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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[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.
[61.] SCHOLIVM II.
[62.] PROPOSITIO XXIX.
[63.] SCHOLIV M.
[64.] PROPOSITIO XXX.
[65.] SCHOLIVM I.
[66.] SCHOLIVM II.
[67.] PROPOSITIO XXXI. Semifuſi parabolici cuiuſcunque, centrum grauitatis reperire.
[68.] SCHOLIVM.
[69.] PROPOSITIO XXXII.
[70.] SCHOLIV M.
[71.] PROPOSITIO XXXIII.
[72.] SCHOLIVM.
[73.] PROPOSITIO XXXIV.
[74.] SCHOLIVM.
[75.] PROPOSITIO XXXV.
[76.] SCHOLIVM.
[77.] PROPOSITIO XXXVI.
[78.] SCHOLIVM.
[79.] PROPOSITIO XXXVII.
[80.] SCHOLIVM.
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          <head xml:id="echoid-head75" xml:space="preserve">PROPOSITIO XXX.</head>
          <p style="it">
            <s xml:id="echoid-s2041" xml:space="preserve">Annulus ſtrictus figuræ antecedentis propoſitionis æquatur
              <lb/>
            quatuor ſolidis, quorum duo ſint, qui oriuntur ex re-
              <lb/>
            uolutione ſemifiguræ circa diametrum, alia duo ex re-
              <lb/>
            uolutione ſemifiguræ circa, parallelam diametro per ex-
              <lb/>
            tremitatem baſis; </s>
            <s xml:id="echoid-s2042" xml:space="preserve">& </s>
            <s xml:id="echoid-s2043" xml:space="preserve">hoc tam ſecundum totum, quam
              <lb/>
            ſecundum partes proportionales. </s>
            <s xml:id="echoid-s2044" xml:space="preserve">Item annulus latus ex
              <lb/>
            eadem figura æquatur duobus primis ſolidis, & </s>
            <s xml:id="echoid-s2045" xml:space="preserve">duobus
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            annulis latis ex ſemifigura circa parallelam diametro
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            extra ipſam.</s>
            <s xml:id="echoid-s2046" xml:space="preserve"/>
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            <s xml:id="echoid-s2047" xml:space="preserve">ESto ergo figura A B C, in primis, quæ reuo-
              <lb/>
            luatur circa C F, diametro B D, parallelam
              <lb/>
            ductam per extremitatem baſis C. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">Dico annulum
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            A B C H G, æqualem eſſe duobus ſolidis ex ſemifi-
              <lb/>
            gura D B C, circa B D, & </s>
            <s xml:id="echoid-s2049" xml:space="preserve">duobus ſolidis ex ea-
              <lb/>
            dem D B C, circa C F. </s>
            <s xml:id="echoid-s2050" xml:space="preserve">Diſponantur iſta ſolida,
              <lb/>
            vt in ſchemate, ſec. </s>
            <s xml:id="echoid-s2051" xml:space="preserve">adeovt contineantur omnia in-
              <lb/>
            ter duo plana A B, C D, parallela. </s>
            <s xml:id="echoid-s2052" xml:space="preserve">Sicuti autem
              <lb/>
            taliter ſunt diſpoſita vt duo genita ex reuolutione
              <lb/>
            D B C, circa diametrum occupent medium locum,
              <lb/>
            ita potuiſſent diſponi quocunque alio modo; </s>
            <s xml:id="echoid-s2053" xml:space="preserve">& </s>
            <s xml:id="echoid-s2054" xml:space="preserve">ſicu-
              <lb/>
            ti diſponuntur vt vnum aliud tangat, ità potuiſſent
              <lb/>
            diſponi vt eſſent ab inuicem diſſita quocunque inter-
              <lb/>
            uallo. </s>
            <s xml:id="echoid-s2055" xml:space="preserve">Diſpoſita autem fuerunt ſic tanquam concin-
              <lb/>
            no modo ad inferrenda pulcherrima, quæ ex tali pro-
              <lb/>
            poſitione deducentur. </s>
            <s xml:id="echoid-s2056" xml:space="preserve">Accipiatur in diametro B </s>
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