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

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            ſemicirculi, vel ſemiellipſis, FQB, eſſe vt quadratum, DB, ad re-
              <lb/>
            ctangulum ſub, DB, BR, quoniam rectanguſa ſub, FD, & </s>
            <s xml:id="echoid-s5413" xml:space="preserve">ſemi-
              <lb/>
            circulo, vel ſemiellipſi, FQB, ſunt maiora omnibus quadratis ſemi-
              <lb/>
            circuli, vel ſemiellipſis, FQB, ideò etiam rectangulum ſub, DB, B
              <lb/>
            E, ſemper maius eſt rectangulo ſub, DB, BR, & </s>
            <s xml:id="echoid-s5414" xml:space="preserve">ideo punctum, R,
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            ſemper cadet inter punctum, B, & </s>
            <s xml:id="echoid-s5415" xml:space="preserve">punctum, E, quocunque deinde
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            cadat punctum, I, vnde patet, &</s>
            <s xml:id="echoid-s5416" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5417" xml:space="preserve"/>
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            <s xml:id="echoid-s5418" xml:space="preserve">Similiter, quia omnia quadrata ſemicirculi, vel ſemiellipſis, FQ
              <lb/>
            B, vna cum rectangulis ſub eodem, & </s>
            <s xml:id="echoid-s5419" xml:space="preserve">ſub quadrilineo, FQBDZ,
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            bis ſumptis, minora ſunt omnibus quadratis, FD, ideò, BV, com-
              <lb/>
            pofita ex tribus, BR, RE, EV, minor eſt ipſa, BD, nam, DB, ad,
              <lb/>
            BV, eſt, vt omnia quadrata, FD, ad compoſitum ex omnibus quadra-
              <lb/>
            tis ſemicirculi, vel ſemiellipſis, FQB, & </s>
            <s xml:id="echoid-s5420" xml:space="preserve">ex rectangulis ſub eodem, & </s>
            <s xml:id="echoid-s5421" xml:space="preserve">
              <lb/>
            ſub quadrilineo, FQBDZ, bis ſumptis, vnde omnia clarè patent.</s>
            <s xml:id="echoid-s5422" xml:space="preserve"/>
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        <div xml:id="echoid-div549" type="section" level="1" n="327">
          <head xml:id="echoid-head344" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s5423" xml:space="preserve">_H_INC habetur omnia quadrata, FD, ad reliquum ſui, demptis
              <lb/>
            omnibus quadratis quadrilinei, FQBDZ, eſſe, vt, DB, ad, BV.</s>
            <s xml:id="echoid-s5424" xml:space="preserve"/>
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        <div xml:id="echoid-div550" type="section" level="1" n="328">
          <head xml:id="echoid-head345" xml:space="preserve">THEOREMA XIV. PROPOS. XV.</head>
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            <s xml:id="echoid-s5425" xml:space="preserve">SI circulo, vel ellipſi circumſcribatur parallelogrammum,
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            habebit latera eorundem diametris parallela; </s>
            <s xml:id="echoid-s5426" xml:space="preserve">ſumpto
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            autem quolibet laterum pro regula; </s>
            <s xml:id="echoid-s5427" xml:space="preserve">omnia quadrata dicti
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            parallelogrammi rectanguli, ad omnia quadrata circuli,
              <lb/>
            vel ellipſis inſcripti, vna cum rectangulis bis ſub codem cir-
              <lb/>
            culo, & </s>
            <s xml:id="echoid-s5428" xml:space="preserve">duobus trilineis cuiliber laterum adiacentibus, quæ
              <lb/>
            non fuerunt ſumpta pro regula, erunt, vt dictum parallelo-
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            grammum ad dictum circulum, vel ellipſim.</s>
            <s xml:id="echoid-s5429" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5430" xml:space="preserve">Sit circulus, vel ellipſis, MBEG, cuius centrum, A, per quod
              <lb/>
            tranſeant diametri, ME, BG, ductis autem tangentibus circulum,
              <lb/>
            vel ellipſim in punctis, M, B, E, G, donec concurrant, ſit eidem cir-
              <lb/>
            cumſcriptum parallelogrammum, HF, quod habebit latera paral-
              <lb/>
              <note position="left" xlink:label="note-0242-01" xlink:href="note-0242-01a" xml:space="preserve">@.l. Con.</note>
            lela ipſis axibus, ME, BG, ſit autem regula vtcunque, DF. </s>
            <s xml:id="echoid-s5431" xml:space="preserve">Di-
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            co ergo omnia quadrata parallelogrammi, HF, ad omnia quadra-
              <lb/>
            ta circuli, vel ellipſis, MBEG, vna cum rectangulis bis ſub eodem
              <lb/>
            circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5432" xml:space="preserve">ſub trilineis, MGN, GFE, adia-
              <lb/>
            centibus lateri, NF, ſumpto vtcunque ex duobus, HD, NF, </s>
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