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

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          <p>
            <s xml:id="echoid-s3776" xml:space="preserve">
              <pb o="160" file="0180" n="180" rhead="GEOMETRIÆ"/>
            omnium quadratorum, CMH, & </s>
            <s xml:id="echoid-s3777" xml:space="preserve">quadrupla omnium quadrato-
              <lb/>
            rum, CMH, vel, CBM, &</s>
            <s xml:id="echoid-s3778" xml:space="preserve">, MEF, ſunt autem omnia quadrata
              <lb/>
            trianguli, CEG, æqualia omnibus quadratis, AF, cum omnibus
              <lb/>
            quadratis triangulorum, CBM, MEF, ergo hæc erunt quadrupla
              <lb/>
            omnium quadratorum triangulorum, CBM, MEF, & </s>
            <s xml:id="echoid-s3779" xml:space="preserve">diuidendo
              <lb/>
              <figure xlink:label="fig-0180-01" xlink:href="fig-0180-01a" number="103">
                <image file="0180-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0180-01"/>
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            omnia quadrata, AF, eruntillorum tripla,
              <lb/>
              <note position="left" xlink:label="note-0180-01" xlink:href="note-0180-01a" xml:space="preserve">9. huius.</note>
            ſunt autem omnia quadrata, AG, ad om-
              <lb/>
            nia quadrata, AF, vt quadratum, GE, ad
              <lb/>
            quadratum, EF, ideſt quadrupla .</s>
            <s xml:id="echoid-s3780" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3781" xml:space="preserve">vt 12.
              <lb/>
            </s>
            <s xml:id="echoid-s3782" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s3783" xml:space="preserve">& </s>
            <s xml:id="echoid-s3784" xml:space="preserve">omnia quadrata, AF, ſunt omnium
              <lb/>
            quadratorum triangulorum, BMC, ME
              <lb/>
            F, tripla, ergo omnia quadrata, AG, e-
              <lb/>
            runt duodecupla omnium quadratorum
              <lb/>
            triangulorum, BMC, MEF, & </s>
            <s xml:id="echoid-s3785" xml:space="preserve">ſunt ad
              <lb/>
            omnia quadrata, AF, vt 12. </s>
            <s xml:id="echoid-s3786" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s3787" xml:space="preserve">ergo om-
              <lb/>
            nia quadrata, AG, ad omnia quadrata, A
              <lb/>
            F, cum omnibus quadratis triangulorum, CBM, MEF, erunt vt
              <lb/>
            12. </s>
            <s xml:id="echoid-s3788" xml:space="preserve">ad 4. </s>
            <s xml:id="echoid-s3789" xml:space="preserve">ſunt autem omnia quadrata, AF. </s>
            <s xml:id="echoid-s3790" xml:space="preserve">cum omnibus quadra-
              <lb/>
            tis triangulorum, CBM, MEF, æqualia omnibus quadratis trian-
              <lb/>
            guli, CEG, vel, AEC, vt oſtenſum eſt, ergo omnia quadrata, A
              <lb/>
            G, ad omnia quadrata trianguli, CEG, vel, AEC, ſunt vt 12. </s>
            <s xml:id="echoid-s3791" xml:space="preserve">
              <lb/>
            ad 4. </s>
            <s xml:id="echoid-s3792" xml:space="preserve">.</s>
            <s xml:id="echoid-s3793" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3794" xml:space="preserve">ſunt eorum tripla. </s>
            <s xml:id="echoid-s3795" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s3796" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div404" type="section" level="1" n="247">
          <head xml:id="echoid-head262" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3797" xml:space="preserve">_H_Inc patet, ſi ducamus intra parallelogrammum, AG, æquidiftan-
              <lb/>
            tem ipſi, EG, vtcunque, RV, ſec antem, CE, in, T, &</s>
            <s xml:id="echoid-s3798" xml:space="preserve">, BF,
              <lb/>
            in, S, quod veluti oſtendimus, RV, æquari vni maximarum abſciſſarum.
              <lb/>
            </s>
            <s xml:id="echoid-s3799" xml:space="preserve">CG, dum, EG, eſt æqualis ipſi, GC, ita namc oſtendemus quadratum,
              <lb/>
            RV, æquari quadrato vnius maxim trum abſciſſarum, CG, & </s>
            <s xml:id="echoid-s3800" xml:space="preserve">quadra-
              <lb/>
            tum, TV, æquari quadrato vnius omnium abſciſſarum, CG, ideſt qua-
              <lb/>
            drato, VC; </s>
            <s xml:id="echoid-s3801" xml:space="preserve">quadratum verò, RT, æquari quadrato @nius reſiduarum
              <lb/>
            omnium abſciſſirum, CG, ideſt quadrato, VG, vnde concludemus om-
              <lb/>
            nia quadrata, AG, regula, EG, æquari quadratis maximarum abſciſ-
              <lb/>
            ſarum, CG, & </s>
            <s xml:id="echoid-s3802" xml:space="preserve">omnia quadrata triangult, CEG, æquari quadratis om-
              <lb/>
            nium abſciſſarum, CG, & </s>
            <s xml:id="echoid-s3803" xml:space="preserve">omnia quadrata trianguli, AEC, æquari
              <lb/>
            quadratis reſiduarum omnium abſciſſarum, CG, & </s>
            <s xml:id="echoid-s3804" xml:space="preserve">rectangula ſub tri-
              <lb/>
            angulis, AEC, CEG, æquari rectangu is ſub omnibus abſctſſis, & </s>
            <s xml:id="echoid-s3805" xml:space="preserve">re-
              <lb/>
            ſiduis omnium abſciſſarum, CG, ita ſumptis, vt quoduts rectangulum
              <lb/>
            intelligatur ſub vna abſciſſirum, & </s>
            <s xml:id="echoid-s3806" xml:space="preserve">eius reſidua: </s>
            <s xml:id="echoid-s3807" xml:space="preserve">Vnde veluti oſtendi-
              <lb/>
            mus omnia quadrata, AG, tripla eſſe omnium quadratorum </s>
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