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-s408" xml:space="preserve">
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            dimidiam G B, cum tertia parte B D. </s>
            <s xml:id="echoid-s409" xml:space="preserve">Quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s410" xml:space="preserve"/>
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        <div xml:id="echoid-div25" type="section" level="1" n="18">
          <head xml:id="echoid-head28" xml:space="preserve">PROPOSITIO VIII.</head>
          <p style="it">
            <s xml:id="echoid-s411" xml:space="preserve">Si ſruſto coni cuìus oppoſita plana parallela, circumſcri-
              <lb/>
            batur cylindrus, & </s>
            <s xml:id="echoid-s412" xml:space="preserve">alter inſcribatur, cuius baſis mi-
              <lb/>
            nor baſis frusti, & </s>
            <s xml:id="echoid-s413" xml:space="preserve">latera trapezij genitoris fruſti pro-
              <lb/>
            ducantur vſque ad concurſum cum diametro. </s>
            <s xml:id="echoid-s414" xml:space="preserve">Tubus
              <lb/>
            cylindricus, qui est exceſſus cylindri circumſcripti ſupra
              <lb/>
            cylindrum inſcriptum, erit ad exceſſum frusti ſupra
              <lb/>
            cylindrum inſcriptum, vt compoſita ex diametro fru-
              <lb/>
            sti, & </s>
            <s xml:id="echoid-s415" xml:space="preserve">ex dupla intercepta inter minorem baſim, & </s>
            <s xml:id="echoid-s416" xml:space="preserve">
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            punctum concurſus laterum trapezij, ad compoſitam ex
              <lb/>
            tali intercepta, & </s>
            <s xml:id="echoid-s417" xml:space="preserve">ex tertia parte diametri fruſti.</s>
            <s xml:id="echoid-s418" xml:space="preserve"/>
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            <s xml:id="echoid-s419" xml:space="preserve">FRuſto coni A B C D, cuius diameter ET, & </s>
            <s xml:id="echoid-s420" xml:space="preserve">
              <lb/>
            oppoſita plana parallela ad inuicem ſint B C,
              <lb/>
            A D, circumſcribatur cylindrus G D, & </s>
            <s xml:id="echoid-s421" xml:space="preserve">inſcri-
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            batur H C; </s>
            <s xml:id="echoid-s422" xml:space="preserve">& </s>
            <s xml:id="echoid-s423" xml:space="preserve">latera A B, D C, producantur vſ-
              <lb/>
            que dum occurrant T E, productæ in I. </s>
            <s xml:id="echoid-s424" xml:space="preserve">Dico tu-
              <lb/>
            bum cylindricum G H C D, eſſe ad exceſſum fruſti
              <lb/>
            A B C D, ſupra cylindrum B L, nempe ad ſolidum
              <lb/>
            genitum ex triangulo A B H, reuoluto circa E T,
              <lb/>
            vt compoſita ex T E, & </s>
            <s xml:id="echoid-s425" xml:space="preserve">ex dupla I E, ad I E, vna
              <lb/>
            cum tertia parte T E. </s>
            <s xml:id="echoid-s426" xml:space="preserve">Cum cnim cylindrus G D,
              <lb/>
            ſit ad cylindrum B L, vt quadratum A T, ad qua-
              <lb/>
            dratum T H, ſeù B E; </s>
            <s xml:id="echoid-s427" xml:space="preserve">nempe vt quadratum T I,
              <lb/>
            ad quadratum I E. </s>
            <s xml:id="echoid-s428" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s429" xml:space="preserve">per conuerſione </s>
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