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

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        <div xml:id="echoid-div941" type="section" level="1" n="561">
          <p>
            <s xml:id="echoid-s10278" xml:space="preserve">
              <pb o="397" file="0417" n="417" rhead="LIBER V."/>
            ergo quadratum, RZ, ad quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10279" xml:space="preserve">quadrati, AV,
              <lb/>
            erit vt {6/3}. </s>
            <s xml:id="echoid-s10280" xml:space="preserve">ad {4/3}. </s>
            <s xml:id="echoid-s10281" xml:space="preserve">.</s>
            <s xml:id="echoid-s10282" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10283" xml:space="preserve">vt 6. </s>
            <s xml:id="echoid-s10284" xml:space="preserve">ad 4. </s>
            <s xml:id="echoid-s10285" xml:space="preserve">.</s>
            <s xml:id="echoid-s10286" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10287" xml:space="preserve">in ratione ſexquialtera, ergo omnia
              <lb/>
            quadriata, FC, ad omnia quadrata figurę, FADCVE, erunt in ra-
              <lb/>
            tione ſexquialtera.</s>
            <s xml:id="echoid-s10288" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10289" xml:space="preserve">Igitur conuertendo omnia quadrata figurę, FADCVE, ad om-
              <lb/>
            nia quadrata, FC, eruntin ratione ſubiexquialtera, .</s>
            <s xml:id="echoid-s10290" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10291" xml:space="preserve">vt 4. </s>
            <s xml:id="echoid-s10292" xml:space="preserve">ad 6.
              <lb/>
            </s>
            <s xml:id="echoid-s10293" xml:space="preserve">ſunt autem omnia quadrata, FC, ad omnia quadrata, NP, vt qua. </s>
            <s xml:id="echoid-s10294" xml:space="preserve">
              <lb/>
            dratum, ZR, ad quadratum, AV, ideſt dupla .</s>
            <s xml:id="echoid-s10295" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10296" xml:space="preserve">vt 6. </s>
            <s xml:id="echoid-s10297" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s10298" xml:space="preserve">& </s>
            <s xml:id="echoid-s10299" xml:space="preserve">om-
              <lb/>
            nia quadrata, NP, ſunt tripla omnium quadratorum triangulo-
              <lb/>
            rum, NYO, OHP, .</s>
            <s xml:id="echoid-s10300" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10301" xml:space="preserve">ſunt ad illa, vt 3. </s>
            <s xml:id="echoid-s10302" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s10303" xml:space="preserve">ergo ex ęquali, omnia
              <lb/>
            quadrata figurę, FADCVE, ad omnia quad. </s>
            <s xml:id="echoid-s10304" xml:space="preserve">triangulorum, NY
              <lb/>
            O, OHP, erunt vt 4. </s>
            <s xml:id="echoid-s10305" xml:space="preserve">ad I. </s>
            <s xml:id="echoid-s10306" xml:space="preserve">.</s>
            <s xml:id="echoid-s10307" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10308" xml:space="preserve">eorum quadrupla, quę erant oſten-
              <lb/>
            denda.</s>
            <s xml:id="echoid-s10309" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div943" type="section" level="1" n="562">
          <head xml:id="echoid-head586" xml:space="preserve">COROLLARIVM. I.</head>
          <p style="it">
            <s xml:id="echoid-s10310" xml:space="preserve">_Q_V oniam Verò in Propoſ. </s>
            <s xml:id="echoid-s10311" xml:space="preserve">antec. </s>
            <s xml:id="echoid-s10312" xml:space="preserve">oſtenſum eſt, ac in eius figura,
              <lb/>
            omnia quadrata, FC, ad omnia quadrata figuræ, F ADCVE, eſſe
              <lb/>
            Vt quadratum, DC, ad quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10313" xml:space="preserve">quadrati, HS, & </s>
            <s xml:id="echoid-s10314" xml:space="preserve">
              <lb/>
            quia omnia quadrata, ZL, ad omnia quadratatrianguli, OSL, vel eo-
              <lb/>
            rum quadrupla .</s>
            <s xml:id="echoid-s10315" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10316" xml:space="preserve">omnia quadrata, RC, ad omnia quadrata trianguli,
              <lb/>
            SOH, oſtenſa ſunt eſſe, Vt quadratum, CL, ad {1/3}. </s>
            <s xml:id="echoid-s10317" xml:space="preserve">quadrati, LS, vel Vt
              <lb/>
            quadratum, CD, ad @. </s>
            <s xml:id="echoid-s10318" xml:space="preserve">quadrati, HS, & </s>
            <s xml:id="echoid-s10319" xml:space="preserve">ſic eorum dupla. </s>
            <s xml:id="echoid-s10320" xml:space="preserve">.</s>
            <s xml:id="echoid-s10321" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10322" xml:space="preserve">Vt quadra.
              <lb/>
            </s>
            <s xml:id="echoid-s10323" xml:space="preserve">tum, LC, ad {1/3}. </s>
            <s xml:id="echoid-s10324" xml:space="preserve">quadrati, SH ita omnia quadrata, FC, ad omnia qua-
              <lb/>
            drata triangulorum, NOR HOS, erant autem omnia quadrata, FC, ad
              <lb/>
            omnia quadrata figuræ, FADCVE, vt quadratum, DC, ad quadratum,
              <lb/>
            AV, cum {1/3}. </s>
            <s xml:id="echoid-s10325" xml:space="preserve">quadrati, HS, ergo omnia quadrata, FC, ad reliquum,
              <lb/>
            demptis omnibus quadratis triangulorum, NOR, HOS, abomnibus
              <lb/>
            quadratis figuræ, FADCVE, erunt, vt quadratum, DC, ad quadratum,
              <lb/>
            AV; </s>
            <s xml:id="echoid-s10326" xml:space="preserve">& </s>
            <s xml:id="echoid-s10327" xml:space="preserve">ideò in præſenti Propoſ. </s>
            <s xml:id="echoid-s10328" xml:space="preserve">omnia quadrata, FC, ad omnia qua-
              <lb/>
            dratà figuræ FAD, CVE, demptis ab ijſdem omnibus quadratis triã-
              <lb/>
            gulorum NOR, HOP, erunt vt quadratum, RZ, ad quadratum, AV,
              <lb/>
            ideſt dupla.</s>
            <s xml:id="echoid-s10329" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div944" type="section" level="1" n="563">
          <head xml:id="echoid-head587" xml:space="preserve">COROLLARIVM. II.</head>
          <head xml:id="echoid-head588" xml:space="preserve">Ex præcedenti deductum.</head>
          <p style="it">
            <s xml:id="echoid-s10330" xml:space="preserve">_P_Atet etiam nos poſsè inuenire parallelogrammum circumſcri-
              <lb/>
            ptum ſectionibus oppoſitis, veluti, FC, ideſt ita quod eius duo
              <lb/>
            oppoſita latera ſint baſes oppoſitarum hyperbolarum, & </s>
            <s xml:id="echoid-s10331" xml:space="preserve">reliqua </s>
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