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

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        <div xml:id="echoid-div918" type="section" level="1" n="547">
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            <s xml:id="echoid-s9931" xml:space="preserve">
              <pb o="386" file="0406" n="406" rhead="GEOMETRIÆ"/>
            D, erunt vt, BD, ad, BED, vna cum exceſſu, quo, BED, ſuperat,
              <lb/>
            {1/3}. </s>
            <s xml:id="echoid-s9932" xml:space="preserve">BD, cu-n {1/6}. </s>
            <s xml:id="echoid-s9933" xml:space="preserve">BM, ergo per conuerſionem rationis omnia qua-
              <lb/>
            drata, BD, ad omnia quadrata, BGD, erunt vt, BD, ad iui reli-
              <lb/>
            quum, ab eodem dempta ſemihyperbola, BED, & </s>
            <s xml:id="echoid-s9934" xml:space="preserve">exceſſu, quo
              <lb/>
            eadem ſuperat {1/3}. </s>
            <s xml:id="echoid-s9935" xml:space="preserve">BD, & </s>
            <s xml:id="echoid-s9936" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s9937" xml:space="preserve">BM, quod erat oſtendendum.</s>
            <s xml:id="echoid-s9938" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div920" type="section" level="1" n="548">
          <head xml:id="echoid-head572" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s9939" xml:space="preserve">HAnc Propoſi@ionem appoſui, vt & </s>
            <s xml:id="echoid-s9940" xml:space="preserve">nonnullas alias inferius
              <lb/>
            quæ licet ſupponant quadraturam byperbolæ iam notam, vt & </s>
            <s xml:id="echoid-s9941" xml:space="preserve">
              <lb/>
            ipſæ completè inteligantur, non inutiliter tamen aliqualiter ſcrriexi-
              <lb/>
            ſtimaui, vt ſi alicuius ind uſtria illius quadratura in lucem prodeat,
              <lb/>
            illico & </s>
            <s xml:id="echoid-s9942" xml:space="preserve">bic appoſita nota fiant; </s>
            <s xml:id="echoid-s9943" xml:space="preserve">vel è conuersò, vt per bæc aliquan-
              <lb/>
            do adinuenta ſtacim illius quadr atura nobis inoteſcat; </s>
            <s xml:id="echoid-s9944" xml:space="preserve">vade cumſcie-
              <lb/>
            mus, quam rationem habeat, BD, ad ſemihyperbolam, BED, appreben-
              <lb/>
            demus ſtatim, quam rationem babeant omnia quadrata, BD, ad omnia
              <lb/>
            quadrata trilinei, BGD: </s>
            <s xml:id="echoid-s9945" xml:space="preserve">Vel è contra, ſi quando notificabimus, quam
              <lb/>
            rationem babeant omnia quadrata, BD, ad omnia quadrata trilinei,
              <lb/>
            BGD, ſtatim compertum babebimus, quam rationembabeat, BD, ad
              <lb/>
            ſemibyperbolam, BED, & </s>
            <s xml:id="echoid-s9946" xml:space="preserve">eius quadratura notareddetur.</s>
            <s xml:id="echoid-s9947" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div921" type="section" level="1" n="549">
          <head xml:id="echoid-head573" xml:space="preserve">THEOREMA XIV. PROPOS. XV.</head>
          <p>
            <s xml:id="echoid-s9948" xml:space="preserve">SI parallelogrammum, & </s>
            <s xml:id="echoid-s9949" xml:space="preserve">hyperbola fuerint in eadem
              <lb/>
            baſi, & </s>
            <s xml:id="echoid-s9950" xml:space="preserve">circa eundem axim, vel diametrum, regula
              <lb/>
            baſi. </s>
            <s xml:id="echoid-s9951" xml:space="preserve">Omnia quadrata dicti parallelogrammi ad omnia
              <lb/>
            quadrata figuræ compoſitæ ex hyperbola, & </s>
            <s xml:id="echoid-s9952" xml:space="preserve">alterutro tri-
              <lb/>
            lineorum extra hyperbolam conſtitutorum, demptis om-
              <lb/>
            nibus quadratis aſſumpti trilinei, eruut vt dictum paral-
              <lb/>
            lelogramum ad inſcriptam hyperbolam.</s>
            <s xml:id="echoid-s9953" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9954" xml:space="preserve">Sit hyperbola, CBD, in baſi, CD,
              <lb/>
              <figure xlink:label="fig-0406-01" xlink:href="fig-0406-01a" number="277">
                <image file="0406-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0406-01"/>
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            circa axim, vel diametrum, BE, eius
              <lb/>
            latus tranſuerſum, AB, in eadem au-
              <lb/>
            tem baſi, CD, & </s>
            <s xml:id="echoid-s9955" xml:space="preserve">circa eundem axim,
              <lb/>
            vel diametrum, BE, ſit parallelogrã-
              <lb/>
            mum, FD, regula verò, CD. </s>
            <s xml:id="echoid-s9956" xml:space="preserve">Dico
              <lb/>
            ergo omnia quadrata, FD, ad omnia
              <lb/>
            quadrata ſiguræ, GBCD, demptis
              <lb/>
            omnibus quadratis trilinei, BGD, al-
              <lb/>
            terutrius ex duobus, BFC, BGD, </s>
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