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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          <p>
            <s xml:id="echoid-s3041" xml:space="preserve">
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            conos eſſe in E, diuidente bifariam A D. </s>
            <s xml:id="echoid-s3042" xml:space="preserve">De ex-
              <lb/>
            ceſſu conoideorum ſupra conos, patuit in ſcholio
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s3043" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3044" xml:space="preserve">De exceſſu portionis ſphæræ, vel ſphæ-
              <lb/>
            roidis patuit in anteced propoſit. </s>
            <s xml:id="echoid-s3045" xml:space="preserve">Quare quoadom-
              <lb/>
            nia patet propoſitum.</s>
            <s xml:id="echoid-s3046" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div149" type="section" level="1" n="96">
          <head xml:id="echoid-head108" xml:space="preserve">PROPOSITIO XLVII.</head>
          <p style="it">
            <s xml:id="echoid-s3047" xml:space="preserve">Si in ſolidis antecedentis propoſitionis inſcribantur coni vt
              <lb/>
            dictum eſt, & </s>
            <s xml:id="echoid-s3048" xml:space="preserve">ſect s diametris ipſorum bifariam ordi-
              <lb/>
            natim applicentur lineœ, ſecantes latus conorum inſcri-
              <lb/>
            ptorum. </s>
            <s xml:id="echoid-s3049" xml:space="preserve">Diametri prœdictorum ſolidorum, & </s>
            <s xml:id="echoid-s3050" xml:space="preserve">etiam
              <lb/>
            coni, ſic ſecabuntur ab ipſorum centris grauitatis, vt
              <lb/>
            partes terminatœ ad verticem ſint ad partes terminatas
              <lb/>
            ad baſim vt quadratum ordinatim applicatœ, vna cum
              <lb/>
            duobus quadratis ductœ in conis, ad quadratum ordi-
              <lb/>
            natim applicatœ.</s>
            <s xml:id="echoid-s3051" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3052" xml:space="preserve">SInt ergo ſolida vt in antecedenti propoſitione, & </s>
            <s xml:id="echoid-s3053" xml:space="preserve">
              <lb/>
            inſuper etiam conus, vt in quarta figura BAC,
              <lb/>
            quorum diametri A D, ſint ſectæ bifariamin E, & </s>
            <s xml:id="echoid-s3054" xml:space="preserve">
              <lb/>
            ord natim applicentur E G F, ſitque horum cen-
              <lb/>
            trum grauitatis punctum O. </s>
            <s xml:id="echoid-s3055" xml:space="preserve">Dico A O, eſſe ad
              <lb/>
            O D, vt quadratum F E, cum duobus quadratis
              <lb/>
            G E, ad quadratum F E. </s>
            <s xml:id="echoid-s3056" xml:space="preserve">In cono res eſt manifeſta,
              <lb/>
            quia ſicuti A O, eſt tripla O D, ſic tria quadrata
              <lb/>
            G E, ſunt tripla vnius quadrati G E. </s>
            <s xml:id="echoid-s3057" xml:space="preserve">In alijs ſic
              <lb/>
            patebit. </s>
            <s xml:id="echoid-s3058" xml:space="preserve">Fiat D P, quarta pars D A. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">Ergo P,
              <lb/>
            erit centrum grauitatis conorum. </s>
            <s xml:id="echoid-s3060" xml:space="preserve">Cum ergo ex </s>
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