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-div191" type="section" level="1" n="126">
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            <s xml:id="echoid-s3745" xml:space="preserve">
              <pb o="205" file="0217" n="217"/>
            dictum conſequens, ſic vnum binarium anteceden-
              <lb/>
            tis, ad vnitatem conſequentis. </s>
            <s xml:id="echoid-s3746" xml:space="preserve">Erit ergo vt duæ par-
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            tes illius magnitudinis diuiſæ in tot partes quotus eſt
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            numerus parabolę duplus, & </s>
            <s xml:id="echoid-s3747" xml:space="preserve">conſequenter ipſius A D,
              <lb/>
            diuiſæ in tot partes quotus eſt numerus parabolę vni-
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            tate auctus, ad A Q. </s>
            <s xml:id="echoid-s3748" xml:space="preserve">Quoderat oſtendendum.</s>
            <s xml:id="echoid-s3749" xml:space="preserve"/>
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        <div xml:id="echoid-div193" type="section" level="1" n="127">
          <head xml:id="echoid-head139" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s3750" xml:space="preserve">Cum autem in propoſit. </s>
            <s xml:id="echoid-s3751" xml:space="preserve">55, viſum ſit, triangulum
              <lb/>
            G Q D, eſſe dimidium trianguli maximi inſcripti in
              <lb/>
            figura conſtante ex duabus ſemiparabolis; </s>
            <s xml:id="echoid-s3752" xml:space="preserve">ſequitur
              <lb/>
            hoc eſſe ad triangulum maximum ſibi inſcriptum in
              <lb/>
            ſupra dicta ratione, continuata ratione A D, ad D Q,
              <lb/>
            diametrum trianguli æqualem G F, vt dictum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s3753" xml:space="preserve">Pariter cum minima trian gula circum ſcripta tam in-
              <lb/>
            finitis parabolis, quam infinitis figuris conſtantibus
              <lb/>
            ex duabus ſemiparabolis, ſint quadrupla maximo-
              <lb/>
            rum triangulorum in ipſis inſcriptorum; </s>
            <s xml:id="echoid-s3754" xml:space="preserve">ſequitur
              <lb/>
            prædictas figuras eſſe ad minima triangula circum-
              <lb/>
            ſcripta, vt idem antecedens ad quadruplum conſe-
              <lb/>
            quentis: </s>
            <s xml:id="echoid-s3755" xml:space="preserve">vel vt quarta pars antecedentis ad idem
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            conſequens.</s>
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        <div xml:id="echoid-div194" type="section" level="1" n="128">
          <head xml:id="echoid-head140" xml:space="preserve">PROPOSITIO LXV.</head>
          <p style="it">
            <s xml:id="echoid-s3757" xml:space="preserve">Quodlibet conoides parabolicum eſt ad maximum conum ſibi
              <lb/>
            inſcriptum, vt pars radij baſis conoidis, quæ ſe habeat ad
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            totum radium vt vnitas ad numerum conoidis </s>
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