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-s258" xml:space="preserve">
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            tentam inter plana HO, AC, æqualem eſſe parti dif-
              <lb/>
            ferentię conorum inter eadem plana contentæ; </s>
            <s xml:id="echoid-s259" xml:space="preserve">quod
              <lb/>
            cum ſit de sè euidens, omittitur. </s>
            <s xml:id="echoid-s260" xml:space="preserve">Patet ergo diffe-
              <lb/>
            rentias conoideorum & </s>
            <s xml:id="echoid-s261" xml:space="preserve">conorum, æquales eſſe inter
              <lb/>
            ſe, tam ſecundum totum, quam ſecundum partes
              <lb/>
            proportionales. </s>
            <s xml:id="echoid-s262" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s263" xml:space="preserve">c.</s>
            <s xml:id="echoid-s264" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div16" type="section" level="1" n="12">
          <head xml:id="echoid-head22" xml:space="preserve">SCHOLIVM I.</head>
          <p>
            <s xml:id="echoid-s265" xml:space="preserve">Non turbetur autem lector videns præſentem
              <lb/>
            propoſitionem probari per indiuiſibilium metho-
              <lb/>
            dum, imo admiretur excellentiam, & </s>
            <s xml:id="echoid-s266" xml:space="preserve">vniuerſalita-
              <lb/>
            tem illius methodi veritatem prodientis etiam illis
              <lb/>
            modis, quibus nequit manifeſtari methodo antiquo-
              <lb/>
            rum. </s>
            <s xml:id="echoid-s267" xml:space="preserve">Nam in ſuperiori conſtructione neſcimus an
              <lb/>
            methodus antiquorum poſſit adhiberi, quia in diffe-
              <lb/>
            rentijs prædictis nequeunt inſcribi cylindri. </s>
            <s xml:id="echoid-s268" xml:space="preserve">Quid
              <lb/>
            ergo? </s>
            <s xml:id="echoid-s269" xml:space="preserve">Concluſio demonſtrata falſa erit, quia per in-
              <lb/>
            diuiſibilia fuit roborata? </s>
            <s xml:id="echoid-s270" xml:space="preserve">Nequaquam. </s>
            <s xml:id="echoid-s271" xml:space="preserve">Nam etiam
              <lb/>
            eadem concluſio probari poteſt methodo antiquo-
              <lb/>
            rum, ſed alia præparatione adhibita, vt patebit ſuo
              <lb/>
            loco.</s>
            <s xml:id="echoid-s272" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div17" type="section" level="1" n="13">
          <head xml:id="echoid-head23" xml:space="preserve">SCHOLIVM II.</head>
          <p>
            <s xml:id="echoid-s273" xml:space="preserve">Sed antequam nos expediamus à præſenti propo-
              <lb/>
            ſitione, opere pretium ducimus manifeſtare eas no-
              <lb/>
            titias, quas ex ipſa, & </s>
            <s xml:id="echoid-s274" xml:space="preserve">ex dictis in noſtro lib. </s>
            <s xml:id="echoid-s275" xml:space="preserve">4. </s>
            <s xml:id="echoid-s276" xml:space="preserve">de
              <lb/>
            infinitis parabolis poſſumus eruere. </s>
            <s xml:id="echoid-s277" xml:space="preserve">Cum enim </s>
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