Angeli, Stefano degli, Miscellaneum hyperbolicum et parabolicum : in quo praecipue agitur de centris grauitatis hyperbolae, partium eiusdem, atque nonnullorum solidorum, de quibus nunquam geometria locuta est, parabola nouiter quadratur dupliciter, ducuntur infinitarum parabolarum tangentes, assignantur maxima inscriptibilia, minimaque circumscriptibilia infinitis parabolis, conoidibus ac semifusis parabolicis aliaque geometrica noua exponuntur scitu digna

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        <div xml:id="echoid-div36" type="section" level="1" n="25">
          <pb o="33" file="0045" n="45"/>
        </div>
        <div xml:id="echoid-div38" type="section" level="1" n="26">
          <head xml:id="echoid-head36" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s645" xml:space="preserve">Tria autem, quæ collecta ſunt in quamplurimis
              <lb/>
            propoſitionibus lib. </s>
            <s xml:id="echoid-s646" xml:space="preserve">3. </s>
            <s xml:id="echoid-s647" xml:space="preserve">colligentur etiam nunc. </s>
            <s xml:id="echoid-s648" xml:space="preserve">Nam
              <lb/>
            primò, tam ſuper D E, quam ſupra A B E, intelle-
              <lb/>
            ctis cylindricis rectis æquealtis reſectis diagonaliter
              <lb/>
            plano tranſeunte per E B, & </s>
            <s xml:id="echoid-s649" xml:space="preserve">per latus oppoſitum ip-
              <lb/>
            ſi D A, colligentur cubationes amborum truncorum
              <lb/>
            cylindrici ſuper ſemihyperbola exiſtentis, cumhac
              <lb/>
            tamen diuerſitate; </s>
            <s xml:id="echoid-s650" xml:space="preserve">quod cubatio trunci ſiniſtri dabi-
              <lb/>
            tur ſemota hyperbolæ quadratura; </s>
            <s xml:id="echoid-s651" xml:space="preserve">quia ſine tali qua-
              <lb/>
            dratura datur ratio D C, cylindri ad conoides
              <lb/>
            A B C; </s>
            <s xml:id="echoid-s652" xml:space="preserve">ſecùs dicendum de cubatione trunci dexte-
              <lb/>
            ri, quæ non habetur niſi ſuppoſita quadratura. </s>
            <s xml:id="echoid-s653" xml:space="preserve">Se-
              <lb/>
            cundum eſt (quadratura ſuppoſita) ratio cylindri ex
              <lb/>
            D E, circa D A, ad annulum ſtrictum ex ſemihyper-
              <lb/>
            bola A B E, circa D A. </s>
            <s xml:id="echoid-s654" xml:space="preserve">Tertium eſt ratio conoi-
              <lb/>
            dis, & </s>
            <s xml:id="echoid-s655" xml:space="preserve">prædicti ſolidi ad inuicem, pariter ſuppoſita
              <lb/>
            quadratura.</s>
            <s xml:id="echoid-s656" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s657" xml:space="preserve">Sed antequam vlterius progrediamur, ſicuti plu-
              <lb/>
            ribus modis patefacta eſt ratio cylindri circumſcri-
              <lb/>
            pti ad conoides, ſic non erit inutile aſſignare centrum
              <lb/>
            grauitatis conoidis. </s>
            <s xml:id="echoid-s658" xml:space="preserve">Sit ergo.</s>
            <s xml:id="echoid-s659" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div39" type="section" level="1" n="27">
          <head xml:id="echoid-head37" xml:space="preserve">PROPOSITIO XIII.</head>
          <p style="it">
            <s xml:id="echoid-s660" xml:space="preserve">Centrum grauitatis conoidis hyperbolici ſic diuidit d uode
              <lb/>
            cimam partem diametri eiuſdem ordine quartam à </s>
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