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

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          <head xml:id="echoid-head105" xml:space="preserve">THEOR. XIX. PROP. XXXVIII.</head>
          <p>
            <s xml:id="echoid-s2343" xml:space="preserve">In Parabolis quibuslibet, vel in ſimilibus Hyperbolis, aut ſimi-
              <lb/>
            libus Ellipſbus, ſegmenta diametrorum ſectionum lateribus pro-
              <lb/>
            portionalia, ſuſcipiunt applicatasijſdem lateribus proportionales.</s>
            <s xml:id="echoid-s2344" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2345" xml:space="preserve">SInt, vt in prima figura, duæquælibet Parabolæ, velvt in ſecunda, duæ
              <lb/>
            ſimiles Hyperbolæ, vel vt in tertia, duæ ſimiles Ellipſes ABC, DEF,
              <lb/>
            quarum diametrorum ſegmenta BG, EH, rectis earum lateribus BI, EL, vel
              <lb/>
            tranſuerſis BM, EN ſint proportionalia, dico & </s>
            <s xml:id="echoid-s2346" xml:space="preserve">applicatas GA, HD ipſis la-
              <lb/>
            teribus eſſe proportionales.</s>
            <s xml:id="echoid-s2347" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2348" xml:space="preserve">Nam in Parabolis pri-
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                <image file="0091-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0091-01"/>
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            mùm, cum ſit rectum BI
              <lb/>
            ad rectum EL, vt ſegmẽ-
              <lb/>
            tum BG ad EH, erit per-
              <lb/>
            mutando IB ad BG, vt
              <lb/>
            LE ad EH, vnde rectan-
              <lb/>
            gulum I B G ſimile erit
              <lb/>
            rectangulo LEH, quare
              <lb/>
            rectangulum IBG ad LE
              <lb/>
            H, erit vt quadratum la-
              <lb/>
            teris I B ad quadratum
              <lb/>
            homologilateris LE, ſed
              <lb/>
            rectãgulum IBG
              <note symbol="a" position="right" xlink:label="note-0091-01" xlink:href="note-0091-01a" xml:space="preserve">1. huius.</note>
            tur quadrato GA, & </s>
            <s xml:id="echoid-s2349" xml:space="preserve">re-
              <lb/>
            ctãgulum LEH quadra-
              <lb/>
            to HD, vnde quadratum
              <lb/>
            GA ad HD, erit vt qua-
              <lb/>
            dratum IB ad LE, vel
              <lb/>
            applicata GA ad HD, vt
              <lb/>
            rectum IB ad rectum LE.
              <lb/>
            </s>
            <s xml:id="echoid-s2350" xml:space="preserve">In Hyperbolis autem, & </s>
            <s xml:id="echoid-s2351" xml:space="preserve">
              <lb/>
            Ellipſibus cum ſit vt BI
              <lb/>
            ad EL, vel ob ſectionum ſimilitudinem, vt MB ad NE, ita BG ad EH, erit
              <lb/>
            permutando MB ad BG, vt NE ad EH, & </s>
            <s xml:id="echoid-s2352" xml:space="preserve">in Hyperbolis, componendo, in
              <lb/>
            Ellipſibus autem diuidendo, MG ád GB, vt NH ad HE, quare rectangulum
              <lb/>
            MGB ſimile erit rectangulo NHE, ſed rectangulum MGB ad quadratum
              <lb/>
            GA eſt, vt MB ad BI, vel vt NE ad EL, vel vtrectangulum NHE ad
              <note symbol="b" position="right" xlink:label="note-0091-02" xlink:href="note-0091-02a" xml:space="preserve">21. pri-
                <lb/>
              mi conic.</note>
            dratum HD, quare permutando rectangulum MGB ad rectangulum NHE,
              <lb/>
            vel (ob ipſorum rectangulorum ſimilitudinem) quadratum BG ad quadra-
              <lb/>
            tum EH, vel quadratum BI ad quadratum EL, erit vt quadratum GA ad
              <lb/>
            quadratum HD, hoc eſt rectum BI ad rectum EL, vt applicata GA ad appli-
              <lb/>
            catam HD. </s>
            <s xml:id="echoid-s2353" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s2354" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2355" xml:space="preserve"/>
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