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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            D B k, & </s>
            <s xml:id="echoid-s814" xml:space="preserve">rectangulum ſub D B, & </s>
            <s xml:id="echoid-s815" xml:space="preserve">ſub illa tertia
              <lb/>
            proportionali (quod eſt æquale quadrato mediæ
              <lb/>
            B k). </s>
            <s xml:id="echoid-s816" xml:space="preserve">Ergo L C, erit ad differentiam fruſtorum co-
              <lb/>
            norum, vt triplum rectangulum G D B, ad quadra-
              <lb/>
            ta D B, B k, cum rectangulo D B K; </s>
            <s xml:id="echoid-s817" xml:space="preserve">nempe ad tria
              <lb/>
            quadrata B k, cum triplo rectangulo B k D, & </s>
            <s xml:id="echoid-s818" xml:space="preserve">cum
              <lb/>
            quadrato D k (, quia quadratum D B, diuiditur
              <lb/>
            in quadrata B k, k D, & </s>
            <s xml:id="echoid-s819" xml:space="preserve">in duo rectangula B k D; </s>
            <s xml:id="echoid-s820" xml:space="preserve">& </s>
            <s xml:id="echoid-s821" xml:space="preserve">
              <lb/>
            pariter rectangulum D B k, diuiditur in quadratum
              <lb/>
            B k, & </s>
            <s xml:id="echoid-s822" xml:space="preserve">in rectangulum B k D). </s>
            <s xml:id="echoid-s823" xml:space="preserve">Cum autem ſupra
              <lb/>
            probatum ſit, eſſe L C, ad fruſtum E N O F, vt
              <lb/>
            idem triplum rectangulum G D B, ad ſeſquialterum
              <lb/>
            rectangulorum G B D, G B k. </s>
            <s xml:id="echoid-s824" xml:space="preserve">Ergo colligendo am-
              <lb/>
            boconſe quentia, erit L C, ad fruſtum, & </s>
            <s xml:id="echoid-s825" xml:space="preserve">ad diffe-
              <lb/>
            rentiam fruſtorum conorum ſimul, nempe ad fru-
              <lb/>
            ſtum A H I C, vt triplum rectangulum G D B, ad
              <lb/>
            triplum quadratum B k, cum triplo rectangulo
              <lb/>
            B k D, cum quadrato K D, & </s>
            <s xml:id="echoid-s826" xml:space="preserve">cum ſeſquialtero re-
              <lb/>
            ctangulorum G B D, G B k. </s>
            <s xml:id="echoid-s827" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s828" xml:space="preserve">vt horum pla-
              <lb/>
            norum tertiæ partes: </s>
            <s xml:id="echoid-s829" xml:space="preserve">nempe L C, erit ad A H I C,
              <lb/>
            vt rectangulum G D B, ad quadratum B K, cum
              <lb/>
            rectangulo B k D, & </s>
            <s xml:id="echoid-s830" xml:space="preserve">cum tertia parte quadrati D k,
              <lb/>
            vna cum dimidio rectangulorum G B D, G B K.
              <lb/>
            </s>
            <s xml:id="echoid-s831" xml:space="preserve">Cum verò dimidium rectanguli G B D, diuidatur
              <lb/>
            in dimidium G B K, & </s>
            <s xml:id="echoid-s832" xml:space="preserve">in dimidium G B, K D. </s>
            <s xml:id="echoid-s833" xml:space="preserve">
              <lb/>
            Ergo dimidium rectangulorum G B D, G B K, erit
              <lb/>
            rectangulum G B k, cum dimidio rectanguli G B,
              <lb/>
            K D. </s>
            <s xml:id="echoid-s834" xml:space="preserve">Si ergo ſimul iunxerimus rectangulum G B K,
              <lb/>
            cum quadrato B K, & </s>
            <s xml:id="echoid-s835" xml:space="preserve">cum rectangulo B K D, </s>
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