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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          <p>
            <s xml:id="echoid-s3210" xml:space="preserve">
              <pb o="175" file="0187" n="187"/>
            natim applicatarum parabolæ congruentes, ęquales
              <lb/>
            ſint poteſtatibus factis ſub prędictis abſciſſis ab or-
              <lb/>
            dinatim applicatis, & </s>
            <s xml:id="echoid-s3211" xml:space="preserve">ſub poteſtate talis lineæ vno
              <lb/>
            gradu depreſſiore poteſtate parabolę. </s>
            <s xml:id="echoid-s3212" xml:space="preserve">Sit ergo.</s>
            <s xml:id="echoid-s3213" xml:space="preserve"/>
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        <div xml:id="echoid-div158" type="section" level="1" n="101">
          <head xml:id="echoid-head113" xml:space="preserve">PROPOSITIO XLIX.</head>
          <p style="it">
            <s xml:id="echoid-s3214" xml:space="preserve">Si fiat vt diameter parabolæ ad ſemibaſim, ſic buius po-
              <lb/>
            testas vno gradu depreſſior poteſtate parabolæ ad ſimi-
              <lb/>
            lem poteſtatem lineæ inueniendæ. </s>
            <s xml:id="echoid-s3215" xml:space="preserve">Potestates applicata-
              <lb/>
            rum ordinatim in parabola eiuſdem gradus cum parabo-
              <lb/>
            la, æquales erunt factis ſub abſciſſis diametri verſus
              <lb/>
            verticem ab ordinatim applicatis, & </s>
            <s xml:id="echoid-s3216" xml:space="preserve">ſub poteſtate li-
              <lb/>
            neæ inuentæ, vno gradu depreſſiore poteſtate para-
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            bolæ.</s>
            <s xml:id="echoid-s3217" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3218" xml:space="preserve">Esto quælibet parabola B A C, in qua fiat vt dia-
              <lb/>
            meter A D, ad ſemibaſim D B, ſic poteſtas
              <lb/>
            huius vnogradu depreſſior poteſtate parabolæ, ad
              <lb/>
            fimilem poteſtatem A H: </s>
            <s xml:id="echoid-s3219" xml:space="preserve">v. </s>
            <s xml:id="echoid-s3220" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3221" xml:space="preserve">ſi parabola eſt qua-
              <lb/>
            dratica, ſic D B, ad A H; </s>
            <s xml:id="echoid-s3222" xml:space="preserve">ſi eſt cubica, ſic quadra-
              <lb/>
            tum D B, ad quædratum A H: </s>
            <s xml:id="echoid-s3223" xml:space="preserve">ſi eſt quadratoqua-
              <lb/>
            dratica, ſic cubus D B, ad cubum A H. </s>
            <s xml:id="echoid-s3224" xml:space="preserve">Dico, quod
              <lb/>
            ſi ordinatim applicentur G L, E k, poteſtas G L,
              <lb/>
            eiuſdem gradus cum parabola ęqualis erit facto ſub
              <lb/>
            L A, & </s>
            <s xml:id="echoid-s3225" xml:space="preserve">ſub poteſtate A H, vno gradu depreſſiore
              <lb/>
            poteſtate parabolæ, & </s>
            <s xml:id="echoid-s3226" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s3227" xml:space="preserve">Quoniam e-
              <lb/>
            nim vt A D, ad D B, ſic poteſtas D B, vno gradu
              <lb/>
            depreſſior poteſtate parabolæ, ad ſimilem </s>
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