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-s3241" xml:space="preserve">
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            ſtàtem G L, eiuſdem gradus cum parabola. </s>
            <s xml:id="echoid-s3242" xml:space="preserve">Cum
              <lb/>
            autem factum ſub D A, & </s>
            <s xml:id="echoid-s3243" xml:space="preserve">ſub poteſtate A H,
              <lb/>
            oſtenſum fuerit ęquale poteſtati prędictę B D. </s>
            <s xml:id="echoid-s3244" xml:space="preserve">Ergo
              <lb/>
            & </s>
            <s xml:id="echoid-s3245" xml:space="preserve">factum ſub L A, & </s>
            <s xml:id="echoid-s3246" xml:space="preserve">ſub poteſtate A H, erit ęqua-
              <lb/>
            le poteſtati G L. </s>
            <s xml:id="echoid-s3247" xml:space="preserve">Idem patebit de reliquis. </s>
            <s xml:id="echoid-s3248" xml:space="preserve">Quare
              <lb/>
            etiam patebit propoſitum.</s>
            <s xml:id="echoid-s3249" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div160" type="section" level="1" n="102">
          <head xml:id="echoid-head114" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s3250" xml:space="preserve">Sed lubet huic tractatui finem imponere infinita-
              <lb/>
            rum parabolarum tangentibus, ac maximis inſcripti-
              <lb/>
            bilibus, minimiſque circumſcriptilibus infinitis para-
              <lb/>
            bolis, infinitis conoidibus, ac ſemifufis parabo-
              <lb/>
            licis. </s>
            <s xml:id="echoid-s3251" xml:space="preserve">Pro quibus reperien dis nobis neceſſaria eſt
              <lb/>
            doctrina quædam, quę cum ſit nimis prolixa, ex alijs
              <lb/>
            eſt petenda. </s>
            <s xml:id="echoid-s3252" xml:space="preserve">Euclides in 6. </s>
            <s xml:id="echoid-s3253" xml:space="preserve">Elementorum libro, pro-
              <lb/>
            poſit. </s>
            <s xml:id="echoid-s3254" xml:space="preserve">27. </s>
            <s xml:id="echoid-s3255" xml:space="preserve">oſtendit. </s>
            <s xml:id="echoid-s3256" xml:space="preserve">_Omnium parallelogrammorum ad_
              <lb/>
            _eandem rectam lineam applicatorum, & </s>
            <s xml:id="echoid-s3257" xml:space="preserve">deficientium figu-_
              <lb/>
            _ris parallelogrammis ſimilibus, & </s>
            <s xml:id="echoid-s3258" xml:space="preserve">ſimiliter poſitis ei, quæ_
              <lb/>
            _à dimidia deſcribitur, maximum eſt quod ad dimidiam eſt_
              <lb/>
            _applicatum, ſimile existens defectur_. </s>
            <s xml:id="echoid-s3259" xml:space="preserve">Quod Euclides de-
              <lb/>
            monſtrauit in planis, Eutocius de ſphæra, & </s>
            <s xml:id="echoid-s3260" xml:space="preserve">cylind.
              <lb/>
            </s>
            <s xml:id="echoid-s3261" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s3262" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3263" xml:space="preserve">Bonauentura Caualerius, in exercit. </s>
            <s xml:id="echoid-s3264" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3265" xml:space="preserve">
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s3266" xml:space="preserve">28. </s>
            <s xml:id="echoid-s3267" xml:space="preserve">Ricardus Albius in ſuo hemiſphę. </s>
            <s xml:id="echoid-s3268" xml:space="preserve">diſ-
              <lb/>
            fecto. </s>
            <s xml:id="echoid-s3269" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s3270" xml:space="preserve">42. </s>
            <s xml:id="echoid-s3271" xml:space="preserve">extenderunt ſuo medo ad ſolida,
              <lb/>
            patefacientes. </s>
            <s xml:id="echoid-s3272" xml:space="preserve">_Omnium parallelepipedorum ad eandem_
              <lb/>
            _rectam lineam applicatorum cubiſque deficientium, maxi-_
              <lb/>
            _mum eſse, quod ad tertiam illius partem applicatur_. </s>
            <s xml:id="echoid-s3273" xml:space="preserve">Hanc
              <lb/>
            denique doctrinam Petrus Paulus Carauaggius </s>
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