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

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            <s xml:id="echoid-s9806" xml:space="preserve">
              <pb o="381" file="0401" n="401" rhead="LIBER V."/>
            OVX, ſimilia rectangulo, XOP, regula, OX, habebunt rationem
              <lb/>
            compoſitam ex ea, quam habetrectangulum ſub, MB, HI, adre-
              <lb/>
            ctangulum ſub, RI, FB, & </s>
            <s xml:id="echoid-s9807" xml:space="preserve">ex ea, quam habet parallelepipedum
              <lb/>
            ſub altitudine hyperbole, ADC, baſi quadrato, AC, ad parallele-
              <lb/>
            bipedum ſub altitudine hyperbole, OVX, baſi rectangulo, XOP,
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            quod erat demonſtrandum.</s>
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        <div xml:id="echoid-div914" type="section" level="1" n="545">
          <head xml:id="echoid-head569" xml:space="preserve">THEOREMA XI. PROPOS. XII.</head>
          <p>
            <s xml:id="echoid-s9809" xml:space="preserve">ASſumptis quibuſcunq; </s>
            <s xml:id="echoid-s9810" xml:space="preserve">hyperbolis, in vnaquaq; </s>
            <s xml:id="echoid-s9811" xml:space="preserve">re-
              <lb/>
            gula baſi, oſtendemus omnia quadrata vnius ad om-
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            nia quadrata alterius, habere rationem compoſitam ex ra-
              <lb/>
            tione rectanguli ſub compoſita ex ſexquialtera tranſuerſi
              <lb/>
            lateris, & </s>
            <s xml:id="echoid-s9812" xml:space="preserve">axi, vel diametro hyperbolæ primò dictæ, & </s>
            <s xml:id="echoid-s9813" xml:space="preserve">ſub
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            compoſita ex tranſuerſo latere, & </s>
            <s xml:id="echoid-s9814" xml:space="preserve">axi, vel diametro hyper-
              <lb/>
            bolæ ſecundò dictæ ad re ctangulum ſub compoſita ex trã-
              <lb/>
            ſuerſi lateris ſexquialtera, & </s>
            <s xml:id="echoid-s9815" xml:space="preserve">axi, vel diametro hyperbolæ
              <lb/>
            ſecundò dictæ, & </s>
            <s xml:id="echoid-s9816" xml:space="preserve">ſub compoſita ex tranſuerſo latere, & </s>
            <s xml:id="echoid-s9817" xml:space="preserve">axi
              <lb/>
            vel diametro hyperbolæ primò dictæ, & </s>
            <s xml:id="echoid-s9818" xml:space="preserve">ex ratione paral-
              <lb/>
            lelepipediſub altitudine hyperbolæ primò dictæ, baſiau-
              <lb/>
            tem quadrato baſis eiuſdem, ad parallelepipedum ſub al-
              <lb/>
            t tudine hyp rbolæ ſecundò dictæ, baſi pariter quadrato
              <lb/>
            b ſis eiuſdem. </s>
            <s xml:id="echoid-s9819" xml:space="preserve">Velſi comparentur omnia quadrata hy-
              <lb/>
            perbolæ primò dictæ, ad omnia rectangula hyperbolæ fe-
              <lb/>
            cundò dictæ ſimilia cuidam rectangulo, illa ad hæchabe-
              <lb/>
            buntrationem compoſitam exratione prædictorum rectã-
              <lb/>
            gulorum, & </s>
            <s xml:id="echoid-s9820" xml:space="preserve">exratione parallelepipedi primò dictiad pa-
              <lb/>
            rallelepipedum ſub altitudine hyperbolæ ſecundò, dictæ
              <lb/>
            baſirectangulo, cuiomnia dicta rectangula ſunt ſimilia.
              <lb/>
            </s>
            <s xml:id="echoid-s9821" xml:space="preserve">Vel tandem ſi comparentur omnia rectangula primæ hy-
              <lb/>
            perbolæ ſimilia cuidam rectangulo ad omnia rectangula
              <lb/>
            ſecundæ hyperbolæ ſimilia pariter cuidam rectangulo, il-
              <lb/>
            la ad hæchabebunt rationem compoſitam ex ratione pa-
              <lb/>
            rallelepipedi ſub altitudine hyperbolæ primò dictæ baſi
              <lb/>
            rectangulo, cuiomnia eiuſdem rectangula ſunt ſimilia, ad
              <lb/>
            parallelepipedum ſub altitudine ecundæ hyperbolæ baſi
              <lb/>
            rectangulo, cuiomnia eiuſdem rectangula iam dicta </s>
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