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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        <div xml:id="echoid-div183" type="section" level="1" n="119">
          <pb o="195" file="0207" n="207"/>
          <figure number="87">
            <image file="0207-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/PVNDER1Y/figures/0207-01"/>
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          <p>
            <s xml:id="echoid-s3594" xml:space="preserve">ITidem ratio data ſit quam habet A D, ad H; </s>
            <s xml:id="echoid-s3595" xml:space="preserve">& </s>
            <s xml:id="echoid-s3596" xml:space="preserve">
              <lb/>
            fiat vt tripla H, cum dupla A D, ad A D, ita
              <lb/>
            A D, ad D B. </s>
            <s xml:id="echoid-s3597" xml:space="preserve">Patet B D, minorem eſſe ſubdupla
              <lb/>
            A D; </s>
            <s xml:id="echoid-s3598" xml:space="preserve">& </s>
            <s xml:id="echoid-s3599" xml:space="preserve">conſequenter tertia parte totius A B. </s>
            <s xml:id="echoid-s3600" xml:space="preserve">Qua-
              <lb/>
            re A D, eſt maior duobus tertijs A B, quȩ ſit A C. </s>
            <s xml:id="echoid-s3601" xml:space="preserve">Di-
              <lb/>
            co A D, eſſe ſic productam in B, vt B D, ſit ad D C,
              <lb/>
            exceſſum A D, ſupra A C, dno tertia A B, vt A D,
              <lb/>
            ad H. </s>
            <s xml:id="echoid-s3602" xml:space="preserve">Quoniam enim factum eſt vt tripla H, cum
              <lb/>
            dupla A D, ad A D, ita A D, ad D B; </s>
            <s xml:id="echoid-s3603" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s3604" xml:space="preserve">dua-
              <lb/>
            bus vicibus diuidendo, erit tripla H, ad AD, vt A D,
              <lb/>
            minus dupla D B, ad D B. </s>
            <s xml:id="echoid-s3605" xml:space="preserve">Et antecedentium ſub-
              <lb/>
            tripla, nempe vt H, ad A D, ita tertia pars A D, mi-
              <lb/>
            nus duobus tertijs B D, ad B D. </s>
            <s xml:id="echoid-s3606" xml:space="preserve">Et conuertendo,
              <lb/>
            vt A D, ad H, ſic B D, ad tertiam partem A D, mi-
              <lb/>
            nus duobus tertijs D B; </s>
            <s xml:id="echoid-s3607" xml:space="preserve">nempe ex prop. </s>
            <s xml:id="echoid-s3608" xml:space="preserve">ant. </s>
            <s xml:id="echoid-s3609" xml:space="preserve">ad D C.
              <lb/>
            </s>
            <s xml:id="echoid-s3610" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s3611" xml:space="preserve"/>
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        <div xml:id="echoid-div184" type="section" level="1" n="120">
          <head xml:id="echoid-head132" xml:space="preserve">PROPOSITIO LXI.</head>
          <p style="it">
            <s xml:id="echoid-s3612" xml:space="preserve">Si diameter cuiuſcunque parabolæ ſic producatur vt pars
              <lb/>
            exterior producta, ſit ad exceſſum diametri ſupra duo </s>
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