus notam rationem,
              <lb/>
            quam habent omnia quadrata, AF, ad omnia quadrata trian-
              <lb/>
            guli, AEC, vel quam habent omnia quadrata, XR, ad omnia qua-
              <lb/>
            drata trapetij, YSN℟, veluti iam eam notam reddidimus, colligi-
              <lb/>
            mus, quam rationem habeant omnia quadrata, AF, ad reliquum,
              <lb/>
            demptis omnibus quadratis ſemicirculi, vel ſemiellipſis, DBF, & </s>
            <s xml:id="echoid-s6572" xml:space="preserve">
              <lb/>
            quam rationem habeant omnia quadrata, XR, adreliquum, dem-
              <lb/>
              <figure xlink:label="fig-0283-01" xlink:href="fig-0283-01a" number="175">
                <image file="0283-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0283-01"/>
              </figure>
            ptis omnibus quadratis portionis, YT
              <lb/>
            I℟, & </s>
            <s xml:id="echoid-s6573" xml:space="preserve">ideò patet, quam rationem ha-
              <lb/>
            beant omnia quadrata, AF, ad om-
              <lb/>
            nia quadrata ſemicircult, vel ſemielli-
              <lb/>
            pſis, DBF, & </s>
            <s xml:id="echoid-s6574" xml:space="preserve">quam rationem habe-
              <lb/>
            ant omnia quadrata, XR, ad omnia
              <lb/>
            quadrata portionis, YTI℟, vnde ap-
              <lb/>
            paret, quam rationem habeat ſolidum
              <lb/>
            ſimilare genitum ex, AF, ſiue ſit cy-
              <lb/>
            lindrus, ſiue priſma, ſiue tantum cy-
              <lb/>
            lindricus, ad ſolidum ſibi ſimilare ge-
              <lb/>
            nitum ex ſemicirculo, vel ſemiellipſi,
              <lb/>
            DBF, ſiue hoc ſit hæmiſphærium,
              <lb/>
            ſiue hæmiſphæroides, ſiue tantum ſolidum ſimilare illi, genitum ex,
              <lb/>
            DBF. </s>
            <s xml:id="echoid-s6575" xml:space="preserve">Item patet, quam rationem habeat ſolidum ſimilare geni-
              <lb/>
            tum ex, XR, quodcunque illud ſit, ad ſibi ſimilare genitum ex por-
              <lb/>
            tione, YTI℟. </s>
            <s xml:id="echoid-s6576" xml:space="preserve">Eodem pacto manifeſta fieret ratio ſolidi ſimilaris
              <lb/>
            geniti ex, AG, ad ſibi ſimilare genitum ex portione, YB℟, & </s>
            <s xml:id="echoid-s6577" xml:space="preserve">ita
              <lb/>
            in reliquis. </s>
            <s xml:id="echoid-s6578" xml:space="preserve">Inuentæ igitur ſunt alio modoa prædictis, rationes fo-
              <lb/>
            lidorum inuicem ſimilarium genitorum ex parallelogrammis in bafi
              <lb/>
            æquali ſecundæ diametro conſtitutis. </s>
            <s xml:id="echoid-s6579" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6580" xml:space="preserve">in baſi æquali ipſi, DF, & </s>
            <s xml:id="echoid-s6581" xml:space="preserve">
              <lb/>
            circa eoidem axes, ſiue diametros vtcunque portionum, YB℟, T
              <lb/>
            Y℟I, DTIF, &</s>
            <s xml:id="echoid-s6582" xml:space="preserve">, DBF, quod explicare opus erat, & </s>
            <s xml:id="echoid-s6583" xml:space="preserve">in ſuprapo-
              <lb/>
            ſita ngura modo ſolito declaratum eſt, ſed tantum vnico exemplo ne
              <lb/>
            ipſa confonderetur.</s>
            <s xml:id="echoid-s6584" xml:space="preserve"/>
          </p>
          <figure number="176">
            <image file="0283-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0283-02"/>
          </figure>
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