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

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          <pb o="149" file="0169" n="169" rhead="LIBER II."/>
          <p>
            <s xml:id="echoid-s3528" xml:space="preserve">Erit enim, AM, parallelogrammum, vnde, MA, ad, AD, erit
              <lb/>
              <figure xlink:label="fig-0169-01" xlink:href="fig-0169-01a" number="98">
                <image file="0169-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0169-01"/>
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            vt, CM, ad, CD, AD, verò ad trian
              <lb/>
              <note position="right" xlink:label="note-0169-01" xlink:href="note-0169-01a" xml:space="preserve">5. huius.</note>
            gulum, FCD; </s>
            <s xml:id="echoid-s3529" xml:space="preserve">eſt vt, CD, ad, {1/2}, C
              <lb/>
              <note position="right" xlink:label="note-0169-02" xlink:href="note-0169-02a" xml:space="preserve">Ex antec.</note>
            D, ergo, AM, ad triangulum, FCD,
              <lb/>
            erit vt, MC, ad, {1/2}, CD, eſt autem,
              <lb/>
            AM, ad, FM, vt, CM, ad, MD,
              <lb/>
            ergo, colligendo, AM, ad, FM, cum
              <lb/>
              <note position="right" xlink:label="note-0169-03" xlink:href="note-0169-03a" xml:space="preserve">5. huius</note>
            triangulo, FCD, ideſt ad trapezium,
              <lb/>
            OFCM, erit vt, CM, ad, MD, cum,
              <lb/>
            {1/2}, DC, quod oſtendendum erat.</s>
            <s xml:id="echoid-s3530" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div369" type="section" level="1" n="224">
          <head xml:id="echoid-head239" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3531" xml:space="preserve">_M_Anifeſtnm eſt autem, ſi, CD, ſit æqualis ipſi, DF, omnes lineas
              <lb/>
              <note position="right" xlink:label="note-0169-04" xlink:href="note-0169-04a" xml:space="preserve">_ExCor. 2._
                <lb/>
              _antec._</note>
            parallelogrammi, AD, regula, CD, eſſe æquales maximis ab-
              <lb/>
            ſciſſarum, FD, & </s>
            <s xml:id="echoid-s3532" xml:space="preserve">omnes lineas trianguli, FCD, regula eadem æquari
              <lb/>
            omnibus abſciſſis, FD. </s>
            <s xml:id="echoid-s3533" xml:space="preserve">Nunc ſi intelligamus cuilibet earum, quæ dicun-
              <lb/>
            tur maximæ abſciſſarum, vel abſciſſæ, adiungirectam, DM, vocantur
              <lb/>
            tunc maximæ abſciſſarum, vel abſciſſæ adiuncta, DM, hæc autem ſunt
              <lb/>
              <note position="right" xlink:label="note-0169-05" xlink:href="note-0169-05a" xml:space="preserve">_Defin. 7._
                <lb/>
              _huius._</note>
            eædem illis, quæ habentur in parallelogrammo, AM, & </s>
            <s xml:id="echoid-s3534" xml:space="preserve">trapezio, FC
              <lb/>
            MO, nam ſi produxeris, NE, vſq; </s>
            <s xml:id="echoid-s3535" xml:space="preserve">ad, OM, in, X, ſiet, EX, adiun-
              <lb/>
            cta tum ipſi, NE, vni ex maximis abſciſſarum, FD, tum ipſi, HE,
              <lb/>
            vni ex omnibus abſciſſis, FD, &</s>
            <s xml:id="echoid-s3536" xml:space="preserve">, EX, adiuncta eſt æqualis ipſi, DM,
              <lb/>
            vnde omnes linea, AD, adiuncta, DM, ſunt omnes lineæ parallelo-
              <lb/>
            grammi, AM, & </s>
            <s xml:id="echoid-s3537" xml:space="preserve">ſunt æquales maximis abſciſſarum ipſius, FD, ad-
              <lb/>
            iuncta, DM, & </s>
            <s xml:id="echoid-s3538" xml:space="preserve">omnes lineæ trianguli, FCD, adiuncta, DM, ſunt om-
              <lb/>
            nes lineæ trapezij, FCMO, & </s>
            <s xml:id="echoid-s3539" xml:space="preserve">ſunt æquales omnibus abſciſſis ipſius, F
              <lb/>
            D, adiuncta, DM. </s>
            <s xml:id="echoid-s3540" xml:space="preserve">Quiaergo, AM, ad trapezium, FCMO, eſt vt, C
              <lb/>
            M, ad, MD, cum, {1/2}, DC, ideò omnes lineæ, AM, ad omnes lineas
              <lb/>
              <note position="right" xlink:label="note-0169-06" xlink:href="note-0169-06a" xml:space="preserve">_3. huius._</note>
            trapezij, FCMO, (regulam hic ſemperintelligeipſam, CM,) .</s>
            <s xml:id="echoid-s3541" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3542" xml:space="preserve">ma-
              <lb/>
            ximæ abſciſſarum, FD, adiuncta, DM, ad omnes abſciſſas, FD, adiun-
              <lb/>
            cta, DM, erunt vt, CM, compoſita nempè ex propoſita linea, CD, ſiue
              <lb/>
            ex propoſita, FD, illi æquali, & </s>
            <s xml:id="echoid-s3543" xml:space="preserve">adiuncta, DM, ad compoſitam ex ad-
              <lb/>
            iuncta, MD, &</s>
            <s xml:id="echoid-s3544" xml:space="preserve">, {1/2}, propoſitæ lineæ, CD, vel, DF.</s>
            <s xml:id="echoid-s3545" xml:space="preserve"/>
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        <div xml:id="echoid-div371" type="section" level="1" n="225">
          <head xml:id="echoid-head240" xml:space="preserve">THE OREMA XXI. PROPOS. XXI.</head>
          <p>
            <s xml:id="echoid-s3546" xml:space="preserve">IN expoſita ſuperioris Propoſ. </s>
            <s xml:id="echoid-s3547" xml:space="preserve">figura, ſiproducatur, CD,
              <lb/>
            ad partes, C, vtcunque, vt in, R, & </s>
            <s xml:id="echoid-s3548" xml:space="preserve">compleatur parallc-
              <lb/>
            logrammum, GC, oſtendemus trapezium, FGRC, ad </s>
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