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

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        <div xml:id="echoid-div371" type="section" level="1" n="225">
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            <s xml:id="echoid-s3548" xml:space="preserve">
              <pb o="150" file="0170" n="170" rhead="GEOMETRI Æ"/>
            pezium, FCMO, eſſe vt compoſita ex, RC, &</s>
            <s xml:id="echoid-s3549" xml:space="preserve">, {1/2}, CD, ad
              <lb/>
            compoſitam ex, MD, &</s>
            <s xml:id="echoid-s3550" xml:space="preserve">, {1/2}, CD.</s>
            <s xml:id="echoid-s3551" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3552" xml:space="preserve">Nam trapezium, CRGF, ad, GD, eſt vt compoſita ex, RC,
              <lb/>
            &</s>
            <s xml:id="echoid-s3553" xml:space="preserve">, {1/2}, CD, ad, RD, inſuper, GD, ad, AM, eſt vt, RD, ad, C
              <lb/>
            M, & </s>
            <s xml:id="echoid-s3554" xml:space="preserve">tandem, AM, ad trapezium, FCMO, eſt vt, CM, ad, M
              <lb/>
            D, cum, {1/2}, CD, ergo ex æquali trapezium, FGRC, ad trape-
              <lb/>
            zium, FCMO, erit vt, RC, cum, {1/2}, CD, ad, MD, cum, {1/2}, D
              <lb/>
            C, quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3555" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div372" type="section" level="1" n="226">
          <head xml:id="echoid-head241" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3556" xml:space="preserve">_H_Inc patet omnes lineas trapezij, FGRC, regula, RM, ad omnes
              <lb/>
              <note position="left" xlink:label="note-0170-01" xlink:href="note-0170-01a" xml:space="preserve">_3. huius._</note>
            lineas trapezij, FCMO, regula eadem eſſe, vt, RC, cum, {1/2},
              <lb/>
            CD, ad, MD, cum, {1/2}, DC, veluti autem in antecedenti oſtendimus,
              <lb/>
            ſi, CD, ſit æqualis ipſi, DF, omnes lineas trapezij, FGMO, regula,
              <lb/>
            CM, æquari omnibus abſciſſis ipſius, FD, adiuncta, DM, ita in præ-
              <lb/>
            ſenti oſtendemus omnes lineas trapezij, FGRC, regula, RD, æquari re-
              <lb/>
            ſiduis omnium abſciſſarum ipſius, AC, vel, FD, adiuucta, RC; </s>
            <s xml:id="echoid-s3557" xml:space="preserve">vnde
              <lb/>
            patebit reſiduas abſciſſarum propoſitæ lineæ, vt, FD, adiuncta, RC, ad
              <lb/>
            omnes abſciſſas eiuſdem, adiuncta alia linea, vt, DM, eſſe vt compoſi-
              <lb/>
            tum ex prima adiuncta, &</s>
            <s xml:id="echoid-s3558" xml:space="preserve">, {1/2}, propoſitæ, CD, ſiue, FD, illi æqualis,
              <lb/>
            ad compoſitum ex ſecunda adiuncta, &</s>
            <s xml:id="echoid-s3559" xml:space="preserve">, {1/2}, propoſitæ lineæ, ideſt vt, R
              <lb/>
            C, cum, {1/2}, CD, vel, DF, ad, MD, cum, {1/2}, CD, vel, DF.</s>
            <s xml:id="echoid-s3560" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div374" type="section" level="1" n="227">
          <head xml:id="echoid-head242" xml:space="preserve">THE OREMA XXII. PROPOS. XXII.</head>
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            <s xml:id="echoid-s3561" xml:space="preserve">EXpoſitis duobus vtcunq; </s>
            <s xml:id="echoid-s3562" xml:space="preserve">parallelogrammis, in eiſdem-
              <lb/>
            que ductis diametris, & </s>
            <s xml:id="echoid-s3563" xml:space="preserve">duobus vtcunq; </s>
            <s xml:id="echoid-s3564" xml:space="preserve">lateribus pro
              <lb/>
            regula ſumptis, nempè in vnoquoq; </s>
            <s xml:id="echoid-s3565" xml:space="preserve">eorum vno: </s>
            <s xml:id="echoid-s3566" xml:space="preserve">Omnia qua-
              <lb/>
            drata cuiuſuis dictorum parallelogrãmorum ad omnia qua-
              <lb/>
            drata cuiuſuis triangulorum per diametrum in ipſo conſtitu-
              <lb/>
            torum, erunt vt omnia quadrata reliqui parallelogrammi ad
              <lb/>
            omnia quadrata cuiuſuis triangulorum per diametrum in
              <lb/>
            iſto ductam pariter conſtitutorum.</s>
            <s xml:id="echoid-s3567" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3568" xml:space="preserve">Sint expoſita vtcunque parallelogramma, AS, Τ β, in ijſque du-
              <lb/>
            ctæ diametri, EO, Z &</s>
            <s xml:id="echoid-s3569" xml:space="preserve">, regulis ſumptis, ES, Ζβ. </s>
            <s xml:id="echoid-s3570" xml:space="preserve">Dico omnia
              <lb/>
            quadrata, AS, ad omnia quadrata trianguli, OES, eſſe vt omnia
              <lb/>
            quadrata, Τ β, ad omnia quadrata, & </s>
            <s xml:id="echoid-s3571" xml:space="preserve">Ζ β. </s>
            <s xml:id="echoid-s3572" xml:space="preserve">Sienim, vtomnia </s>
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