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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[Item 1.]
[2.] MISCELL ANEVM HYPERBOLICVM, ET PARABOLICVM. IN QVO PRÆCIPVE AGITVR DE CENTRIS Grauitatis Hyperbolæ, 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. AVTHORE F. STEPHANODE ANGELIS VENETO, Ordinis Ieſuatorum S. HIERONY MI, in Veneta Prouincia Definitore Prouinciali. AD ILLVSTRISSIMOS, ET SAPIENTISSIMOS SENATVS BONONIENSIS QVINQVAGINTA VIROS.
[3.] VENETIIS, MD CLIX. Apud Ioannem La Noù. SVPERIORVM PERMISSV.
[4.] Illuſtriſſimis, & Sapientiſſimis BONONIENSIS SENATVS QVINQVAGINTA VIRIS Dominis Colendiſſimis. F. STEPHANVS ANGELI VENETVS Ord. leſuatorum S. Hieronymi, ac in Prouincia Veneta Prouincialis Definitor P.P.P.
[5.] LECTORI BENEVOLO.
[6.] Noi Reformatori dello Studio di Padoa.
[7.] MISCELLANEVM HYPERBOLICVM, PARABOLICVMQVE.
[8.] PROPOSITIO PRIMA.
[9.] PROPOSITIO II.
[10.] PROPOSITIO III.
[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.
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          <head xml:id="echoid-head35" xml:space="preserve">PROPOSITIO XII.</head>
          <p style="it">
            <s xml:id="echoid-s594" xml:space="preserve">Si fiat vt ſemihyperbola ad dimidium parallelogrammi ſibi
              <lb/>
            circumſcripti, ſic compoſita ex ſemilatere tranſuerſo hy-
              <lb/>
            perbolæ, & </s>
            <s xml:id="echoid-s595" xml:space="preserve">ex tertia parte axis eiuſdem, ad aliam: </s>
            <s xml:id="echoid-s596" xml:space="preserve">dein-
              <lb/>
            de fiat vt compoſita ex latere tranſuerſo & </s>
            <s xml:id="echoid-s597" xml:space="preserve">ex axi, ad
              <lb/>
            inuentam, ſic baſis ſemihyperbolæ ad ſui partem abſcin-
              <lb/>
            dendam incipiendo ab axi. </s>
            <s xml:id="echoid-s598" xml:space="preserve">Centrum grauitatis ſemihy-
              <lb/>
            perbolæ erit in line a per punctum ducta axi parallela.</s>
            <s xml:id="echoid-s599" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s600" xml:space="preserve">ESto hyperbola A B C, cuius axis B E; </s>
            <s xml:id="echoid-s601" xml:space="preserve">centrum
              <lb/>
            G; </s>
            <s xml:id="echoid-s602" xml:space="preserve">latus tranſuerſum F B; </s>
            <s xml:id="echoid-s603" xml:space="preserve">parallelogrammum
              <lb/>
            ei circumſcriptum ſit D C; </s>
            <s xml:id="echoid-s604" xml:space="preserve">ſitque B H, tertia pars
              <lb/>
            B E; </s>
            <s xml:id="echoid-s605" xml:space="preserve">& </s>
            <s xml:id="echoid-s606" xml:space="preserve">fiat vt A B E, ad dimidium D E, ſic G H,
              <lb/>
            ad E k; </s>
            <s xml:id="echoid-s607" xml:space="preserve">& </s>
            <s xml:id="echoid-s608" xml:space="preserve">pariter fiat vt F E, ad E k, ſic A E, ad
              <lb/>
            E L; </s>
            <s xml:id="echoid-s609" xml:space="preserve">ac per L, ducatur L M, parallela B E. </s>
            <s xml:id="echoid-s610" xml:space="preserve">Dico
              <lb/>
            in M L, eſſe centrum grauitatis ſemihyperbolæ
              <lb/>
            A B E. </s>
            <s xml:id="echoid-s611" xml:space="preserve">Intelligamus D E, cum ſemihyperbola.
              <lb/>
            </s>
            <s xml:id="echoid-s612" xml:space="preserve">A B E, rotari circa B E. </s>
            <s xml:id="echoid-s613" xml:space="preserve">Quoniam ex propoſit. </s>
            <s xml:id="echoid-s614" xml:space="preserve">5. </s>
            <s xml:id="echoid-s615" xml:space="preserve">7. </s>
            <s xml:id="echoid-s616" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s617" xml:space="preserve">11. </s>
            <s xml:id="echoid-s618" xml:space="preserve">cylindrus D C, eſt ad conoides A B C, vt
              <lb/>
            F E, ad G H; </s>
            <s xml:id="echoid-s619" xml:space="preserve">& </s>
            <s xml:id="echoid-s620" xml:space="preserve">ratio F E, ad GH (de foris ſumpta
              <lb/>
            E k) componitur ex rationibus F E, ad E k, & </s>
            <s xml:id="echoid-s621" xml:space="preserve">hu-
              <lb/>
            ius ad G H. </s>
            <s xml:id="echoid-s622" xml:space="preserve">Ergo etiam ratio cylindri ad conoides
              <lb/>
            componetur ex ijſdem rationibus. </s>
            <s xml:id="echoid-s623" xml:space="preserve">Sed ex ſchol. </s>
            <s xml:id="echoid-s624" xml:space="preserve">1. </s>
            <s xml:id="echoid-s625" xml:space="preserve">
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s626" xml:space="preserve">3. </s>
            <s xml:id="echoid-s627" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s628" xml:space="preserve">3. </s>
            <s xml:id="echoid-s629" xml:space="preserve">ratio cylindri ad conoides compo-
              <lb/>
            nitur etiam ex ratione dimidij D E, ad A B E, & </s>
            <s xml:id="echoid-s630" xml:space="preserve">ex
              <lb/>
            ratione A E, ad interceptam inter E B, & </s>
            <s xml:id="echoid-s631" xml:space="preserve">centrum
              <lb/>
            æquilibrij A B E, ſeù grauitatis duplicatæ A B </s>
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