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-div25" type="section" level="1" n="18">
          <pb o="23" file="0035" n="35"/>
        </div>
        <div xml:id="echoid-div27" type="section" level="1" n="19">
          <head xml:id="echoid-head29" xml:space="preserve">PROPOSITIO IX.</head>
          <p style="it">
            <s xml:id="echoid-s472" xml:space="preserve">Si recta A B, ſit ſecta bifariam in C, & </s>
            <s xml:id="echoid-s473" xml:space="preserve">in D, E, æque
              <lb/>
            remotè à C, & </s>
            <s xml:id="echoid-s474" xml:space="preserve">pariter in F, G, æque remotè à C; </s>
            <s xml:id="echoid-s475" xml:space="preserve">ſit-
              <lb/>
            que rectangulum A F B, æquale quadrato D C. </s>
            <s xml:id="echoid-s476" xml:space="preserve">Erit
              <lb/>
            etiam rectangulum A D B, æquale quadrato F C.</s>
            <s xml:id="echoid-s477" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s478" xml:space="preserve">CVm enim rectangulum A F B, diuidatur in re-
              <lb/>
            ctangulum ſub A F, in D B, & </s>
            <s xml:id="echoid-s479" xml:space="preserve">in rectangulum
              <lb/>
            A F D, nempe in rectangulum ſub F D, in G B. </s>
            <s xml:id="echoid-s480" xml:space="preserve">Er-
              <lb/>
            go rectangula A F, D B; </s>
            <s xml:id="echoid-s481" xml:space="preserve">F D, G B, erunt æqualia
              <lb/>
            quadrato D C. </s>
            <s xml:id="echoid-s482" xml:space="preserve">Quare addito communi rectangu-
              <lb/>
            lo F D G. </s>
            <s xml:id="echoid-s483" xml:space="preserve">Ergo rectangula A F, D B; </s>
            <s xml:id="echoid-s484" xml:space="preserve">F D, G B;
              <lb/>
            </s>
            <s xml:id="echoid-s485" xml:space="preserve">
              <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a" number="15">
                <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/PVNDER1Y/figures/0035-01"/>
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            F D G, erunt æqualia quadrato D C, & </s>
            <s xml:id="echoid-s486" xml:space="preserve">rectangulo
              <lb/>
            F D G; </s>
            <s xml:id="echoid-s487" xml:space="preserve">nempe quadrato F C. </s>
            <s xml:id="echoid-s488" xml:space="preserve">At rectangula F D G,
              <lb/>
            & </s>
            <s xml:id="echoid-s489" xml:space="preserve">F D, G B, faciunt rectangulum F D B. </s>
            <s xml:id="echoid-s490" xml:space="preserve">Quod cum
              <lb/>
            rectangulo A F, D B, facit rectangulum A D B.
              <lb/>
            </s>
            <s xml:id="echoid-s491" xml:space="preserve">Quare etiam rectangulum A D B, erit æquale qua-
              <lb/>
            drato F C. </s>
            <s xml:id="echoid-s492" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s493" xml:space="preserve">c.</s>
            <s xml:id="echoid-s494" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div29" type="section" level="1" n="20">
          <head xml:id="echoid-head30" xml:space="preserve">PROPOSITIO X.</head>
          <p style="it">
            <s xml:id="echoid-s495" xml:space="preserve">Si conoides byperbolicum includatur intra fruſtum conicum
              <lb/>
            habens oppoſitas baſes parallelas, & </s>
            <s xml:id="echoid-s496" xml:space="preserve">latera trapezij geni-
              <lb/>
            toris frusti ſint partes aſymptoton hyperbolæ </s>
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