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-div177" type="section" level="1" n="114">
          <pb o="191" file="0203" n="203"/>
          <figure number="84">
            <image file="0203-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/PVNDER1Y/figures/0203-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s3524" xml:space="preserve">CVm enim A C, ſit tertia pars A B; </s>
            <s xml:id="echoid-s3525" xml:space="preserve">ergo C B,
              <lb/>
            erit duo tertia A B; </s>
            <s xml:id="echoid-s3526" xml:space="preserve">nempe duo tertia A D,
              <lb/>
            cum duobus tertijs D B. </s>
            <s xml:id="echoid-s3527" xml:space="preserve">Ergo C D, erit duo ter-
              <lb/>
            tia A D, minus tertia parte D B. </s>
            <s xml:id="echoid-s3528" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s3529" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3530" xml:space="preserve"/>
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        <div xml:id="echoid-div178" type="section" level="1" n="115">
          <head xml:id="echoid-head127" xml:space="preserve">PROPOSITIO LVII.</head>
          <p style="it">
            <s xml:id="echoid-s3531" xml:space="preserve">Datam A D, taliter producere in B, vt B D, ſit ad ex-
              <lb/>
            ceſſum D A, ſupra tertiam partem A B, in
              <lb/>
            data proportione.</s>
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          <figure number="85">
            <image file="0203-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/PVNDER1Y/figures/0203-02"/>
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          <p>
            <s xml:id="echoid-s3533" xml:space="preserve">DAta proportio ſit, quam habet A D, ad H;
              <lb/>
            </s>
            <s xml:id="echoid-s3534" xml:space="preserve">& </s>
            <s xml:id="echoid-s3535" xml:space="preserve">fiat vt tripla H, cum A D, ad A D, ità
              <lb/>
            dupla A D, ad D B. </s>
            <s xml:id="echoid-s3536" xml:space="preserve">Patet B D, minorem eſſe
              <lb/>
            dupla A D. </s>
            <s xml:id="echoid-s3537" xml:space="preserve">Quare ſi fiat A C, tertia pars A B,
              <lb/>
            punctum C, cadet inter A, D. </s>
            <s xml:id="echoid-s3538" xml:space="preserve">Sit ergo A C,
              <lb/>
            tertia pars A B.</s>
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          </p>
          <p>
            <s xml:id="echoid-s3540" xml:space="preserve">Quoniam vt tripla H, cum A D, ad A D, ſic
              <lb/>
            dupla A D, ad D B; </s>
            <s xml:id="echoid-s3541" xml:space="preserve">ergo diuidendo vt tripla </s>
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