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

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          <pb o="237" file="0257" n="257" rhead="LIBER III."/>
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        <div xml:id="echoid-div579" type="section" level="1" n="342">
          <head xml:id="echoid-head359" xml:space="preserve">THEOREMA XXI. PROPOS. XXII.</head>
          <p>
            <s xml:id="echoid-s5840" xml:space="preserve">SI intra parallelogrammum, quod circulo, vel ellipſi ſit
              <lb/>
            circumſcriptum, ducatur lateribus eiuſdem parallela
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            quædam rectalinea, per circuli, vel ellipſis centrum non
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            tranſiens, altero reliquorum laterum regula exiſtente. </s>
            <s xml:id="echoid-s5841" xml:space="preserve">Om-
              <lb/>
            nia quadrata parallelogrammi, quod maiori portioni circu-
              <lb/>
            li, vel ellipſis iam dicti, remanent circumſcriptum, ad om-
              <lb/>
            nia quadrata figuræ compoſitæ ex maiori portione, & </s>
            <s xml:id="echoid-s5842" xml:space="preserve">duo-
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            bus trilineis, quiad baſim eiuſdem hinc inde extra conſtitu-
              <lb/>
            untur, demptis eorundem trilineorum omnibus quadratis,
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            erunt in circulo, vt parallelepipedum ſub baſi parallelo-
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            grammo dictæ portioni maiori circumſcripto, altitudine
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            eiuſdem portionis diametro ad cylindricum ſub baſi eadem
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            maiori portione, altitudine differentia diametrorum maio-
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            ris, acminoris factarum portionum, vna cum ſexta parte cu-
              <lb/>
            bi baſis eiuſdem portionis In ellipſi verò erunt, vt paralle-
              <lb/>
            lepipedum ſub baſi parallelogrammo maiori portioni ſimili-
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            ter circumſcripto, altitudine eiuſdem portionis diametro,
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            ad cylindricum ſub baſi eadem maiori portione, altitudine
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            differentia diametrorum maioris, ac minoris factarum por-
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            tionum, vna cum ea porte cubi baſis eiuſdem portionis, ad
              <lb/>
            quam ſexta pars eiuſdem cubi ſit, vt quadratum primæ dia-
              <lb/>
            metriad quadratum ſecundæ, vel, ſi diametrinon ſint axes,
              <lb/>
            vna cum ea parte parallelepipedi ſub altitudine baſi eiu-
              <lb/>
            ſdem portionis, ac ſub baſi rhombo ab eadem deſcripto, ad
              <lb/>
            quam eiuſdem parallelepipedi pars ſexta ſit, vt quadratum
              <lb/>
            primę diametri ad quadratum ſecundæ.</s>
            <s xml:id="echoid-s5843" xml:space="preserve"/>
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            <s xml:id="echoid-s5844" xml:space="preserve">Sit ergo circulus, vel ellipſis, CFEH, cui ſit circumſcriptum pa-
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            rallelogrammum, AQ, & </s>
            <s xml:id="echoid-s5845" xml:space="preserve">centrum ſit, N, diametriautem tranſeun-
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            tesper puncta contactuum laterum circumſcripti parallelogrammi,
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            & </s>
            <s xml:id="echoid-s5846" xml:space="preserve">per centrum, N. </s>
            <s xml:id="echoid-s5847" xml:space="preserve">ſint, CE, FH; </s>
            <s xml:id="echoid-s5848" xml:space="preserve">ſit autem, FH, regula, cui in-
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            ſiſtens, & </s>
            <s xml:id="echoid-s5849" xml:space="preserve">lateribus, AP, DQ, parallela intra ipſum ducta ſit, LG.
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            </s>
            <s xml:id="echoid-s5850" xml:space="preserve">Dico ergo omnia quadrata parallelogrammi, AG, ad omnia qua-
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            drata figuræ, LCFEG, demptis omnibus quadratis trilineorum,
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            CLI, YGE, eſſe, in circulo, vt parallelepipedum ſub </s>
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