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

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        <div xml:id="echoid-div303" type="section" level="1" n="188">
          <pb o="123" file="0143" n="143" rhead="LIBER II."/>
        </div>
        <div xml:id="echoid-div305" type="section" level="1" n="189">
          <head xml:id="echoid-head204" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2888" xml:space="preserve">_E_Ademratione, ſi vice quadratorum ſumamus alias figuras ſimiles,
              <lb/>
            oſtendemus omnus figuras ſimiles parallelogram morum in eadem,
              <lb/>
              <note position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">A. Def 8.
                <lb/>
              Huius.</note>
            baſi exiſtentium eſſe, vt altitudines, vel vt latera baſi æqualiter incli-
              <lb/>
            nata, dum illa ſunt æquiangula.</s>
            <s xml:id="echoid-s2889" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div307" type="section" level="1" n="190">
          <head xml:id="echoid-head205" xml:space="preserve">THEOREMA XI. PROPOS. XI.</head>
          <p>
            <s xml:id="echoid-s2890" xml:space="preserve">QVorumlibet parallelogrammorum omnia quadrata te-
              <lb/>
            gulis duobus quibuſuis in eiſdem aſſumptis lateribus,
              <lb/>
            habent inter ſe rationem compoſitam exratione
              <lb/>
            quadratorum dictorum laterum, & </s>
            <s xml:id="echoid-s2891" xml:space="preserve">altitudinum, vel laterum,
              <lb/>
            quę cum prędictis ęqualiter inclinãtur, ſi illa ſint ęquiangula.</s>
            <s xml:id="echoid-s2892" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2893" xml:space="preserve">Sint parallelogramma vtcunq; </s>
            <s xml:id="echoid-s2894" xml:space="preserve">AD, FM, in quibus regulæ ex-
              <lb/>
            tent latera vtcunque, CD, GM, altitudines autem iuxta dictas re-
              <lb/>
            gulas ſumptæ, BV, ON. </s>
            <s xml:id="echoid-s2895" xml:space="preserve">Dico omnia quadrata, AD, ad omnia
              <lb/>
            quadrata, FM, habere rationem compoſitam ex ea, quam habet
              <lb/>
            quadratum, CD, ad quadratum, GM, & </s>
            <s xml:id="echoid-s2896" xml:space="preserve">ex ea, quam habet, B
              <lb/>
            V, altitudo ad altitudinem, ON, vel etiam, BD, ad. </s>
            <s xml:id="echoid-s2897" xml:space="preserve">OM, ſi illa
              <lb/>
            ſint æquiangula, lateraq; </s>
            <s xml:id="echoid-s2898" xml:space="preserve">BD, OM, æqualiter ſint inclinata cum
              <lb/>
              <figure xlink:label="fig-0143-01" xlink:href="fig-0143-01a" number="83">
                <image file="0143-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0143-01"/>
              </figure>
            lateribus, CD, GM; </s>
            <s xml:id="echoid-s2899" xml:space="preserve">abicindatur
              <lb/>
            à, BV, verſus, V, ipſa, XV, æ-
              <lb/>
            qualis, ON, & </s>
            <s xml:id="echoid-s2900" xml:space="preserve">per, X, ducatur, X
              <lb/>
            P, parallela ipſi, CD, ſecans, BD,
              <lb/>
            in, R, erit autem, DR, æqualis
              <lb/>
            ipſi, OM, ſi ſint æquiangula, quod
              <lb/>
            facilè probari poteſt, erit etiam pa-
              <lb/>
            rallelogrammum, PD, in eadem
              <lb/>
            baſi cum parallelogrammo, AD,
              <lb/>
            ſed in eadem altitudine cum parallelogrammo, FM, omnia ergo
              <lb/>
              <note position="right" xlink:label="note-0143-02" xlink:href="note-0143-02a" xml:space="preserve">Defin. 12.
                <lb/>
              lib. 1.</note>
            quadrata parallelogrammi, AD, ad omnia quadrata, FM, habent
              <lb/>
            rationem compoſitam ex ea, quam habent omnia quadrata, AD,
              <lb/>
            ad omnia quadrata, DP, .</s>
            <s xml:id="echoid-s2901" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2902" xml:space="preserve">ex ea, quam habet, BV, ad, VX, ſiue,
              <lb/>
              <note position="right" xlink:label="note-0143-03" xlink:href="note-0143-03a" xml:space="preserve">Ex antec.</note>
            ON, vel ex ea, quam habet, BD, ad, DR, ſiue, OM, ſi ſint æ-
              <lb/>
            quiangula parallelogramma, AD, DP; </s>
            <s xml:id="echoid-s2903" xml:space="preserve">& </s>
            <s xml:id="echoid-s2904" xml:space="preserve">componitur ex ea, quam
              <lb/>
            habent omnia quadrata, PD, ad omnia quadrata, FM, .</s>
            <s xml:id="echoid-s2905" xml:space="preserve">. ex ea,
              <lb/>
              <note position="right" xlink:label="note-0143-04" xlink:href="note-0143-04a" xml:space="preserve">9. huius.</note>
            quam habet quadratum, CD, ad quadratum, GM, ergo omnia
              <lb/>
            quadrata, AD, ad omnia quadrata, FM, habent rationem </s>
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