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

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            <s xml:id="echoid-s10207" xml:space="preserve">
              <pb o="395" file="0415" n="415" rhead="LIBER V."/>
            ctanguli fub, AZ, ZV, .</s>
            <s xml:id="echoid-s10208" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10209" xml:space="preserve">erit æquale rectangulo ſub, AZ, & </s>
            <s xml:id="echoid-s10210" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10211" xml:space="preserve">Z
              <lb/>
            V, & </s>
            <s xml:id="echoid-s10212" xml:space="preserve">ideò omnia quadrata, FC, ad omnia quadrata figuræ, FAD
              <lb/>
            CVE, erunt vt quadratum, ZO, ad quadratum, OV, cum rectan.
              <lb/>
            </s>
            <s xml:id="echoid-s10213" xml:space="preserve">gulo ſub, AZ, & </s>
            <s xml:id="echoid-s10214" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10215" xml:space="preserve">ZV, .</s>
            <s xml:id="echoid-s10216" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10217" xml:space="preserve">vt horum quadrupla, nempè, vt qua-
              <lb/>
            dratum, RZ, ad quadratum, AV, cum rectangulo ſub, AZ, & </s>
            <s xml:id="echoid-s10218" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10219" xml:space="preserve">
              <lb/>
            ZV, .</s>
            <s xml:id="echoid-s10220" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10221" xml:space="preserve">ſub, AZ, & </s>
            <s xml:id="echoid-s10222" xml:space="preserve">ſexquitertia, ZV, quæ ratio ſic proponebatur
              <lb/>
            explicanda, quæque, vt libet, retineri poterit.</s>
            <s xml:id="echoid-s10223" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div940" type="section" level="1" n="560">
          <head xml:id="echoid-head584" xml:space="preserve">COROLLARIVM:</head>
          <p style="it">
            <s xml:id="echoid-s10224" xml:space="preserve">_H_Inc patet quadratum dimidiæ eius, quælateri tranſuerſo op-
              <lb/>
            poſitarum ſectionum æquidiſtanter ducitur, ſubtenditurq; </s>
            <s xml:id="echoid-s10225" xml:space="preserve">an-
              <lb/>
            gulo, qui deinceps eſt angulo ſub aſymptotis comprebenſo, ſectiones
              <lb/>
            continenti æquale eſſe rectangulo ſub compoſita ex latere tranſuerſo,
              <lb/>
            & </s>
            <s xml:id="echoid-s10226" xml:space="preserve">axi, vel diametro alterutrius conſtitutarum hyperbolarum per or-
              <lb/>
            d natim applicatas à punctis, quibus dicta ſubtenſa incidit, producta,
              <lb/>
            ipſis oppoſitis ſectionibus, & </s>
            <s xml:id="echoid-s10227" xml:space="preserve">ſub eodem axi, vel diametro, quod pa-
              <lb/>
            tet, veluti oſtenſum eſt quadratum, SL, æquari rectangulo, .</s>
            <s xml:id="echoid-s10228" xml:space="preserve">AZV.</s>
            <s xml:id="echoid-s10229" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div941" type="section" level="1" n="561">
          <head xml:id="echoid-head585" xml:space="preserve">THEOREMA XXI. PROPOS. XXII.</head>
          <p>
            <s xml:id="echoid-s10230" xml:space="preserve">SI per vertices oppoſitarum ſectionum rectæ lineæ or-
              <lb/>
            dinatim ad eorum axim, vel diametrum applicentur
              <lb/>
            vſque ad aſymptotos productæ, quarum extrema ad eaſdé
              <lb/>
            partes ſumpta iungantur rectis lineis, iungenteſq; </s>
            <s xml:id="echoid-s10231" xml:space="preserve">vſq; </s>
            <s xml:id="echoid-s10232" xml:space="preserve">ad
              <lb/>
            oppoſitas ſectiones producantur, erunt iſtæ parallelogrã,
              <lb/>
            mi oppoſita latera, quod parallelogrammum ſi complea-
              <lb/>
            tur, regula exiſtente latere tranſuerſo: </s>
            <s xml:id="echoid-s10233" xml:space="preserve">Omnia quadrata
              <lb/>
            conſtituti parallelogrammi erunt ſexquialtera omnium
              <lb/>
            quadratorum figuræ comprehenſæ ſub lateribus dictipa-
              <lb/>
            rallelogrammi lateri tranſuerſo æquidiſtantibus, & </s>
            <s xml:id="echoid-s10234" xml:space="preserve">ſub
              <lb/>
            oppoſitarum ſectionum portionibus inter eadem latera cõ-
              <lb/>
            cluſis: </s>
            <s xml:id="echoid-s10235" xml:space="preserve">Omnia verò quadrata dictæ figuræ erunt quadru-
              <lb/>
            pla omnium quadratorum triangulorum, quiſub aſympto-
              <lb/>
            tis & </s>
            <s xml:id="echoid-s10236" xml:space="preserve">ijſdem incluſis portionibus laterum parallelogram-
              <lb/>
            mi, tranſuerſo lateri æquidiſtantium continentur.</s>
            <s xml:id="echoid-s10237" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10238" xml:space="preserve">Sint oppofitæ fectiones, FAD, EVC, quarum latus </s>
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