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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            <s xml:id="echoid-s3802" xml:space="preserve">
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            tes A Q, quotus eſt numerus conoidis. </s>
            <s xml:id="echoid-s3803" xml:space="preserve">Aſt cum ex
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s3804" xml:space="preserve">15, lib. </s>
            <s xml:id="echoid-s3805" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3806" xml:space="preserve">ſit conuertendo, conoides A B C,
              <lb/>
            ad cylindrum ſibi circum ſcriptum vt numerus co-
              <lb/>
            noidis ad numerum conoidis binario auctum; </s>
            <s xml:id="echoid-s3807" xml:space="preserve">nempe
              <lb/>
            vt triplus numerus conoidis, ad triplum numerum
              <lb/>
            conoidis ſenario auctum: </s>
            <s xml:id="echoid-s3808" xml:space="preserve">erit idem conoides ad co-
              <lb/>
            num A B C, tertiam partem talis cylindri, vt tri-
              <lb/>
            plus numerus conoidis, ad numerum conoidis bina-
              <lb/>
            rio auctum: </s>
            <s xml:id="echoid-s3809" xml:space="preserve">nempe vt tot partes A D, diuiſæ in tot
              <lb/>
            partes quotus eſt numerus conoidis binario auctus,
              <lb/>
            quotus eſt triplus numerus conoidis, ad A D. </s>
            <s xml:id="echoid-s3810" xml:space="preserve">Ergo
              <lb/>
            ex æquali, erit conoides A B C, ad conum G D H,
              <lb/>
            vt prædictæ partes A D, quotus eſt triplus numerus
              <lb/>
            conoidis, ad tot medietates A Q, quotus eſt nume-
              <lb/>
            rus conoidis. </s>
            <s xml:id="echoid-s3811" xml:space="preserve">Et diuiſis vtriſque terminis per 3, erit
              <lb/>
            conoides A B C, ad conum G D H, vt tres partes
              <lb/>
            A D, diuiſæ prædicto modo, ad dimidiam A Q. </s>
            <s xml:id="echoid-s3812" xml:space="preserve">Et
              <lb/>
            ſubtriplando hos terminos, vt vnica talium partium
              <lb/>
            A D, ad ſextam partem A Q. </s>
            <s xml:id="echoid-s3813" xml:space="preserve">Quod erat oſtenden-
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            dum.</s>
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        <div xml:id="echoid-div195" type="section" level="1" n="129">
          <head xml:id="echoid-head141" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s3815" xml:space="preserve">Cum ex ſupra dictis, conſtet, minimum conum.
              <lb/>
            </s>
            <s xml:id="echoid-s3816" xml:space="preserve">k E L, conoidi circumſcriptum, eſſe maximum cir-
              <lb/>
            cumſcriptum cono G D H; </s>
            <s xml:id="echoid-s3817" xml:space="preserve">& </s>
            <s xml:id="echoid-s3818" xml:space="preserve">cum ex ſchol. </s>
            <s xml:id="echoid-s3819" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s3820" xml:space="preserve">
              <lb/>
            52, conſtet conum G D H, eſſe ad conum k E L, vt
              <lb/>
            4, ad 27, ſequitur conoides eſſe ad conum K E L, vt
              <lb/>
            prædicta pars A D, ad A Q, cum eius octaua parte.</s>
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