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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            uidatur ergo X ℟, in Z, vt ſit X Z, ad Z ℟, vt qua-
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            drata D B, B K, cum rectangulo D B K, ad ſeſqui-
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            alterum rectangulorum G B D, G B K; </s>
            <s xml:id="echoid-s977" xml:space="preserve">ſeù vt rectan-
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            gulum D B K, cum tertia parte quadrati D K, ad re-
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            ctangulum G B K, cum dimidio rectanguli G B, K D;
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            </s>
            <s xml:id="echoid-s978" xml:space="preserve">nenipe ex propoſit. </s>
            <s xml:id="echoid-s979" xml:space="preserve">anteced. </s>
            <s xml:id="echoid-s980" xml:space="preserve">vt eſt differentia fruſto-
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            rum conoideo rum ad fruſtum conoidis parabolici
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            E N O F. </s>
            <s xml:id="echoid-s981" xml:space="preserve">Dico inuentum eſſe Z, centrum grauita-
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            tis fruſti conoidis hyperbolici A H I C. </s>
            <s xml:id="echoid-s982" xml:space="preserve">Cum au-
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            tem res ſit de sè euidens ex doctrinis Archimedis in
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            æqueponderantibus, relinquitur conſiderationi le-
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            ctoris.</s>
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          <head xml:id="echoid-head47" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s984" xml:space="preserve">Alij modi ex ſuperioribus non deſunt reperiendi
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            tale centrum grauitatis; </s>
            <s xml:id="echoid-s985" xml:space="preserve">ſed nè lectorem nimis quam
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            par ſit defatigemus, ad alia, & </s>
            <s xml:id="echoid-s986" xml:space="preserve">noua tranſeamus; </s>
            <s xml:id="echoid-s987" xml:space="preserve">præ-
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            cipuè ad centrum grauitatis hyperbolæ reperien-
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            dum. </s>
            <s xml:id="echoid-s988" xml:space="preserve">Quod tamen non reperietur niſi præmiſſis qui-
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            buſdam demonſtrationibus.</s>
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          <head xml:id="echoid-head48" xml:space="preserve">PROPOSITIO XVIII.</head>
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            <s xml:id="echoid-s990" xml:space="preserve">Si ſemihyperbola cum ſibi circumſcripto parallelogrammo
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            rotetur circa ſecundam coniugatam diametrum. </s>
            <s xml:id="echoid-s991" xml:space="preserve">An-
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            nulus latus ortus ex rotatione exceſſus parallelogram-
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            mi ſupra ſemihyperbolam, erit æqualis cono ex triangu-
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            lo, cuius vnum latus dimidia ſecundæ diametri, </s>
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