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

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            <s xml:id="echoid-s4373" xml:space="preserve">
              <pb o="177" file="0197" n="197" rhead="LIBER II."/>
            lum, DES, ad rectangulum ſub, DE, & </s>
            <s xml:id="echoid-s4374" xml:space="preserve">compoſita ex, SF, &</s>
            <s xml:id="echoid-s4375" xml:space="preserve">, {1/2}, FE,
              <lb/>
            vna cum rectangulo ſub, EF, & </s>
            <s xml:id="echoid-s4376" xml:space="preserve">compoſita ex, {1/6}, EF, &</s>
            <s xml:id="echoid-s4377" xml:space="preserve">, {1/2}, FS .</s>
            <s xml:id="echoid-s4378" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4379" xml:space="preserve">vt
              <lb/>
            rectangulum, ZEV, quod eſt vnum rectangulorum maximis æqualium,
              <lb/>
            ad rectangulum ſub, ZE, & </s>
            <s xml:id="echoid-s4380" xml:space="preserve">ſub compoſita ex, VB, &</s>
            <s xml:id="echoid-s4381" xml:space="preserve">, {1/2}, BE, vna
              <lb/>
            cum rectangulo ſub, EB, & </s>
            <s xml:id="echoid-s4382" xml:space="preserve">compoſita ex, {1/6}, EB, &</s>
            <s xml:id="echoid-s4383" xml:space="preserve">, {1/2}, BV, regulam
              <lb/>
            autem bic pariter ſuppone ipſam, DS, & </s>
            <s xml:id="echoid-s4384" xml:space="preserve">abſciſſas, reſiduas & </s>
            <s xml:id="echoid-s4385" xml:space="preserve">maxi-
              <lb/>
            mas abſciſſarum tum bic, tum in ſupradictis, & </s>
            <s xml:id="echoid-s4386" xml:space="preserve">ſequentibus, niſi aliud
              <lb/>
            dicatur, ſemper intellige, vel recti, vel ei uſdem obliqui tranſitus, recti
              <lb/>
              <note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">_Hux. diff .i._
                <lb/>
              _huius._</note>
            nempè, cum parallelogramma ſunt rectangula, obliqui autem, cum
              <lb/>
            non ſuerint rectangula, cum diffinitiones de his allatas.</s>
            <s xml:id="echoid-s4387" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div440" type="section" level="1" n="264">
          <head xml:id="echoid-head279" xml:space="preserve">THEOREMA XXXIII. PROPOS. XXXIII.</head>
          <p>
            <s xml:id="echoid-s4388" xml:space="preserve">EXpoſitis duabus vtcunq; </s>
            <s xml:id="echoid-s4389" xml:space="preserve">figuris planis, & </s>
            <s xml:id="echoid-s4390" xml:space="preserve">in earum vna-
              <lb/>
            quaque ſumpta vtcumque regula, vt omnia quadrata
              <lb/>
            earumdem figurarum ſumpta iuxta dictas regulas, ita erunt
              <lb/>
            ſolida quæcumq; </s>
            <s xml:id="echoid-s4391" xml:space="preserve">ad inuicem ſimilaria ex eiſ dem figuris ge-
              <lb/>
            nita iuxta eaſdem regulas.</s>
            <s xml:id="echoid-s4392" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4393" xml:space="preserve">Sint duæ vtcunque ſiguræ planæ, ABC, DEF, in quibus duæ
              <lb/>
            vtcunque ſint iumptæ regulæ, BC, EF, rectæ lineæ. </s>
            <s xml:id="echoid-s4394" xml:space="preserve">Dico igitur,
              <lb/>
            vt omnia quadrata figuræ, ABC, regula, BC, ad omnia quadrata
              <lb/>
            figuræ, DEF, regula, EF, ita eſſe ſolidum fimilare quodcunque
              <lb/>
              <note position="right" xlink:label="note-0197-02" xlink:href="note-0197-02a" xml:space="preserve">Vide B.
                <lb/>
              Definit. 8.
                <lb/>
              huius.</note>
            genitum ex figura, ABC, iuxta regulam, BC, ad ſibi ſimilare ge-
              <lb/>
            nitum ex figura, DEF, iuxta regulam, EF. </s>
            <s xml:id="echoid-s4395" xml:space="preserve">Ducatur in altera di-
              <lb/>
            ctarum figurarum, vtin, DEF, vtcumque regulæ, EF, parallela,
              <lb/>
              <figure xlink:label="fig-0197-01" xlink:href="fig-0197-01a" number="116">
                <image file="0197-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0197-01"/>
              </figure>
            HM, quia ergo quadrata habent inter ſe du-
              <lb/>
            plam rationem laterum, à quibus deſcribun-
              <lb/>
              <note position="right" xlink:label="note-0197-03" xlink:href="note-0197-03a" xml:space="preserve">8. & 15.
                <lb/>
              huius.</note>
            tur, ideò quadratum, EF, ad quadratum,
              <lb/>
            HM, habebit duplam rationem eius, quam
              <lb/>
            habet, EF, ad, HM, ſed etiam aliæ duæ
              <lb/>
            quæcumque figuræ planę ſimiles ab eiſdem
              <lb/>
            tanquam lineis, vel lateribus homologis ea
              <lb/>
              <note position="right" xlink:label="note-0197-04" xlink:href="note-0197-04a" xml:space="preserve">15. huius.</note>
            rumdem deſcriptę habent duplam rationem
              <lb/>
            earumdem, ergo, vt quadratum, EF, ad
              <lb/>
            quadratum, HM, ita erit alia quælibet figura plana deſcripta ab, E
              <lb/>
            F, ad ſimilem ſibi deicriptam ab, HM, ua vt, EF, HM, ſint ea-
              <lb/>
            rum homologæ, &</s>
            <s xml:id="echoid-s4396" xml:space="preserve">, permutando, quadratum, EF, ad aliam ngu-
              <lb/>
            ram deſcriptam ab, EF, erit vt quadratum, HM, ad figuram præ-
              <lb/>
            dictę ſimilem ab, HM, deſcriptam. </s>
            <s xml:id="echoid-s4397" xml:space="preserve">Sic etiam eſſe oſtendemus qua-
              <lb/>
            dratum cuiuſcumque in figura, DEF, ductæ ipſi, EF, </s>
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