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

Table of contents

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[11.] PROPOSITIO IV.
[12.] SCHOLIVM I.
[13.] SCHOLIVM II.
[14.] PROPOSITIO V.
[15.] PROPOSITIO VI.
[16.] SCHOLIV M.
[17.] PROPOSITIO VII.
[18.] PROPOSITIO VIII.
[19.] PROPOSITIO IX.
[20.] PROPOSITIO X.
[21.] SCHOLIVM I.
[22.] SCHOLIVM II.
[23.] SCHOLIVM III.
[24.] PROPOSITIO XI.
[25.] PROPOSITIO XII.
[26.] SCHOLIVM.
[27.] PROPOSITIO XIII.
[28.] SCHOLIV M.
[29.] PROPOSITIO XIV.
[30.] SCHOLIV M.
[31.] PROPOSITIO XV.
[32.] SCHOLIVM.
[33.] PROPOSITIO XVI.
[34.] SCHOLIVM.
[35.] PROPOSITIO XVII. Segmenti fupradicti conoidis hyperbolici centrum grauitatis reperire.
[36.] SCHOLIVM.
[37.] PROPOSITIO XVIII.
[38.] SCHOLIVM I.
[39.] SCHOLIVM II.
[40.] SCHOLIVM III.
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            <s xml:id="echoid-s937" xml:space="preserve">Quod verò T F, cylindrus ſit ad ſegmentum.
              <lb/>
            </s>
            <s xml:id="echoid-s938" xml:space="preserve">E N O F, vt dupla D B, ad D B, B k, patet. </s>
            <s xml:id="echoid-s939" xml:space="preserve">Quía
              <lb/>
            ex propoſit. </s>
            <s xml:id="echoid-s940" xml:space="preserve">3. </s>
            <s xml:id="echoid-s941" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s942" xml:space="preserve">4. </s>
            <s xml:id="echoid-s943" xml:space="preserve">cylindrus T F, eſt ad ſegmen-
              <lb/>
            tum conoidis parabolici E N O F, vt parallelo-
              <lb/>
            grammum T F, ad trapezium lineare E R S F, At
              <lb/>
            ex propoſit. </s>
            <s xml:id="echoid-s944" xml:space="preserve">9. </s>
            <s xml:id="echoid-s945" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s946" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s947" xml:space="preserve">eſt parallelogrammum ad
              <lb/>
            trapezium vt dupla D B, ad D B, & </s>
            <s xml:id="echoid-s948" xml:space="preserve">B k. </s>
            <s xml:id="echoid-s949" xml:space="preserve">Qua-
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            re patet propoſitum.</s>
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          <head xml:id="echoid-head44" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s951" xml:space="preserve">Ratio autem prædictorum ſolidorum collecta in
              <lb/>
            ſupradicta propoſitione, poteſt etiam reduci ad mi-
              <lb/>
            nora plana; </s>
            <s xml:id="echoid-s952" xml:space="preserve">quia poteſt reduci ad eam, quam habet
              <lb/>
            rectangulum D B k, cum tertia parte quadrati D k,
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            ad rectangulum G B K, cum dimidio rectanguli
              <lb/>
            G B, K D. </s>
            <s xml:id="echoid-s953" xml:space="preserve">Patet quia hæc plana ſunt tertiæ partes
              <lb/>
            priorum planorum.</s>
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          <head xml:id="echoid-head45" xml:space="preserve">PROPOSITIO XVII.</head>
          <head xml:id="echoid-head46" style="it" xml:space="preserve">Segmenti fupradicti conoidis hyperbolici centrum
            <lb/>
          grauitatis reperire.</head>
          <p>
            <s xml:id="echoid-s955" xml:space="preserve">SEgmenti conoidis hyperbolici A H I C, cen-
              <lb/>
            trum grauitatis reperietur ſic. </s>
            <s xml:id="echoid-s956" xml:space="preserve">Inſcriptis ſoli-
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            dis vt ſupra, ſecetur K D, ſic in X, vt K X, ſit ad
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            X D, vt duplum quadratum E D, cum quadrato
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            N K, ad duplum quadratum N K, cum </s>
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