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

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          <p>
            <s xml:id="echoid-s2690" xml:space="preserve">
              <pb o="80" file="0104" n="104" rhead=""/>
            erunt ſimiles, at ſunt per verticem E ſimul adſcriptæ, vnde PEQ minorum
              <lb/>
            laterum inſcripta erit Hyperbolæ DEF maiorum laterum: </s>
            <s xml:id="echoid-s2691" xml:space="preserve">& </s>
            <s xml:id="echoid-s2692" xml:space="preserve">infra
              <note symbol="a" position="left" xlink:label="note-0104-01" xlink:href="note-0104-01a" xml:space="preserve">5. Co-
                <lb/>
              roll. 19. h.</note>
            applicata quacunque TVP; </s>
            <s xml:id="echoid-s2693" xml:space="preserve">cum Hyperbolæ ABC, PEQ ſint congruentes,
              <lb/>
            & </s>
            <s xml:id="echoid-s2694" xml:space="preserve">per diuerſos vertices ſimul adſcriptæ erit intercepta AX maior
              <note symbol="b" position="left" xlink:label="note-0104-02" xlink:href="note-0104-02a" xml:space="preserve">44. h.</note>
            pta TP: </s>
            <s xml:id="echoid-s2695" xml:space="preserve">cumque Hyperbolæ DEF, PEQ ſint ſimiles, ac per eundem verti-
              <lb/>
            cem ſimul adſcriptæ erit intercepta DX minor intercepta VP, vnde
              <note symbol="c" position="left" xlink:label="note-0104-03" xlink:href="note-0104-03a" xml:space="preserve">41. h.</note>
            intercepta AD omnino erit maior reliqua intercepta TV; </s>
            <s xml:id="echoid-s2696" xml:space="preserve">& </s>
            <s xml:id="echoid-s2697" xml:space="preserve">hoc ſemper:
              <lb/>
            </s>
            <s xml:id="echoid-s2698" xml:space="preserve">quare huiuſmodi Hyperbolæ ABC, DEF ſunt ad ſe propiùs accedentes. </s>
            <s xml:id="echoid-s2699" xml:space="preserve">
              <lb/>
            Quod erat ſecundò, &</s>
            <s xml:id="echoid-s2700" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2701" xml:space="preserve"/>
          </p>
          <figure number="72">
            <image file="0104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0104-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s2702" xml:space="preserve">Tandem, bifariam ſectis tranſuerſis lateribus GB, GE, RE, in Y, Z, K,
              <lb/>
            erit Y centrum Hyperbolæ ABC, Z verò centrum DEF, ac demum K cen-
              <lb/>
            trum PEQ: </s>
            <s xml:id="echoid-s2703" xml:space="preserve">& </s>
            <s xml:id="echoid-s2704" xml:space="preserve">cum ſit GB minor GE, erit dimidium GY minus dimidio GZ;
              <lb/>
            </s>
            <s xml:id="echoid-s2705" xml:space="preserve">quare punctũ Z cadit infra Y: </s>
            <s xml:id="echoid-s2706" xml:space="preserve">cumq; </s>
            <s xml:id="echoid-s2707" xml:space="preserve">ſit EG maior ER, erit dimidiũ EZ maius
              <lb/>
            dimidio EK, vnde K punctum cadit infra Z. </s>
            <s xml:id="echoid-s2708" xml:space="preserve">Si ergo ex Hyperbolarum cen-
              <lb/>
            tris Y, Z, ducantur earum aſymptoti Y 2, Z 3, K 4, erit Z 3, parallela
              <note symbol="d" position="left" xlink:label="note-0104-04" xlink:href="note-0104-04a" xml:space="preserve">Coroll.
                <lb/>
              41. huius.</note>
            K 4, & </s>
            <s xml:id="echoid-s2709" xml:space="preserve">Y 2 æquidiſtabit eidem K 4; </s>
            <s xml:id="echoid-s2710" xml:space="preserve">quare aſymptoti omnes Y 2, Z 3,
              <note symbol="e" position="left" xlink:label="note-0104-05" xlink:href="note-0104-05a" xml:space="preserve">Coroll.
                <lb/>
              44. h.</note>
            erunt inter ſe parallelæ: </s>
            <s xml:id="echoid-s2711" xml:space="preserve">& </s>
            <s xml:id="echoid-s2712" xml:space="preserve">cum Y 2 ſit aſymptotos ABC, & </s>
            <s xml:id="echoid-s2713" xml:space="preserve">Z 3 ſit intra an-
              <lb/>
            gulum ab aſymptotis comprehenſum, ipſa ſectionem ABC ſecabit, vt in
              <note symbol="f" position="left" xlink:label="note-0104-06" xlink:href="note-0104-06a" xml:space="preserve">Coroll.
                <lb/>
              11. h.</note>
            per quod ordinatim ducta recta 2 3 4, alias aſymptotos ſecantin 2 4, infra
              <lb/>
            ipſam applicetur quælibet alia TVP, ſingulas Hyperbolas ſecans in T, V, P.
              <lb/>
            </s>
            <s xml:id="echoid-s2714" xml:space="preserve">Erit intercepta TP maior ſemper interuallo 2 4, ſed ablata intercepta
              <note symbol="g" position="left" xlink:label="note-0104-07" xlink:href="note-0104-07a" xml:space="preserve">44. h.</note>
            eſt ſemper minor ablato interuallo 3 4, vnde reliqua intercepta TV
              <note symbol="b" position="left" xlink:label="note-0104-08" xlink:href="note-0104-08a" xml:space="preserve">41. h.</note>
            datas ſectiones A B C, D E F, erit omnino maior reliquo interuallo 2 3,
              <lb/>
            quod inter datarum ſectionum parallelas aſymptotos eſt interceptum, ac
              <lb/>
            iuxta ordinatim ductis æquidiſtantes metitur. </s>
            <s xml:id="echoid-s2715" xml:space="preserve">Quod erat vltimò demon-
              <lb/>
            ſtrandum.</s>
            <s xml:id="echoid-s2716" xml:space="preserve"/>
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