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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[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.
[41.] PROPOSITIO XIX.
[42.] SCHOLIVM I.
[43.] SCHOLIVM II.
[44.] PROPOSITIO XX.
[45.] SCHOLIVM.
[46.] PROPOSITIO XXI.
[47.] PROPOSITIO XXII.
[48.] SCHOLIVMI.
[49.] SCHOLIVM II.
[50.] PROPOSITIO XXIII.
[51.] PROPOSITIO XXIV.
[52.] PROPOSITIO XXV.
[53.] PROPOSITIO XXVI.
[54.] SCHOLIVM I.
[55.] SCHOLIVM II.
[56.] SCHOLIVM III.
[57.] PROPOSITIO XXVII.
[58.] ALITER.
[59.] PROPOSITIO XXVIII.
[60.] SCHOLIVMI.
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            <s xml:id="echoid-s888" xml:space="preserve">
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            A H k D, intellectis cylindricis rectis æquealtis ſe-
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            ctis diagonaliter plano tranſeunte per D k, & </s>
            <s xml:id="echoid-s889" xml:space="preserve">per
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            latus oppoſitum ipſi L A, minimè ignorabimus cu-
              <lb/>
            bationes truncorum cylindrici ſuper A H k D, exi-
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            ſtentis. </s>
            <s xml:id="echoid-s890" xml:space="preserve">Hac tamen differentia, quod cubationem
              <lb/>
            trunci ſiniſtri habebimus ſine ſuppoſitione alicu-
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            ius quadraturæ; </s>
            <s xml:id="echoid-s891" xml:space="preserve">non ſic cubationem trunci dex-
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            teri.</s>
            <s xml:id="echoid-s892" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s893" xml:space="preserve">His oſtenſis non erit inutile oſtendere modum.
              <lb/>
            </s>
            <s xml:id="echoid-s894" xml:space="preserve">inueniendi centrum grauitatis ſegmenti conoidis
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            hyperbolici A H I C. </s>
            <s xml:id="echoid-s895" xml:space="preserve">Sed prius oſtendatur ſequens
              <lb/>
            propoſitio.</s>
            <s xml:id="echoid-s896" xml:space="preserve"/>
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          <head xml:id="echoid-head43" xml:space="preserve">PROPOSITIO XVI.</head>
          <p style="it">
            <s xml:id="echoid-s897" xml:space="preserve">Differentia ſupradictorum fruſtorum conoideorum eſt ad
              <lb/>
            ſegmentum conoidis parabolici, vt quadrata axium to-
              <lb/>
            tius conoidis, & </s>
            <s xml:id="echoid-s898" xml:space="preserve">conoidis ad verticem, vna cum re-
              <lb/>
            ctangulo contento ſub his axibus, ad ſeſquialterum re-
              <lb/>
            ctangulorum contentorum ſub latere tranſuerſo, & </s>
            <s xml:id="echoid-s899" xml:space="preserve">ſub
              <lb/>
            prædictis axibus.</s>
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            <s xml:id="echoid-s901" xml:space="preserve">SInt ergo ſegmenta anteced, propoſit. </s>
            <s xml:id="echoid-s902" xml:space="preserve">Dico dif-
              <lb/>
            ferentiam fruſtorum A H I C, E N O F, eſſe
              <lb/>
            ad ſegmentum parabolicum E N O F, vt quadrata
              <lb/>
            D B, B k, cum rectangulo D B k, ad ſeſquialterum
              <lb/>
            rectangulorum G B D, G B K. </s>
            <s xml:id="echoid-s903" xml:space="preserve">Differentia enim.
              <lb/>
            </s>
            <s xml:id="echoid-s904" xml:space="preserve">prædicta ad ſegmentum E N O F, habet rationem
              <lb/>
            compoſitam ex ratione differentiæ ad tubum </s>
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