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-s446" xml:space="preserve">
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            ſub tertia proportionali (quod rectangulum eſt æ-
              <lb/>
            quale quadrato I E): </s>
            <s xml:id="echoid-s447" xml:space="preserve">nempe ſubtriplando terminos,
              <lb/>
            eſt G D, ad A B C D, vt quadratum TI, ad ter-
              <lb/>
            tiam partem quadratorum T1, I E, & </s>
            <s xml:id="echoid-s448" xml:space="preserve">rectanguli
              <lb/>
            T I E, quæ tertia pars eſt æqualis quadrato I E, re-
              <lb/>
            ctangulo I E T, & </s>
            <s xml:id="echoid-s449" xml:space="preserve">tertiæ parti quadrati T E. </s>
            <s xml:id="echoid-s450" xml:space="preserve">At
              <lb/>
            idem cylindrus G D, eſt ad cylindrum B L, vt
              <lb/>
            quadratum A T, ad quadratum HT, feù B E; </s>
            <s xml:id="echoid-s451" xml:space="preserve">hoc
              <lb/>
            eſt vt quadratum T I, ad quadratum I E. </s>
            <s xml:id="echoid-s452" xml:space="preserve">Ergo
              <lb/>
            idem cylindrus G D, erit ad exceſſum fruſti A B C D,
              <lb/>
            ſupra cylindrum B L, vt quadratum T I, ad re-
              <lb/>
            ctangulum I E T, vna cum tertia parte quadrati
              <lb/>
            T E; </s>
            <s xml:id="echoid-s453" xml:space="preserve">nempe vna cum rectangulo contento ſub
              <lb/>
            T E, & </s>
            <s xml:id="echoid-s454" xml:space="preserve">ſub tertia parte T E. </s>
            <s xml:id="echoid-s455" xml:space="preserve">Aſt erat ſupra
              <lb/>
            tubus G H K, ad cylindrum G D, vt rectangulum
              <lb/>
            ſub compoſita ex dupla I E, & </s>
            <s xml:id="echoid-s456" xml:space="preserve">ex E T, & </s>
            <s xml:id="echoid-s457" xml:space="preserve">ſub T E,
              <lb/>
            ad quadratum I T. </s>
            <s xml:id="echoid-s458" xml:space="preserve">Ergo ex æquali, erit tubus GHk,
              <lb/>
            ad exceſſum fruſti A B C D, ſupra cylindrum B L,
              <lb/>
            vt prædictum rectangulum, ad rectangulum I E T,
              <lb/>
            vna cum rectangulo ſub T E, & </s>
            <s xml:id="echoid-s459" xml:space="preserve">ſub tertia parte E T.
              <lb/>
            </s>
            <s xml:id="echoid-s460" xml:space="preserve">Quæ duo rectangula cum ſint idem ac rectangulum
              <lb/>
            ſub compoſita ex I E, & </s>
            <s xml:id="echoid-s461" xml:space="preserve">ex tertia parte E T, & </s>
            <s xml:id="echoid-s462" xml:space="preserve">ſub
              <lb/>
            T E. </s>
            <s xml:id="echoid-s463" xml:space="preserve">Sequitur G H k, eſſe ad exceſſum prædictum,
              <lb/>
            vt rectangulum ſub compoſita ex dupla I E, & </s>
            <s xml:id="echoid-s464" xml:space="preserve">ex
              <lb/>
            E T, & </s>
            <s xml:id="echoid-s465" xml:space="preserve">ſub E T, ad rectangulum ſub eadem E T,
              <lb/>
            & </s>
            <s xml:id="echoid-s466" xml:space="preserve">ſub compoſita ex I E, & </s>
            <s xml:id="echoid-s467" xml:space="preserve">ex tertia parte E T; </s>
            <s xml:id="echoid-s468" xml:space="preserve">nem-
              <lb/>
            pepropter commune latus E T, vt compoſita ex du-
              <lb/>
            pla I E, & </s>
            <s xml:id="echoid-s469" xml:space="preserve">ex E T, ad I E, cum tertia parte E T. </s>
            <s xml:id="echoid-s470" xml:space="preserve">
              <lb/>
            Quod erat oſtendendum.</s>
            <s xml:id="echoid-s471" xml:space="preserve"/>
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