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

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            <s xml:id="echoid-s10238" xml:space="preserve">
              <pb o="396" file="0416" n="416" rhead="GEOMETRIÆ"/>
            ſum ſit, AV, centrum, O, aſymptoti indefinitè producti, NP, HY,
              <lb/>
            per puncta autem, AV, ſint ductæ ordinatim, NH, YP, productæ
              <lb/>
            vſq; </s>
            <s xml:id="echoid-s10239" xml:space="preserve">ad aſymptotos, in punctis, N, H, Y, P, ipſis incidentes, quæ
              <lb/>
            fectiones tangent, deinde iunctis, NY, HP, producantur ipſæ tun-
              <lb/>
              <figure xlink:label="fig-0416-01" xlink:href="fig-0416-01a" number="283">
                <image file="0416-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0416-01"/>
              </figure>
            gentes vſq; </s>
            <s xml:id="echoid-s10240" xml:space="preserve">ad ſectiones illis in punctis, F, E, C, D,
              <lb/>
            occurrentes, iunganturque, FD, EC, & </s>
            <s xml:id="echoid-s10241" xml:space="preserve">per, O, ad
              <lb/>
              <note position="left" xlink:label="note-0416-01" xlink:href="note-0416-01a" xml:space="preserve">37. Secun.
                <lb/>
              Con.</note>
            ipfam, AV, ordinatim applicetur, XL, incidens, F
              <lb/>
            E, in, X, &</s>
            <s xml:id="echoid-s10242" xml:space="preserve">, DC, in, L, quæ erit ſecunda diameter,
              <lb/>
            & </s>
            <s xml:id="echoid-s10243" xml:space="preserve">producatur, AV, indeſinitè incidens ipſis, FD,
              <lb/>
            EC, in punctis, R, Z, erit ergo, FC, parailelogrã-
              <lb/>
              <note position="left" xlink:label="note-0416-02" xlink:href="note-0416-02a" xml:space="preserve">3. 1. Secun.
                <lb/>
              Con.</note>
            mum, nam rectangulum, YFN, .</s>
            <s xml:id="echoid-s10244" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10245" xml:space="preserve">rectangulum, E
              <lb/>
            NF, eſt æquale quadrato, AO, ideſt rectangulo, C
              <lb/>
            HD, item quadratum; </s>
            <s xml:id="echoid-s10246" xml:space="preserve">NX, eſt æquale quadrato,
              <lb/>
            HL, & </s>
            <s xml:id="echoid-s10247" xml:space="preserve">ideo rectangulum, ENF, cum quadrato, NX, .</s>
            <s xml:id="echoid-s10248" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10249" xml:space="preserve">quadra-
              <lb/>
              <note position="left" xlink:label="note-0416-03" xlink:href="note-0416-03a" xml:space="preserve">4. Sec. Hle,</note>
            tum, XF, erit æquale rectangulo, CHD, cum quadrato, LH, .</s>
            <s xml:id="echoid-s10250" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s10251" xml:space="preserve">quadrato, LD, & </s>
            <s xml:id="echoid-s10252" xml:space="preserve">ideò, XF, erit æqualis ipſi, LD, & </s>
            <s xml:id="echoid-s10253" xml:space="preserve">eius dupla, F
              <lb/>
            E, æqualis duplæ, CD, & </s>
            <s xml:id="echoid-s10254" xml:space="preserve">eidem parallela, vnde, FD, erit, EC,
              <lb/>
            parallela, & </s>
            <s xml:id="echoid-s10255" xml:space="preserve">ambæ ordinatim ad axim, vel diametrum, RZ, or-
              <lb/>
            dinatim applicatæ, & </s>
            <s xml:id="echoid-s10256" xml:space="preserve">ideò in, R, Z, bifatiam ſectæ, &</s>
            <s xml:id="echoid-s10257" xml:space="preserve">, FC, erit
              <lb/>
            parallelogrammum, ſitregula latus tranſuerſum, AV, Dico nũc
              <lb/>
            omnia quadrata parallelogrammi, FC, eſſe ſexquialtera omnium
              <lb/>
              <note position="left" xlink:label="note-0416-04" xlink:href="note-0416-04a" xml:space="preserve">31, huius.</note>
            quadratorum figuræ, FADCVE; </s>
            <s xml:id="echoid-s10258" xml:space="preserve">& </s>
            <s xml:id="echoid-s10259" xml:space="preserve">hęc eſſe quadrupla omnium
              <lb/>
            quadratorum triangulorum, NOY, HOP; </s>
            <s xml:id="echoid-s10260" xml:space="preserve">nam omnia quadrata,
              <lb/>
            FC, ad omnia quadrata figuræ, FADCVE, oſtenſa ſunt eſſe, vt
              <lb/>
            quadratum, DC, ad quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10261" xml:space="preserve">quadrati, HP, eſt
              <lb/>
            autem quadratum, HP, æquale quadrato, AV, & </s>
            <s xml:id="echoid-s10262" xml:space="preserve">ideò ſunt, vt
              <lb/>
            quadratum, DC, ad quadratum, HP, cum {1/3}. </s>
            <s xml:id="echoid-s10263" xml:space="preserve">quadrati, HP, vel vt
              <lb/>
            quadratum, RZ, ad quadratum, AV, cum, {1/3}. </s>
            <s xml:id="echoid-s10264" xml:space="preserve">quadrati, AV. </s>
            <s xml:id="echoid-s10265" xml:space="preserve">Pro-
              <lb/>
            ducantur nunc aſymptoti, NP, HY, verſus, EC, cui productæ in-
              <lb/>
            cidant in S, I, eſt ergo rectangulum, SEI, æquale quadrato, YV,
              <lb/>
              <note position="left" xlink:label="note-0416-05" xlink:href="note-0416-05a" xml:space="preserve">11. Secun.
                <lb/>
              Con.</note>
            .</s>
            <s xml:id="echoid-s10266" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10267" xml:space="preserve">quadrato, EZ, & </s>
            <s xml:id="echoid-s10268" xml:space="preserve">ideò rectangulum, SEI, cum quadrato, EZ,
              <lb/>
            duplum eſt quadrati, EZ, vel quadrati, YV, eſt autem rectangulũ,
              <lb/>
            SEI, cum quadrato, EZ, ęquale quadrato, SZ, & </s>
            <s xml:id="echoid-s10269" xml:space="preserve">ideò quadratũ,
              <lb/>
            SZ, duplum eſt quadrati, YV, eſt autem, vt quadratum, SZ, ad
              <lb/>
            quadratum, YV, ita quadratum, ZO, ad quadratum, OV, ergo
              <lb/>
            quadratum, ZO, erit duplum quadrati, OV, vel eorum quadru pla
              <lb/>
            .</s>
            <s xml:id="echoid-s10270" xml:space="preserve">f. </s>
            <s xml:id="echoid-s10271" xml:space="preserve">quadratum, ZR, duplum quadrati, AV; </s>
            <s xml:id="echoid-s10272" xml:space="preserve">quia verò dictum eſt
              <lb/>
            omnia quadrata, FC, ad omnia quadrata figuræ, FADCVE, eſſe
              <lb/>
            vt quadratum, RZ, ad quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10273" xml:space="preserve">quadrati, AV, .</s>
            <s xml:id="echoid-s10274" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s10275" xml:space="preserve">vt quadratum, RZ, ad {1/3}. </s>
            <s xml:id="echoid-s10276" xml:space="preserve">quadrati, AV, & </s>
            <s xml:id="echoid-s10277" xml:space="preserve">eſt quadratum, RZ,
              <lb/>
            duplum quadrati, AV, ideò quadratum, RZ, erit {6/3}. </s>
            <s xml:id="echoid-s10278" xml:space="preserve">quadrati, </s>
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