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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            <s xml:id="echoid-s378" xml:space="preserve">
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            B D, eſt 12, talium P N, erit 1. </s>
            <s xml:id="echoid-s379" xml:space="preserve">Cum verò ſi ſiat
              <lb/>
            vt exceſſus conoidis ſupra conum ad conum, nem-
              <lb/>
            pe vt 1, ad 2, ſic reciprocè N P, ad P M, ſit M,
              <lb/>
            centrum grauitatis exceſſus prædicti. </s>
            <s xml:id="echoid-s380" xml:space="preserve">Sequitur qua-
              <lb/>
            lium B D, erat 12, P N, 1, & </s>
            <s xml:id="echoid-s381" xml:space="preserve">B P, 8, talium P M,
              <lb/>
            eſſe 2, & </s>
            <s xml:id="echoid-s382" xml:space="preserve">B M, 6. </s>
            <s xml:id="echoid-s383" xml:space="preserve">Quare patet propoſitum.</s>
            <s xml:id="echoid-s384" xml:space="preserve"/>
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        <div xml:id="echoid-div23" type="section" level="1" n="17">
          <head xml:id="echoid-head27" xml:space="preserve">PROPOSITIO VII.</head>
          <p style="it">
            <s xml:id="echoid-s385" xml:space="preserve">Cylindrus circumſcriptus conoidi hyperbolico eſt ad ipſum,
              <lb/>
            vt compoſita ex axi, ſeù diametro, & </s>
            <s xml:id="echoid-s386" xml:space="preserve">ex latere tran-
              <lb/>
            ſuerſo conoidis, ad dimidium lateris tranſuerſi, vna
              <lb/>
            cum tertia parte axis, ſeù diametri.</s>
            <s xml:id="echoid-s387" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s388" xml:space="preserve">PRopoſitio ergo quinta probatur alio modo. </s>
            <s xml:id="echoid-s389" xml:space="preserve">Sint
              <lb/>
            ſolida prædicta, &</s>
            <s xml:id="echoid-s390" xml:space="preserve">c. </s>
            <s xml:id="echoid-s391" xml:space="preserve">Dico cylindrum Q C, eſ-
              <lb/>
            ſe ad conoides hyperbolicum A B C, vt G D, ad
              <lb/>
            dimidiam G B, cum tertia parte D B. </s>
            <s xml:id="echoid-s392" xml:space="preserve">Cum enim
              <lb/>
            conoides A B C, diuidatur in conum A B C, & </s>
            <s xml:id="echoid-s393" xml:space="preserve">in
              <lb/>
            exceſſum ipſius ſupraipſum; </s>
            <s xml:id="echoid-s394" xml:space="preserve">ſequitur Q C, cylin-
              <lb/>
            drum eſſe ad conoides A B C, vt eſt etiam ad co-
              <lb/>
            num A B C, & </s>
            <s xml:id="echoid-s395" xml:space="preserve">ad exceſſum conoidis ſupra conum.
              <lb/>
            </s>
            <s xml:id="echoid-s396" xml:space="preserve">Cylindrus Q C, eſt ad conum A B C, vt quadra-
              <lb/>
            tum A D, ad ſui tertiam partem: </s>
            <s xml:id="echoid-s397" xml:space="preserve">& </s>
            <s xml:id="echoid-s398" xml:space="preserve">ex ſchol. </s>
            <s xml:id="echoid-s399" xml:space="preserve">ant. </s>
            <s xml:id="echoid-s400" xml:space="preserve">
              <lb/>
            eſt ad exceſſum conoidis A B C, ſupra ſuum co-
              <lb/>
            num vt quadratum A D, ad ſextam partem quadra-
              <lb/>
            ti D E. </s>
            <s xml:id="echoid-s401" xml:space="preserve">Ergo colligendo ambo conſequentia, erit
              <lb/>
            QC, ad conum, & </s>
            <s xml:id="echoid-s402" xml:space="preserve">ad exceſſum, nempe ad conoides
              <lb/>
            A B C, vt quadratum A D, ad ſui tertiam </s>
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