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

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            <s xml:id="echoid-s2740" xml:space="preserve">
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            occurrat in P, O; </s>
            <s xml:id="echoid-s2741" xml:space="preserve">quoniam datæ ſectiones ſunt ſimiles, erit HB ad BI, vt LE
              <lb/>
            ad EM, ſuntque anguli ad B, E æquales, (cum ſectiones ſint ſimul adſcriptæ)
              <lb/>
            quare triangula HBI, LEM æquiangula erunt, ideoque regula HIP æquidi-
              <lb/>
            ſtabit regulæ LMO; </s>
            <s xml:id="echoid-s2742" xml:space="preserve">& </s>
            <s xml:id="echoid-s2743" xml:space="preserve">triangula LNO, HNP inter ſe ſimilia.</s>
            <s xml:id="echoid-s2744" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2745" xml:space="preserve">Iam cum ſit GE æqualis ipſi GL, & </s>
            <s xml:id="echoid-s2746" xml:space="preserve">ablata GB æqualis ablatæ GH, erit
              <lb/>
            reliqua BE, reliquæ HL æqualis, ſed eſt EN minor HN, quare BE ad EN
              <lb/>
            maiorem habet rationem, quàm LH ad HN, & </s>
            <s xml:id="echoid-s2747" xml:space="preserve">componendo BN ad NE,
              <lb/>
            maiorem item rationem quàm LN ad NH, vel quàm ON ad NP, ergo re-
              <lb/>
            ctangulum ſub extremis BN, NP, ſiue quadratum applicatæ AN,
              <note symbol="a" position="left" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">Coroll.
                <lb/>
              1. huius.</note>
            erit rectangulo ſub medijs EN, NO, ſiue quadrato applicatę DN, hoc
              <note symbol="b" position="left" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">17. ſept.
                <lb/>
              Pappi.</note>
              <note symbol="c" position="left" xlink:label="note-0106-03" xlink:href="note-0106-03a" xml:space="preserve">Coroll.
                <lb/>
              1. huius.</note>
            ipſa AN maior DN, ac propterea punctum D cadit intra Hyperbolen ABC,
              <lb/>
            idemque de quolibet alio puncto ſectionis DEF: </s>
            <s xml:id="echoid-s2748" xml:space="preserve">vnde ipſa DEF inſcripta
              <lb/>
            erit ipſi ABC, vel erunt nunquam ſimul coeuntes. </s>
            <s xml:id="echoid-s2749" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s2750" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2751" xml:space="preserve"/>
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          <figure number="74">
            <image file="0106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0106-01"/>
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            <s xml:id="echoid-s2752" xml:space="preserve">Ampliùs applicata infra ADT qualibet alia QRS, & </s>
            <s xml:id="echoid-s2753" xml:space="preserve">Hyperbolę DEF per
              <lb/>
            eundem verticem E adſcripta Hyperbola ETV, quæ ſit æqualium laterum,
              <lb/>
            ſiue congruens Hyperbolæ ABC, applicatas ſecans in T, V: </s>
            <s xml:id="echoid-s2754" xml:space="preserve">cum duæ Hy-
              <lb/>
            perbolæ EDR, ETV, ſint ſimiles, & </s>
            <s xml:id="echoid-s2755" xml:space="preserve">per eundem verticem ſimul adſcriptæ
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            erit ETV, cuius latera æqualia ſunt ipſis lateribus HB, BI, inſcripta
              <note symbol="d" position="left" xlink:label="note-0106-04" xlink:href="note-0106-04a" xml:space="preserve">5. Co-
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              roll. 19. h.</note>
            ni EDR, cuius maiora ſunt latera LE, EM: </s>
            <s xml:id="echoid-s2756" xml:space="preserve">ſed erunt ſimul ſemper
              <note symbol="e" position="left" xlink:label="note-0106-05" xlink:href="note-0106-05a" xml:space="preserve">41. h.</note>
            tes; </s>
            <s xml:id="echoid-s2757" xml:space="preserve">quare intercepta DT minor erit intercepta RV, eſt autem tota AT
              <note symbol="f" position="left" xlink:label="note-0106-06" xlink:href="note-0106-06a" xml:space="preserve">44. h.</note>
            ior tota QV; </s>
            <s xml:id="echoid-s2758" xml:space="preserve">quapropter reliqua AD erit omnino maior reliqua QR; </s>
            <s xml:id="echoid-s2759" xml:space="preserve">& </s>
            <s xml:id="echoid-s2760" xml:space="preserve">hoc
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            ſemper: </s>
            <s xml:id="echoid-s2761" xml:space="preserve">Vnde ſimiles concentricæ Hyperbolæ per diuerſos vertices ſimul
              <lb/>
            adſcriptæ, ſunt ad ſe propiùs accedentes. </s>
            <s xml:id="echoid-s2762" xml:space="preserve">Quod ſecundò erat, &</s>
            <s xml:id="echoid-s2763" xml:space="preserve">c.</s>
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