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

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        <div xml:id="echoid-div553" type="section" level="1" n="329">
          <head xml:id="echoid-head346" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s5466" xml:space="preserve">OMnia quadrata, BF, ad rectangula ſub, BF, & </s>
            <s xml:id="echoid-s5467" xml:space="preserve">ſub portione,
              <lb/>
            BEG, ſunt vt, BF, ad portionem, BEG, rectangula verò
              <lb/>
              <note position="left" xlink:label="note-0244-01" xlink:href="note-0244-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              26.lib.2.
                <lb/>
              per A.23.
                <lb/>
              lib. 2.</note>
            ſub portione, BEG, & </s>
            <s xml:id="echoid-s5468" xml:space="preserve">parallelogrammo, BF, diuiduntur in re-
              <lb/>
            ctangula ſub, BEG, &</s>
            <s xml:id="echoid-s5469" xml:space="preserve">, BDE, trilineo .</s>
            <s xml:id="echoid-s5470" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5471" xml:space="preserve">ſub trilineo, GEF, & </s>
            <s xml:id="echoid-s5472" xml:space="preserve">
              <lb/>
            ſub, BEG, & </s>
            <s xml:id="echoid-s5473" xml:space="preserve">trilineo, GEF, & </s>
            <s xml:id="echoid-s5474" xml:space="preserve">ſub, BEG, & </s>
            <s xml:id="echoid-s5475" xml:space="preserve">eadem portione,
              <lb/>
            BEG, .</s>
            <s xml:id="echoid-s5476" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5477" xml:space="preserve">in omnia quadrata portionis, BEG, ergo omnia quadra-
              <lb/>
            ta, BF, ad omnia quadrata portionis, BEG, ſimul cum rectangu-
              <lb/>
            lis ſub portione, BEG, & </s>
            <s xml:id="echoid-s5478" xml:space="preserve">trilineo, GEF, bis ſumptis, vel omnia
              <lb/>
            quadrata, HF, ad omnia quadrata circuli, vel ellipſis, MBEG,
              <lb/>
            ſimul cum rectangulis ſub circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5479" xml:space="preserve">trilineis,
              <lb/>
            MNG, GFE, bis ſumptis, erunt vt, BF, ad portionem, BEG,
              <lb/>
            vel vt, HF, ad circulum, vel ellipſim, MBEG, quod erat oſten,
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s5480" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div555" type="section" level="1" n="330">
          <head xml:id="echoid-head347" xml:space="preserve">THEOREMA XV. PROPOS. XVI.</head>
          <p>
            <s xml:id="echoid-s5481" xml:space="preserve">SI à parallelogrammo per lineam lateribus parallelam
              <lb/>
            parallelogrammum abſcindatur, quod intelligatur cir-
              <lb/>
            culo, vel ellipſi circumſcriptum, regula autem ſit parallelo-
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            grammi baſis : </s>
            <s xml:id="echoid-s5482" xml:space="preserve">Omnia quadrata circumſcripti parallelo-
              <lb/>
            grammi, ſimul cum rectangulis bis ſub eodem, & </s>
            <s xml:id="echoid-s5483" xml:space="preserve">ſub reli-
              <lb/>
            quo parallelogrammo per dictam parallelam conſtituto, ad
              <lb/>
            omnia quadrata dicti circuli, vel ellipſis, ſimul cum rectan-
              <lb/>
            gulis bis ſub eodem circulo, vel ellipſi, & </s>
            <s xml:id="echoid-s5484" xml:space="preserve">ſub quadrilineo
              <lb/>
            duabus parallelis circulum, vel ellipſim tangentibus, inclu-
              <lb/>
            ſaque ab ijſdem curua, & </s>
            <s xml:id="echoid-s5485" xml:space="preserve">latere totius parallelogrammi,
              <lb/>
            quod circulum, vel ellipſim non tangit, comprehenſo, erunt,
              <lb/>
            vt dictum circumſcriptum parallelogrammum ad eundem
              <lb/>
            circulum, velellipſim.</s>
            <s xml:id="echoid-s5486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5487" xml:space="preserve">Sit ergo parallelogrammum, HO, cuius baſis, & </s>
            <s xml:id="echoid-s5488" xml:space="preserve">regula, DO,
              <lb/>
            ductaque, NF, intra ipſum lateribus, HD, CO, parallela, ſit ab-
              <lb/>
            ſciſſum à toto parallelogrammo, HO, parallelogrammum, HF, in-
              <lb/>
            telligatur autem circumſcriptum circulo, vel ellipſi, MBEG, cuics
              <lb/>
            centrum, A, per quod tranſeant diametri, ME, &</s>
            <s xml:id="echoid-s5489" xml:space="preserve">, BG, quæ ſit
              <lb/>
            producta vſque in, P, erunt autem dictæ diametri parallelæ paralle-
              <lb/>
            logrammi, HO, lateribus, tranſibuntque per puncta </s>
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