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-s3290" xml:space="preserve">
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            ctor debet ſupponere, velin citat. </s>
            <s xml:id="echoid-s3291" xml:space="preserve">opere Carauaggij
              <lb/>
            inſpicere.</s>
            <s xml:id="echoid-s3292" xml:space="preserve"/>
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        <div xml:id="echoid-div162" type="section" level="1" n="103">
          <head xml:id="echoid-head115" xml:space="preserve">PROPOSITIO L.</head>
          <p style="it">
            <s xml:id="echoid-s3293" xml:space="preserve">Sì in qualibet infinitarum parabolarum ſumatur aliquod
              <lb/>
            punctum à quo ad diametrum recta linea ordinatim
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            applicetur, diameterque ità producatur vt pars extra
              <lb/>
            parabolam ſit ad partem diametri abſciſſam ab ordina-
              <lb/>
            tim applicata verſus verticem vt numerus parabolæ
              <lb/>
            vnitate minutus ad vnitatem. </s>
            <s xml:id="echoid-s3294" xml:space="preserve">Recta linea, quæ ab ex-
              <lb/>
            tremitate inuentæ lineæ ducitur ad illud punctum, quod
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            ſumptum fuer at, parabolam continget.</s>
            <s xml:id="echoid-s3295" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3296" xml:space="preserve">ESto quælibet ſemiparabola cuius vertex B, dia-
              <lb/>
            meter B D, & </s>
            <s xml:id="echoid-s3297" xml:space="preserve">in curua parabolica ſumatur
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            quodlibet punctum E, per quod ordinatim appli-
              <lb/>
            cetur E H, producaturque H B, in G, vt G B, ſit
              <lb/>
            ad B H, vt numerus parabolæ vnitate minutus ad
              <lb/>
            vnitatem: </s>
            <s xml:id="echoid-s3298" xml:space="preserve">v. </s>
            <s xml:id="echoid-s3299" xml:space="preserve">g ſi parabola ſit quadratica, fiat æqua-
              <lb/>
            lis B G, ipſi B H: </s>
            <s xml:id="echoid-s3300" xml:space="preserve">ſi ſit cubica ſit G B, dupla B H,
              <lb/>
            & </s>
            <s xml:id="echoid-s3301" xml:space="preserve">ſic in infinitum (ſupponatur in præſenti parabo-
              <lb/>
            lam eſſe cubicam) & </s>
            <s xml:id="echoid-s3302" xml:space="preserve">iungatur G E. </s>
            <s xml:id="echoid-s3303" xml:space="preserve">Dico hanc pa-
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            rabolam contingere. </s>
            <s xml:id="echoid-s3304" xml:space="preserve">Sinon, cadat intra; </s>
            <s xml:id="echoid-s3305" xml:space="preserve">& </s>
            <s xml:id="echoid-s3306" xml:space="preserve">intelli-
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            gatur ordinatim applicata A K D. </s>
            <s xml:id="echoid-s3307" xml:space="preserve">Quoniam A D,
              <lb/>
            maior eſt D K, ergo quælibet poteſtas A D, maior
              <lb/>
            erit qualibet poteſtate K D, eiuſdem gradus. </s>
            <s xml:id="echoid-s3308" xml:space="preserve">Ergo
              <lb/>
            quælibet poteſtas A D, eiuſdem gradus cum para-
              <lb/>
            bola ad poteſtatem E H, eiuſdem gradus, </s>
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