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

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          <pb o="159" file="0179" n="179" rhead="LIBER II."/>
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        <div xml:id="echoid-div402" type="section" level="1" n="246">
          <head xml:id="echoid-head261" xml:space="preserve">THEOREMA XXIV. PROPOS. XXIV.</head>
          <p>
            <s xml:id="echoid-s3757" xml:space="preserve">EXpoſito parallelogrammo quocunq; </s>
            <s xml:id="echoid-s3758" xml:space="preserve">in eoque ducta dia-
              <lb/>
            metro; </s>
            <s xml:id="echoid-s3759" xml:space="preserve">omnia quadrata parallelogrammiad omnia qua-
              <lb/>
            drata cuiuſuis triangulorum per dictam diametrum conſtitu-
              <lb/>
            torum erunt in ratione tripla, vno laterum parallelogrammi
              <lb/>
            communiregula exiſtente.</s>
            <s xml:id="echoid-s3760" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3761" xml:space="preserve">Sit parallelogrammum, AG, in eo ducta diameter, CE, regula
              <lb/>
            vtcunque latus, EG. </s>
            <s xml:id="echoid-s3762" xml:space="preserve">Dico omnia quadrata, AG, eſſe tripla om-
              <lb/>
            nium quadratorum trianguli cuiuſuis, AEC, ſiue, CEG. </s>
            <s xml:id="echoid-s3763" xml:space="preserve">Diui-
              <lb/>
            dantur bifariam latera, AC, CG, in punctis, B, H, & </s>
            <s xml:id="echoid-s3764" xml:space="preserve">per, B, ip-
              <lb/>
            ſi, CG, perque, H, ipſi, CA, parallelę ducantur, BF, DH, quę
              <lb/>
            ſe cum recta, CE, communiter bifariam ſecabuntin puncto, M.
              <lb/>
            </s>
            <s xml:id="echoid-s3765" xml:space="preserve">Quia igitur in figura, ſiue parallelogrammo, AG, ducitur linea, B
              <lb/>
            F, quę omnes æquidiſtantes ipſi, EG, bifariam ſecat, &</s>
            <s xml:id="echoid-s3766" xml:space="preserve">, CE, quæ
              <lb/>
              <figure xlink:label="fig-0179-01" xlink:href="fig-0179-01a" number="102">
                <image file="0179-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0179-01"/>
              </figure>
            eaſdem in partes inæquales diuidit, pręter-
              <lb/>
            quam, DH, omnia quadrata trianguli, A
              <lb/>
              <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">Per I. Co-
                <lb/>
              rol. antec.</note>
            EC, cum omnibus quadratis trianguli, C
              <lb/>
            EG, & </s>
            <s xml:id="echoid-s3767" xml:space="preserve">cum omnibus quadratis duorum
              <lb/>
              <note position="right" xlink:label="note-0179-02" xlink:href="note-0179-02a" xml:space="preserve">Vide D.
                <lb/>
              lib. 7. An-
                <lb/>
              not. Pro-
                <lb/>
              pofit. 8.</note>
            triangulorum, CBM, EMF, dupla erunt
              <lb/>
            omnium quadratorum, AF, licet enim, D
              <lb/>
            H, perlineam, CE, fit non bifariam diui-
              <lb/>
            ſa, nihil tamen hoc obſtat noſtro propoſi-
              <lb/>
            to, nam & </s>
            <s xml:id="echoid-s3768" xml:space="preserve">ipſi, DH, contingit, veluti ijs,
              <lb/>
            quæ inæqualiter ſecantur, quadratum ſe-
              <lb/>
            ctarum partium, ſcilicet quadrata, DM,
              <lb/>
            MH, dupla eſſe quadratorum dimidiæ, nempè quadrati, DM, & </s>
            <s xml:id="echoid-s3769" xml:space="preserve">
              <lb/>
            eius, quæ inter ſectiones interijcitur, quæ hic nulla eſt, cum duę ſe-
              <lb/>
            cantes, BF, CE, vniantur in puncto, M: </s>
            <s xml:id="echoid-s3770" xml:space="preserve">Sunt autem omnia qua-
              <lb/>
            drata trianguli, AEC, æqualia omnibus quadratis trianguli, CE
              <lb/>
            G, quia ſunt triangula in æqualibus baſibus, EG, AC, & </s>
            <s xml:id="echoid-s3771" xml:space="preserve">eadem al-
              <lb/>
              <note position="right" xlink:label="note-0179-03" xlink:href="note-0179-03a" xml:space="preserve">Ex B. vel
                <lb/>
              C. Corol.
                <lb/>
              Prop. 22.
                <lb/>
              huius.</note>
            titudine licet euersè poſita, & </s>
            <s xml:id="echoid-s3772" xml:space="preserve">ideò omnia quadrata trianguli, CE
              <lb/>
            G, ſunt æqualia omnibus quadratis, AF, cum omnibus quadratis
              <lb/>
            triangulorum, CBM, MEF. </s>
            <s xml:id="echoid-s3773" xml:space="preserve">Quoniam verò omnia quadrata tri-
              <lb/>
            anguli, BMC, funt æqualia omnibus quadratis trianguli, CMH,
              <lb/>
            omnia verò quadrata trianguli, CEG, ad omnia quadrata triangu-
              <lb/>
            li, CMH, ſunt in tripla ratione eius, quam habet, GC, ad, CH,
              <lb/>
            quæ eſt dupla .</s>
            <s xml:id="echoid-s3774" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3775" xml:space="preserve">in ratione octupla, & </s>
            <s xml:id="echoid-s3776" xml:space="preserve">hoc, quia triangula, CEG,
              <lb/>
            CMH, ſunt ſimilia, ideò omnia quadrata, CEG, erunt </s>
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