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

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          <p>
            <s xml:id="echoid-s4091" xml:space="preserve">
              <pb o="169" file="0189" n="189" rhead="LIBER II."/>
            omnia quadrata, CE, ſunt vt quadratum, BC, ad quadratum, C
              <lb/>
            M, quod ſerua. </s>
            <s xml:id="echoid-s4092" xml:space="preserve">Inſuper omnia quadrata, AC, ad omnia quadra-
              <lb/>
              <note position="right" xlink:label="note-0189-01" xlink:href="note-0189-01a" xml:space="preserve">9. huius.</note>
            ta, AM, ſunt vt quadratum, CB, ad quadratum, BM, item om-
              <lb/>
            nia quadrata, AM, ſunt tripla omnium quadratorum trianguli, EB
              <lb/>
              <note position="right" xlink:label="note-0189-02" xlink:href="note-0189-02a" xml:space="preserve">24. huius.</note>
            M, .</s>
            <s xml:id="echoid-s4093" xml:space="preserve">l. </s>
            <s xml:id="echoid-s4094" xml:space="preserve">ſunt ad illa, vt quadratum, BM, ad, {1/3}, quadrati, BM, er-
              <lb/>
            go, ex &</s>
            <s xml:id="echoid-s4095" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4096" xml:space="preserve">quali, omnia quadrata, AC, ad omnia quadrata trianguli,
              <lb/>
              <note position="right" xlink:label="note-0189-03" xlink:href="note-0189-03a" xml:space="preserve">14. huius.</note>
            EBM, erunt vt, BC, ad, {1/3}, quadrati, BM, quod pariter ſerua. </s>
            <s xml:id="echoid-s4097" xml:space="preserve">Tan-
              <lb/>
            dem omnia quadrata, AC, ad rectangula ſub, AM, MD, erunt vt
              <lb/>
            quadratum, BC, ad rectangulum, BMC, rectangula verò ſub, A
              <lb/>
              <note position="right" xlink:label="note-0189-04" xlink:href="note-0189-04a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. huius.</note>
            M, MD, ad rectangula ſub triangulo, EBM, & </s>
            <s xml:id="echoid-s4098" xml:space="preserve">ſub, MD, ſunt vt,
              <lb/>
            AM, ad triangulum, EBM, (quia illa ſunt omnia rectangula pa-
              <lb/>
            rallelogrammi, AM, & </s>
            <s xml:id="echoid-s4099" xml:space="preserve">trianguli, EBM, &</s>
            <s xml:id="echoid-s4100" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4101" xml:space="preserve">què alta, altitudinis
              <lb/>
            nempè &</s>
            <s xml:id="echoid-s4102" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4103" xml:space="preserve">qualis ipſi, MC, ſumpta regula, BM,) .</s>
            <s xml:id="echoid-s4104" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4105" xml:space="preserve">dupla .</s>
            <s xml:id="echoid-s4106" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4107" xml:space="preserve">vtre-
              <lb/>
            ctangulum, BMC, ad eiuſdem dimidium, ergo, ex &</s>
            <s xml:id="echoid-s4108" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4109" xml:space="preserve">quali, omnia
              <lb/>
            quadrata, AC, ad rectangula ſub triangulo, EBM, & </s>
            <s xml:id="echoid-s4110" xml:space="preserve">ſub, MD,
              <lb/>
            erunt vt quadratum, BC, ad dimidium rectanguli, BMC, ad ea-
              <lb/>
            dem verò bis ſumpta erunt, vt quadratum, BC, ad rectangulum, B
              <lb/>
            MC, ergo, colligendo, omnia quadrata, AC, ad omnia quadra-
              <lb/>
            ta, EC, ad omnia quadrata trianguli, EBM, & </s>
            <s xml:id="echoid-s4111" xml:space="preserve">ad rectangula bis
              <lb/>
            ſub triangulo, EBM, & </s>
            <s xml:id="echoid-s4112" xml:space="preserve">ſub, EC, erunt vt quadratum, BC, ad qua-
              <lb/>
            dratum, CM, cum rectangulo, CMB, &</s>
            <s xml:id="echoid-s4113" xml:space="preserve">, {1/3}, quadrati, BM, ſed
              <lb/>
            rectangulum, BMC, cum quadrato, MC, conficit rectangulum
              <lb/>
            ſub, BC, CM, ergo omnia quadrata, AC, ad omnia quadrata tri-
              <lb/>
            anguli, EBM, parallelogrammi, MD, & </s>
            <s xml:id="echoid-s4114" xml:space="preserve">rectangula bis ſub eiſdem,
              <lb/>
            .</s>
            <s xml:id="echoid-s4115" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4116" xml:space="preserve">ad omnia quadrata trapezij, EDCB, .</s>
            <s xml:id="echoid-s4117" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4118" xml:space="preserve">ad omnia quadrata tra-
              <lb/>
              <note position="right" xlink:label="note-0189-05" xlink:href="note-0189-05a" xml:space="preserve">PerD. Co
                <lb/>
              roll. 23.
                <lb/>
              huius.
                <lb/>
              Exantec.</note>
            pezij, IBCO, (quia, O, ED, ſunt &</s>
            <s xml:id="echoid-s4119" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4120" xml:space="preserve">qu@les) erunt, vt quadratum,
              <lb/>
            BC, ad rectangulum ſub, BC, CM, .</s>
            <s xml:id="echoid-s4121" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4122" xml:space="preserve">ſub, BC, ED, vel, IO,
              <lb/>
            vna cum, {1/3}, quadrati, BM, quę eſt differentia parallelarum, BC, E
              <lb/>
            D, ſiue, BC, IO, ipſius trapezij, IBCO, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s4123" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div420" type="section" level="1" n="255">
          <head xml:id="echoid-head270" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4124" xml:space="preserve">_P_Atet autem ſi ipſi, ME adiungamus in directum, EF, &</s>
            <s xml:id="echoid-s4125" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4126" xml:space="preserve">qualem,
              <lb/>
            ipſi, MC, & </s>
            <s xml:id="echoid-s4127" xml:space="preserve">ſi ſupponamus, BM, &</s>
            <s xml:id="echoid-s4128" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4129" xml:space="preserve">quari ipſi, ME, facillimè pro-
              <lb/>
            bari poſſe omnia quadrata, AC, &</s>
            <s xml:id="echoid-s4130" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4131" xml:space="preserve">quari quadratis maximarum abſciſ-
              <lb/>
            ſarum ipſius, ME, adiuncta, EF, & </s>
            <s xml:id="echoid-s4132" xml:space="preserve">omnia quadrata trapezij, EBC
              <lb/>
            D, &</s>
            <s xml:id="echoid-s4133" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4134" xml:space="preserve">quari quadratis omnium abſciſſarum, ME, adiuncta, EF, nam ex.
              <lb/>
            </s>
            <s xml:id="echoid-s4135" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4136" xml:space="preserve">ducta ipſi, BC, parallela vtcunque, VR, quæ ſecet, EB, in, S, &</s>
            <s xml:id="echoid-s4137" xml:space="preserve">,
              <lb/>
            EM, in, T, patet, quod, VT, eſt &</s>
            <s xml:id="echoid-s4138" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4139" xml:space="preserve">qualis ipſi, ME, &</s>
            <s xml:id="echoid-s4140" xml:space="preserve">, TR, adiun-
              <lb/>
            ctæ, EF, & </s>
            <s xml:id="echoid-s4141" xml:space="preserve">ideò tota, VR, &</s>
            <s xml:id="echoid-s4142" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4143" xml:space="preserve">qualis toti, MF; </s>
            <s xml:id="echoid-s4144" xml:space="preserve">ſimiliter, ST, eſt &</s>
            <s xml:id="echoid-s4145" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4146" xml:space="preserve">qua-
              <lb/>
            lis ipſi, TE, &</s>
            <s xml:id="echoid-s4147" xml:space="preserve">, TR, adiunctæ, EF, vnde patet, SR, &</s>
            <s xml:id="echoid-s4148" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s4149" xml:space="preserve">quari compo-
              <lb/>
            ſitæ ex, TE, vnaabſciſſarum, & </s>
            <s xml:id="echoid-s4150" xml:space="preserve">adiuncta: </s>
            <s xml:id="echoid-s4151" xml:space="preserve">Conſimiliter in cæteris </s>
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