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

Table of Notes

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          <p>
            <s xml:id="echoid-s9846" xml:space="preserve">
              <pb o="383" file="0403" n="403" rhead="LIBER V."/>
            ne hyperbolæ, BAD, bafi rectangulo ſub, BD, FY, adparallele-
              <lb/>
            pipedum ſub eadem altitudine baſi quadrato, BD: </s>
            <s xml:id="echoid-s9847" xml:space="preserve">pariter omnia
              <lb/>
            quadrata hyperbolæ, BAD, ad omnia rectangula hyperbolę, HM
              <lb/>
            Q, ſimilia rectangulo ſub, HQ, EN, habent rationem compofitã
              <lb/>
            ex ratione rectanguli ſub, VC, XP, ad rectangulum ſub, RP, GC,
              <lb/>
            & </s>
            <s xml:id="echoid-s9848" xml:space="preserve">parallelepipedi ſub altitudine hyperbolæ, BAD, & </s>
            <s xml:id="echoid-s9849" xml:space="preserve">ſub quadra-
              <lb/>
            to, BD, ad parallelepipedum ſub altitudine hyperbolæ, HMQ,
              <lb/>
            bafi rectangulo ſub, HQ, EN, ergo, ex æquo, omnia rectangula
              <lb/>
            hyperbolæ, BAD, ſimilia rectangulo ſub, BD, FY, regula, BD, ad
              <lb/>
            omnia rectangula hyperbolæ, HMQ, ſimilia rectangulo ſub, HQ,
              <lb/>
            EN, regula, HQ, habebunt rationem compoſitam ex ratione re-
              <lb/>
            ctanguli, ſub, VC, XP, ad rectangulum ſub, RP, GC, & </s>
            <s xml:id="echoid-s9850" xml:space="preserve">ex ratio-
              <lb/>
            ne parallelepipedi ſub altitudine hyperbolæ, BAD, baſi rectangu-
              <lb/>
            lo ſub, BD, FY, ad parallelepipedum ſub eadem altitudine, & </s>
            <s xml:id="echoid-s9851" xml:space="preserve">baſi
              <lb/>
            quadrato, BD, & </s>
            <s xml:id="echoid-s9852" xml:space="preserve">ex ratione huius parallelepipedi ad parallelepi-
              <lb/>
            pedum ſub altitudine hyperbolę, HMQ, baſi rectangulo ſub, HQ,
              <lb/>
            EN; </s>
            <s xml:id="echoid-s9853" xml:space="preserve">.</s>
            <s xml:id="echoid-s9854" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9855" xml:space="preserve">compoſitã ex ratione parallelepipedi ſub altitudine hy-
              <lb/>
            perbolę, ABD, baſi rectangulo ſub, BD, FY, ad parallelepipedum
              <lb/>
            ſub altitudine hyperbolę, HMQ, baſi rectangulo ſub, HQ, EN,
              <lb/>
            quę erant oſtend.</s>
            <s xml:id="echoid-s9856" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div916" type="section" level="1" n="546">
          <head xml:id="echoid-head570" xml:space="preserve">THEOREMA XII. PROPOS. XIII.</head>
          <p>
            <s xml:id="echoid-s9857" xml:space="preserve">SImilium hyperbolarum omnia quadrata, regulis ea-
              <lb/>
            rum baſibus, ſunt in tripla ratione axium, vel diame-
              <lb/>
            trorum earundem.</s>
            <s xml:id="echoid-s9858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9859" xml:space="preserve">Sint ſimiles hyperbolæ, BAD, HMQ, earum latera tranſuerſa,
              <lb/>
            GA, XM, quorum ſint ſexquialteræ, AV, MR, in directum axi-
              <lb/>
            bus, vel diametris, AC, MP, baſes, & </s>
            <s xml:id="echoid-s9860" xml:space="preserve">regulæ ſint, BD, HQ. </s>
            <s xml:id="echoid-s9861" xml:space="preserve">Di-
              <lb/>
            co omnia quadrata hyperbolæ, BAD, ad omnia quadrata hyper-
              <lb/>
            bolæ, HMQ, eſſe in tripla ratione eius, quam habet, AC, ad, M
              <lb/>
            P, iungantur, BA, AD, HM, MQ. </s>
            <s xml:id="echoid-s9862" xml:space="preserve">Quoniam ergo hyperbolæ
              <lb/>
              <note position="right" xlink:label="note-0403-01" xlink:href="note-0403-01a" xml:space="preserve">Iuxta def.
                <lb/>
              Apoll. 6.
                <lb/>
              Con.</note>
            ſunt ſimiles baſis, BD, ad, CA, erit vt baſis, HQ, ad, PM, & </s>
            <s xml:id="echoid-s9863" xml:space="preserve">ſunt
              <lb/>
            anguli in clinationis, AC, ad, BD, & </s>
            <s xml:id="echoid-s9864" xml:space="preserve">MP, ad, HQ, inter ſe æqua-
              <lb/>
            les, ergo triangula, BAD, HMQ, ſunt ſimilia, & </s>
            <s xml:id="echoid-s9865" xml:space="preserve">ideo omnia qua.
              <lb/>
            </s>
            <s xml:id="echoid-s9866" xml:space="preserve">drata eorundem, regulis ijſdem, erunt inter ſe in triplaratione la-
              <lb/>
            terum homologorum .</s>
            <s xml:id="echoid-s9867" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9868" xml:space="preserve">eius, quam habet, BD, ad, HQ, vel, AC,
              <lb/>
            ad, MP; </s>
            <s xml:id="echoid-s9869" xml:space="preserve">quia verò quadratum, BC, ad rectangulum, GCA, eſt vt
              <lb/>
            hyperbolæ, BAD, rectum latus ad tranſuerſum .</s>
            <s xml:id="echoid-s9870" xml:space="preserve">I. </s>
            <s xml:id="echoid-s9871" xml:space="preserve">vt rectum latus
              <lb/>
              <note position="right" xlink:label="note-0403-02" xlink:href="note-0403-02a" xml:space="preserve">F Cor. 22
                <lb/>
              l. 2.</note>
            ad tranſuerſum hyperbolæ, HMQ, quia ille ſunt ſimiles .</s>
            <s xml:id="echoid-s9872" xml:space="preserve">I. </s>
            <s xml:id="echoid-s9873" xml:space="preserve">vt </s>
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