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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        <div xml:id="echoid-div69" type="section" level="1" n="48">
          <p>
            <s xml:id="echoid-s1277" xml:space="preserve">
              <pb o="70" file="0082" n="82"/>
            habetur ſine tali quadratura; </s>
            <s xml:id="echoid-s1278" xml:space="preserve">ſine quanon habemus
              <lb/>
            nec etiam tertium, nempe rationem cylindri ex
              <lb/>
            G C, circa A C, ad ſolidum ex figura A G H C B,
              <lb/>
            circa eandem A C.</s>
            <s xml:id="echoid-s1279" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1280" xml:space="preserve">Sed hyperbolæ A B C, intellecto circumſcripto
              <lb/>
            parallelogrammo, cum hyperbolæ inuentum ſit cen-
              <lb/>
            trum grauitatis, tria ordinatia colligentur etiam in
              <lb/>
            ſolidis genitis ex hyperbola. </s>
            <s xml:id="echoid-s1281" xml:space="preserve">Sed hæc non colligen-
              <lb/>
            turniſi ſuppoſita ipſiu, quadratura. </s>
            <s xml:id="echoid-s1282" xml:space="preserve">Hac ergo ſup-
              <lb/>
            poſita habebimus rationem cylindri ex parallelo-
              <lb/>
            grammo hyperbolæ circumſcripto ad alterutrum ſo-
              <lb/>
            lidorum ex pſa reuoluta ſiue circa A C, ſiue circa
              <lb/>
            latus parallelogrammi tranſiens per B. </s>
            <s xml:id="echoid-s1283" xml:space="preserve">Item habebi-
              <lb/>
            mus rationem horum ſolidorum ad inuicem. </s>
            <s xml:id="echoid-s1284" xml:space="preserve">Ft cu-
              <lb/>
            bationem truncorum cylindrici recti ſupra ipſa exi-
              <lb/>
            ſtentis, reſectique plano conſueto modo diagonali-
              <lb/>
            ter tranſennte. </s>
            <s xml:id="echoid-s1285" xml:space="preserve">Ex quibus pater ſuppoſita hyperbo-
              <lb/>
            læ quadratura, nos aſſignaſſe rationem cylindri cir-
              <lb/>
            cumſcripti ſuſo hyperbolico, ad ipſum; </s>
            <s xml:id="echoid-s1286" xml:space="preserve">quod pari-
              <lb/>
            ter alio modo præſtitit Bonauentura Caualerius in
              <lb/>
            exercit. </s>
            <s xml:id="echoid-s1287" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1288" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1289" xml:space="preserve">35.</s>
            <s xml:id="echoid-s1290" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div71" type="section" level="1" n="49">
          <head xml:id="echoid-head60" xml:space="preserve">SCHOLIVM II.</head>
          <p>
            <s xml:id="echoid-s1291" xml:space="preserve">Repertum eſt ergo centrum grauitatis hyperbo-
              <lb/>
            læ, ſuppoſita ipſius quadratura, quod nullus (quod
              <lb/>
            ſciamus) ante nos tentauit. </s>
            <s xml:id="echoid-s1292" xml:space="preserve">Sed non modo licet re-
              <lb/>
            perire hoc, ſed etiam poſſumus aſſignare centrum-
              <lb/>
            æquilibrij cuiuſcunque eius partis conſtitutæ ex </s>
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