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

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              <pb o="398" file="0418" n="418" rhead="GEOMETRIÆ"/>
            lateri tranſ uerſo parallela, quod ſumabur pro regula, ita inquám, vt
              <lb/>
            omnia quadrata deſeripti parallelogram ni ad omnia quadrata figuræ
              <lb/>
            dictis lateribus, quæ tranſuerſo lateri æ quidiſtant, & </s>
            <s xml:id="echoid-s10332" xml:space="preserve">ab ijſdem ſe-
              <lb/>
            ctionum oppoſitarum in cluſis portionibus compræbenſæ, demptis om-
              <lb/>
            bus quadratis triangulorum ſub aſymptotis, & </s>
            <s xml:id="echoid-s10333" xml:space="preserve">ab ijs incluſis portio-
              <lb/>
            nibus laterum, parallelogrammi tranſuerſo lateri æquidiſta ntium,
              <lb/>
            babeant datam rationem, dummodo ea ſit maioris inæqualitatis: </s>
            <s xml:id="echoid-s10334" xml:space="preserve">Sit
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            in figura Propos. </s>
            <s xml:id="echoid-s10335" xml:space="preserve">21. </s>
            <s xml:id="echoid-s10336" xml:space="preserve">data ratio maioris inæ quadlitatis, quam babet,
              <lb/>
            KB, ad, GM, & </s>
            <s xml:id="echoid-s10337" xml:space="preserve">ſupponatur ductam ſuiſſe, FE, æqudiſtantem lateri
              <lb/>
            tranſuerſo, AV, ita vt quadratum, FE, ad quadratum, Av, ſit vt, K
              <lb/>
            B, ad, GM, & </s>
            <s xml:id="echoid-s10338" xml:space="preserve">conſtructam fuiſſe figuram, velutibi factum eſt, patet
              <lb/>
            igitur, quia omnia quadrata, FC, ad omnia quadrata figurę, FADCV
              <lb/>
            E, ſunt vt quadratum, FE, ad quadratum, AV, ex Coroll, antec. </s>
            <s xml:id="echoid-s10339" xml:space="preserve">dem-
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            ptis tamen ab omnibus quadratis dictæ figuræ, omnibus quadratis
              <lb/>
            triangulorum, NOR, HOS, quod ideò ad eadom erunt in ratione da-
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            ta .</s>
            <s xml:id="echoid-s10340" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10341" xml:space="preserve">m ea quam babet, KB, ad, GM.</s>
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          <head xml:id="echoid-head589" xml:space="preserve">THEOREMA XXII. PROPOS. XXIII.</head>
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            <s xml:id="echoid-s10343" xml:space="preserve">SI duo parallelogramma vtcunq; </s>
            <s xml:id="echoid-s10344" xml:space="preserve">fectionibus oppoſitis
              <lb/>
            circumſcripta fuerint modo ſolito, habentia ſcilicet
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            duo oppoſita latera, quæ ſint oppoſitarum hyperbolarum
              <lb/>
            baſes, & </s>
            <s xml:id="echoid-s10345" xml:space="preserve">reliqua duo lateri rianſuerſo æ quidiſtantia, regu-
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            la vna dictarum baſium: </s>
            <s xml:id="echoid-s10346" xml:space="preserve">Omnia quadrata vnius paralle-
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            logrammi, demptis omnibus quadratis oppoſitarum hy-
              <lb/>
            perbolarum communes cum eo baſes habentium, ad om-
              <lb/>
            nia quadrata alterius parallelogrammi, demptis omnibus
              <lb/>
            quadratis oppoſitarum hyperbolarum communes cum eo
              <lb/>
            baſes habentium, erunt vt parallelepipedum ſub altitudi-
              <lb/>
            ne axi, vel diametro vnius hyperbolarum, cuius eſt com-
              <lb/>
            munis baſis cum parallelogrammo primò dicto, baſirectã-
              <lb/>
            gulo ſub dimidia tranſuerſi lateris, & </s>
            <s xml:id="echoid-s10347" xml:space="preserve">ſub compoſita ex ea-
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            dem dimidia, & </s>
            <s xml:id="echoid-s10348" xml:space="preserve">axi, vel diametro dictæ hyperbolæ, vna
              <lb/>
            cum. </s>
            <s xml:id="echoid-s10349" xml:space="preserve">quadrati eiuſdem axis, vel diametri, ad parallele-
              <lb/>
            pipedum ſub altitudine axi, vel diametro hyperbolæ, cui-
              <lb/>
            us eſt communis baſis cum parallelogrammo ſecundò di-
              <lb/>
            cto, baſirectangulo ſub dimidia tranſuerſi lateris, & </s>
            <s xml:id="echoid-s10350" xml:space="preserve">ſub
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            compoſita ex eadem dimidia, & </s>
            <s xml:id="echoid-s10351" xml:space="preserve">axi, vel diametro </s>
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