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-s1210" xml:space="preserve">
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            ad quadratum EB, cum tertia parte rectanguli k A B.
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            </s>
            <s xml:id="echoid-s1211" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s1212" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1213" xml:space="preserve">His oſtenſis adinuenietur centrum grauitatis hy-
              <lb/>
            perbolæ ſic.</s>
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          </p>
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        <div xml:id="echoid-div67" type="section" level="1" n="47">
          <head xml:id="echoid-head58" xml:space="preserve">PROPOSITIO XXII.</head>
          <p style="it">
            <s xml:id="echoid-s1215" xml:space="preserve">Si hyperbolæ circumſcriptum par allelogrammum intelliga-
              <lb/>
            tur productum vſque ad ſecundam diametrum, & </s>
            <s xml:id="echoid-s1216" xml:space="preserve">fiat
              <lb/>
            vt quadratum compoſitæ ex axi hyperbolæ, & </s>
            <s xml:id="echoid-s1217" xml:space="preserve">ex di-
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            midia lateris tranſuerſi, ad quadratum dimidiæ lateris
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            tranſuerſi cum rectangulo ſub axi, & </s>
            <s xml:id="echoid-s1218" xml:space="preserve">ſub compoſita
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            ex axi, & </s>
            <s xml:id="echoid-s1219" xml:space="preserve">ex latere tranſuerſo, ſic compoſita ex di-
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            midia lateris tranſuerſi, & </s>
            <s xml:id="echoid-s1220" xml:space="preserve">ex axi, ad aliam: </s>
            <s xml:id="echoid-s1221" xml:space="preserve">item
              <lb/>
            fiat vt dimidium prædicti parallelogrammi ad exceſſum
              <lb/>
            totius parallelogrammi ſupra hyperbolam, ſic compoſita
              <lb/>
            ex axi, & </s>
            <s xml:id="echoid-s1222" xml:space="preserve">ex dimidia lateris tranſuerſi, ad aliam:
              <lb/>
            </s>
            <s xml:id="echoid-s1223" xml:space="preserve">tandem fiat vt ſecunda inuenta ad primam inuentam,
              <lb/>
            ſic compoſita ex axi, & </s>
            <s xml:id="echoid-s1224" xml:space="preserve">ex dimidia lateris tranſuerſi
              <lb/>
            ad ſui partem abſcindendam incipiendo à ſecunda dia-
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            metro. </s>
            <s xml:id="echoid-s1225" xml:space="preserve">Erit punctum quod est alter terminus huius ab-
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            ſciſſæ centrum grauitatis exceſſus parallelogrammi ſupra
              <lb/>
            hyperbolam.</s>
            <s xml:id="echoid-s1226" xml:space="preserve"/>
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            <s xml:id="echoid-s1227" xml:space="preserve">ESto hyperbola A B C, cuius axis B D; </s>
            <s xml:id="echoid-s1228" xml:space="preserve">latus
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            tranſuerſum B E; </s>
            <s xml:id="echoid-s1229" xml:space="preserve">centrum F; </s>
            <s xml:id="echoid-s1230" xml:space="preserve">ſecunda dia-
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            meter G H; </s>
            <s xml:id="echoid-s1231" xml:space="preserve">& </s>
            <s xml:id="echoid-s1232" xml:space="preserve">G C, ſit parallclogrammum: </s>
            <s xml:id="echoid-s1233" xml:space="preserve">fiat
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            vt quadratum F D, ad quadratum F B, cum </s>
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