Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <p>
            <s xml:id="echoid-s3477" xml:space="preserve">
              <pb o="104" file="0128" n="128" rhead=""/>
            cum quadrato intermediæ partis DC; </s>
            <s xml:id="echoid-s3478" xml:space="preserve">rectangulum ergo ACB ſuperat re-
              <lb/>
            ctangulum ADB; </s>
            <s xml:id="echoid-s3479" xml:space="preserve">& </s>
            <s xml:id="echoid-s3480" xml:space="preserve">hoc ſemper; </s>
            <s xml:id="echoid-s3481" xml:space="preserve">ergo rectangulum ACB, ſub æqualibus
              <lb/>
            partibus compræhenſum, eſt _MAXIMV M._ </s>
            <s xml:id="echoid-s3482" xml:space="preserve">Quod primo, &</s>
            <s xml:id="echoid-s3483" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3484" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3485" xml:space="preserve">Item, quadrato dimidiæ A C æquatur
              <lb/>
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                <image file="0128-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0128-01"/>
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            rectangulum A D B, vna cum quadrato
              <lb/>
            DC, & </s>
            <s xml:id="echoid-s3486" xml:space="preserve">eidem quadrato AC æquatur re-
              <lb/>
            ctangulum AED vna cum quadrato EC,
              <lb/>
            ergo rectangulum A D C cum quadrato
              <lb/>
            DC, æquale erit rectangulo AEB, cum
              <lb/>
            quadrato EC, eſt autem quadratum DC
              <lb/>
            minus quadrato EC, cum ſit linea DC mi-
              <lb/>
            nor EC, ex hypoteſi; </s>
            <s xml:id="echoid-s3487" xml:space="preserve">ergo rectangulum
              <lb/>
            ADC maius erit rectangulo AEB. </s>
            <s xml:id="echoid-s3488" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s3489" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head150" xml:space="preserve">THEOR. XXXII. PROP. LXI.</head>
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            <s xml:id="echoid-s3491" xml:space="preserve">Si fuerint duæ quæcunque coni-ſectiones, non excepto circulo,
              <lb/>
            eiuſdem, vel diuerſi nominis per diuerſos vertices ſimul adſcriptæ,
              <lb/>
            quæ in eiuſdem communis ordinatim ductæ extremis punctis ſimul
              <lb/>
            conueniant, è quorum altero eadem recta linea vtranque ſectionem
              <lb/>
            contingat, ea coni-ſectio cuius vertex cadit infra verticem alterius
              <lb/>
            erit alteri inſcripta, & </s>
            <s xml:id="echoid-s3492" xml:space="preserve">in ijſdem tantùm applicatæ extremis ſe con-
              <lb/>
            tingent.</s>
            <s xml:id="echoid-s3493" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3494" xml:space="preserve">SInt duæ quælibet coni-ſectiones ABC, ADC non excepto circulo, eiuſ-
              <lb/>
            dem, vel diuerſi nominis per diuerſos vertices B, D ſimul adſcriptæ,
              <lb/>
              <figure xlink:label="fig-0128-02" xlink:href="fig-0128-02a" number="94">
                <image file="0128-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0128-02"/>
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            quarum communis diameter ſit BH, communiſq; </s>
            <s xml:id="echoid-s3495" xml:space="preserve">applicata ſit AC, in cuius
              <lb/>
            extremis A, C, ſectiones ſimul occurrant, & </s>
            <s xml:id="echoid-s3496" xml:space="preserve">ex eorum altero veluti ex </s>
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