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

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            <s xml:id="echoid-s4307" xml:space="preserve">
              <pb o="175" file="0195" n="195" rhead="LIBER II."/>
            abſciſſarum, BM, adiuncta, MZ, & </s>
            <s xml:id="echoid-s4308" xml:space="preserve">omnes lineas, BO, æquari ma-
              <lb/>
            ximis abſciſſarum, BM, adiuncta, ME, & </s>
            <s xml:id="echoid-s4309" xml:space="preserve">omnes lineas trapezij, A
              <lb/>
            HNC, æquari omnibus abſciſſis, BM, adiuncta, MZ, & </s>
            <s xml:id="echoid-s4310" xml:space="preserve">omnes lineas
              <lb/>
            trapezij, BMNC, æquari omnibus abſciſſis ipſius, BM, adiuncta, M
              <lb/>
            E, quorum exemplum patere poteſt in recta, HO, in qua, HO, æquatur
              <lb/>
            ipſi, BZ, &</s>
            <s xml:id="echoid-s4311" xml:space="preserve">, HN, ipſi, MZ, &</s>
            <s xml:id="echoid-s4312" xml:space="preserve">, MN, ipſi, ME, æquari autem ſu-
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            pradicta ſic intellige, vt ſemper cuilibet aſſumptæ in parallelogrammo,
              <lb/>
            AO, reperiatur ſibi æqualis reſpondens in recta, BZ, & </s>
            <s xml:id="echoid-s4313" xml:space="preserve">ſic cuilibet aſ-
              <lb/>
            ſumptæ in trapezijs iam dictis, reperiatur illi æqualis correſpondens in
              <lb/>
            recta, BZ, quæ erit vna abſciſſarum, BM, adiuncta, MZ, vel, ME,
              <lb/>
            ea nempè, que terminatur ad idem punctum, per quod tranſit ea, quæ
              <lb/>
            æquidiſtat ipſi, DF, & </s>
            <s xml:id="echoid-s4314" xml:space="preserve">cum eadem comparata illi reperitur æqualis (ſic
              <lb/>
            autem intellige in cæteris, cum dicimus omnes lineas alicuius figuræ,
              <lb/>
            quæ eſt parallelogrammum, vel trapezium, vel triangulum æquari om-
              <lb/>
            nibus abſciſſis, vel maximis, vel reſiduis omnium abſciſſarum alicuius
              <lb/>
            lineæ, adiuncta, vel non adiuncta aliqua linea.) </s>
            <s xml:id="echoid-s4315" xml:space="preserve">Rectangula ergo ſub
              <lb/>
            maximis abſciſſarum, BM, adiuncta, MZ, & </s>
            <s xml:id="echoid-s4316" xml:space="preserve">ſub maximis abſciſſarum,
              <lb/>
            BM, adiuncta, ME, ad rectangula ſub omnibus abſciſſis, BM, adiun-
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            cta, MZ, & </s>
            <s xml:id="echoid-s4317" xml:space="preserve">ſub omnibus abſciſſis, BM, adiuncta, ME, erunt vt re-
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            ctangulum ſub, HO, OM, ideſt ſub, ZB, BE, ad rectangulum ſub, H
              <lb/>
            O, MN, vnà cum rectangulo ſub compoſita ex, {1/2}, HM, &</s>
            <s xml:id="echoid-s4318" xml:space="preserve">, {1/3}, NO,
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            & </s>
            <s xml:id="echoid-s4319" xml:space="preserve">ſub, NO, ideſt ad rectangulum ſub, ZB, ME, vna cum rectangulo
              <lb/>
            ſub compoſita ex, {1/2}, ZE, &</s>
            <s xml:id="echoid-s4320" xml:space="preserve">, {1/3}, MB, & </s>
            <s xml:id="echoid-s4321" xml:space="preserve">ſub, MB.</s>
            <s xml:id="echoid-s4322" xml:space="preserve"/>
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        <div xml:id="echoid-div435" type="section" level="1" n="262">
          <head xml:id="echoid-head277" xml:space="preserve">THEOREMA XXXII. PROPOS. XXXII.</head>
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            <s xml:id="echoid-s4323" xml:space="preserve">EXpoſita adhuc antecedentis Theorematis figura, ſi ipſi,
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            EF, ad punctum, F, iungatur in directum quædam re-
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            cta linea, vt, FS, & </s>
            <s xml:id="echoid-s4324" xml:space="preserve">compleatur parallelogrammum, FR, re-
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            gula ſumpta, DS, oſtendemus rectangula ſub, AE, ER, ad
              <lb/>
            rectangula ſub trapezijs, ADEC, CESR, eſſe vt rectan-
              <lb/>
            gulum, DES, ad rectangulum ſub, DE, & </s>
            <s xml:id="echoid-s4325" xml:space="preserve">compoſita ex, S
              <lb/>
            F, &</s>
            <s xml:id="echoid-s4326" xml:space="preserve">, {1/2}, FE, vna cum rectangulo ſub, EF, & </s>
            <s xml:id="echoid-s4327" xml:space="preserve">compoſita ex,
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            {1/6}, EF, &</s>
            <s xml:id="echoid-s4328" xml:space="preserve">, {1/2}, FS.</s>
            <s xml:id="echoid-s4329" xml:space="preserve"/>
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            <s xml:id="echoid-s4330" xml:space="preserve">Rectangula enim ſub, AE, ER, ad rectangula ſub, AE, & </s>
            <s xml:id="echoid-s4331" xml:space="preserve">tra-
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              <note position="right" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">Coroll .1.
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              26. huius.</note>
            pezio, CESR, ſunt vt, ER, ad trapezium, CESR, .</s>
            <s xml:id="echoid-s4332" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4333" xml:space="preserve">vt, ES,
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            ad, SF, cum, {1/2}, FE, .</s>
            <s xml:id="echoid-s4334" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4335" xml:space="preserve">tumpta, DE, communi altitudine, vt re-
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              <note position="right" xlink:label="note-0195-02" xlink:href="note-0195-02a" xml:space="preserve">20. huius.
                <lb/>
              5. huius.</note>
            ctangulum, DES, ad rectangulum ſub, DE, & </s>
            <s xml:id="echoid-s4336" xml:space="preserve">ſub compoſita ex,
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            SF, &</s>
            <s xml:id="echoid-s4337" xml:space="preserve">, {1/2}, FE, quod ſerua.</s>
            <s xml:id="echoid-s4338" xml:space="preserve"/>
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