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-s1241" xml:space="preserve">
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            pe ex conſtructionē, vt D F, ad F O; </s>
            <s xml:id="echoid-s1242" xml:space="preserve">& </s>
            <s xml:id="echoid-s1243" xml:space="preserve">ratio D F,
              <lb/>
            ad F O (de foris ſumpta F L) componitur ex ratio-
              <lb/>
            ne D F, ad F L, & </s>
            <s xml:id="echoid-s1244" xml:space="preserve">huius ad F O. </s>
            <s xml:id="echoid-s1245" xml:space="preserve">Ergo etiam ra-
              <lb/>
            tio cylindri prædicti ex G C, ad ſolidum ex exceſſu
              <lb/>
            G C, ſupra hyperbolam componetur ex ijſdem ra-
              <lb/>
            tionibus. </s>
            <s xml:id="echoid-s1246" xml:space="preserve">At ex ſchol. </s>
            <s xml:id="echoid-s1247" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s1248" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1249" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1250" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1251" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1252" xml:space="preserve">ratio
              <lb/>
            prædicti cylindri ad antedictum ſolidum componi-
              <lb/>
            tur etiam ex ratione parallelogrammi G D, ad figu-
              <lb/>
            ram A G H C B, & </s>
            <s xml:id="echoid-s1253" xml:space="preserve">ex ratione D F, ad interceptam
              <lb/>
            inter F, & </s>
            <s xml:id="echoid-s1254" xml:space="preserve">centrum grauitatis figuræ A G H C B.
              <lb/>
            </s>
            <s xml:id="echoid-s1255" xml:space="preserve">Ergo etiam rationes D F, ad F L, & </s>
            <s xml:id="echoid-s1256" xml:space="preserve">F L, ad FO,
              <lb/>
            erunt æquales rationibus G D, ad A G H C B, & </s>
            <s xml:id="echoid-s1257" xml:space="preserve">
              <lb/>
            D F, ad prædictam interceptam. </s>
            <s xml:id="echoid-s1258" xml:space="preserve">Sed ex conſtru-
              <lb/>
            ctione, rationes G D, ad A G H C B, & </s>
            <s xml:id="echoid-s1259" xml:space="preserve">D F, ad
              <lb/>
            F L, ſunt æquales. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">Ergo ſi hæ rationes auferantur à
              <lb/>
            prædictis, etiam reliquæ erunt æquales. </s>
            <s xml:id="echoid-s1261" xml:space="preserve">Ergo ratio
              <lb/>
            L F, ad F O, erit æqualis rationi D F, ad interce-
              <lb/>
            ptam prædictam. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">Sed factum fuit ſupra vt L F, ad
              <lb/>
            F O, ſic D F, ad F k. </s>
            <s xml:id="echoid-s1263" xml:space="preserve">Ergo k, erit centrum gra-
              <lb/>
            uitatis figuræ A G H C B. </s>
            <s xml:id="echoid-s1264" xml:space="preserve">Quod erat oſtenden-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s1265" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div69" type="section" level="1" n="48">
          <head xml:id="echoid-head59" xml:space="preserve">SCHOLIVMI.</head>
          <p>
            <s xml:id="echoid-s1266" xml:space="preserve">Inuento autem centro prædicto, facile erit etiam
              <lb/>
            centrum grauitatis hyperbolæ reperire. </s>
            <s xml:id="echoid-s1267" xml:space="preserve">Si enim
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            ſupponamus F D, ſectam bifariam in O, & </s>
            <s xml:id="echoid-s1268" xml:space="preserve">ſuppo-
              <lb/>
            namus k, eſſe centrum grauitatis figuræ A G H C B,
              <lb/>
            ſi fiat vt A B C, ad A G H C B, ſic reciprocè k </s>
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