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

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        <div xml:id="echoid-div561" type="section" level="1" n="332">
          <pb o="229" file="0249" n="249" rhead="LIBER III."/>
        </div>
        <div xml:id="echoid-div563" type="section" level="1" n="333">
          <head xml:id="echoid-head350" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s5619" xml:space="preserve">_H_INC etiam patet, quoniam omnia quadrata, MF, ad omnià
              <lb/>
            quadrata trilineorum, MNG, GFE, ſunt, vt 21. </s>
            <s xml:id="echoid-s5620" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s5621" xml:space="preserve">pro.
              <lb/>
            </s>
            <s xml:id="echoid-s5622" xml:space="preserve">ximè, quod ad ſuireliquum erunt, vt 21. </s>
            <s xml:id="echoid-s5623" xml:space="preserve">ad 19. </s>
            <s xml:id="echoid-s5624" xml:space="preserve">proximè, ſunt autem
              <lb/>
            omnia quadrata, HF, quadrupla omnium quadratorum, MF, & </s>
            <s xml:id="echoid-s5625" xml:space="preserve">ideò
              <lb/>
            omnia quadrata, HF, ad reſiduum, demptis omnibus quadratis trili-
              <lb/>
            neorum, MNG, GFE, ab omnibus quadratis, MF, erunt proximè,
              <lb/>
            vt 84. </s>
            <s xml:id="echoid-s5626" xml:space="preserve">ad 19. </s>
            <s xml:id="echoid-s5627" xml:space="preserve">ſunt autem omnia quadrata, HF, ad reſiduum, demptis
              <lb/>
            omnibus quadratis, MF, ab omnibus quadratis figuræ, NMBEF, vt
              <lb/>
            84. </s>
            <s xml:id="echoid-s5628" xml:space="preserve">ad 47. </s>
            <s xml:id="echoid-s5629" xml:space="preserve">proximè, ergo reſiduum primum .</s>
            <s xml:id="echoid-s5630" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5631" xml:space="preserve">quod relinquitur, demptis
              <lb/>
            omnibus quadratis trilineorum, MNG, GFE, ab omnibus quadratis,
              <lb/>
            MF, ad reſiduum ſecundum .</s>
            <s xml:id="echoid-s5632" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5633" xml:space="preserve">ad id, quod relinquitur, demptis omni-
              <lb/>
            bus quadratis, MF, ab omnibus quadratis figuræ, NMBEF, erit pro-
              <lb/>
            ximè, vt 19.</s>
            <s xml:id="echoid-s5634" xml:space="preserve">ad 47. </s>
            <s xml:id="echoid-s5635" xml:space="preserve">vnde patet, &</s>
            <s xml:id="echoid-s5636" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5637" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div564" type="section" level="1" n="334">
          <head xml:id="echoid-head351" xml:space="preserve">THEOREMA XVII. PROPOS. XVIII.</head>
          <p>
            <s xml:id="echoid-s5638" xml:space="preserve">EXponatur denuo figura Prop. </s>
            <s xml:id="echoid-s5639" xml:space="preserve">16. </s>
            <s xml:id="echoid-s5640" xml:space="preserve">Dico omnia quadra-
              <lb/>
            ta, HO, (regula eadem ibi ſumpta) ad omnia quadra-
              <lb/>
            ta figuræ compoſitæ ex parallelogrammo, MO, & </s>
            <s xml:id="echoid-s5641" xml:space="preserve">ſemicir-
              <lb/>
            culo, vel ſemiellipſi, MBE, eſſe, vt quadratum, DO, ad
              <lb/>
            rectangulum ſub, DO, OE, vna cum rectangulo ſub, OE,
              <lb/>
            & </s>
            <s xml:id="echoid-s5642" xml:space="preserve">ſub exceſlu, quo dupla, EI, ſuperat, EF, cum, {2/3}, quadra-
              <lb/>
            ti, DE.</s>
            <s xml:id="echoid-s5643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5644" xml:space="preserve">QVoniam ergo omnia quadrata figuræ, CMBEO, diuiduntur
              <lb/>
            per lineam, ME, in omnia quadrata parallelogrammi, MO,
              <lb/>
            in omnia quadrata ſemicirculi, vel ſemiellipſis, MBE, & </s>
            <s xml:id="echoid-s5645" xml:space="preserve">in re-
              <lb/>
              <note position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">Per D.23.
                <lb/>
              lib.2.</note>
            ctangula bis ſub, MO, & </s>
            <s xml:id="echoid-s5646" xml:space="preserve">ſub ſemicirculo, vel ſemiellipſi, MBE,
              <lb/>
            patet primò, quod omnia quadrata, HO, ad omnia quadrata, MO,
              <lb/>
            ſunt, vt quadratum, DO, ad quadratum, OE. </s>
            <s xml:id="echoid-s5647" xml:space="preserve">Inſuper omnia
              <lb/>
            quadrata, HO, ad omnia quadrata, HE, ſunt vt quadratum, OD,
              <lb/>
            ad quadratum, DE, omnia verò quadrata, HE, ad omnia qua-
              <lb/>
              <note position="right" xlink:label="note-0249-02" xlink:href="note-0249-02a" xml:space="preserve">Coroll.1.
                <lb/>
              huius.</note>
            drata ſemicirculi, vel ſemiellipſis, MBE, ſunt vt quadratum, DE,
              <lb/>
            ad ſui ipſius, {2/3}, ergo ex æquali omnia quadrata, HO, ad omnia
              <lb/>
            quadrata ſemicirculi, vel ſemiellipſis, MBE, ſunt vt quadratum,
              <lb/>
            OD, ad, {2/3}, quadrati, DE. </s>
            <s xml:id="echoid-s5648" xml:space="preserve">Vlterius omnia quadrata, HO, ad </s>
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