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

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        <div xml:id="echoid-div202" type="section" level="1" n="95">
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        <div xml:id="echoid-div205" type="section" level="1" n="96">
          <head xml:id="echoid-head101" xml:space="preserve">THEOR. XVI. PROP. XXXV.</head>
          <p>
            <s xml:id="echoid-s2235" xml:space="preserve">Si recta linea diametro Hyperbolæ vltrà centrum occurrens, al-
              <lb/>
            teram ipſius aſymptoton ſecet, producta ſectionem quoq; </s>
            <s xml:id="echoid-s2236" xml:space="preserve">ſecabit.</s>
            <s xml:id="echoid-s2237" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2238" xml:space="preserve">ESto Hyperbole ABC, cuius cẽtrum
              <lb/>
              <figure xlink:label="fig-0088-01" xlink:href="fig-0088-01a" number="58">
                <image file="0088-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0088-01"/>
              </figure>
            D, aſymptotos DE, diameter BD
              <lb/>
            F, è cuius puncto G vltrà cẽtrum aſſum-
              <lb/>
            pto ducta ſit quæpiam linea GE aſym-
              <lb/>
            ptoton ſecans in E; </s>
            <s xml:id="echoid-s2239" xml:space="preserve">Dico, ſi produca-
              <lb/>
            tur, ſectionem quoque ſecare.</s>
            <s xml:id="echoid-s2240" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2241" xml:space="preserve">Ducta enim ex vertice B recta BH
              <lb/>
            parallela ad DE, ipſa ad partes A nun-
              <lb/>
            quam ſectioni occurret, cum ei
              <note symbol="a" position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">Coroll.
                <lb/>
              11. huius.</note>
            rat in B, ſed GE ſecat alteram Paralle-
              <lb/>
            larum DE, quare producta ſecabit, & </s>
            <s xml:id="echoid-s2242" xml:space="preserve">
              <lb/>
            reliquam BH, vnde neceſſariò ſectio-
              <lb/>
            nem priùs ſecabit. </s>
            <s xml:id="echoid-s2243" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s2244" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2245" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div208" type="section" level="1" n="97">
          <head xml:id="echoid-head102" xml:space="preserve">THEOR. XVII. PROP. XXXVI.</head>
          <p>
            <s xml:id="echoid-s2246" xml:space="preserve">Hyperbolæ per eundem verticem ſimul adſcriptæ, æquale re-
              <lb/>
            ctum latus habentes ſunt inter ſe nunquam coeuntes, & </s>
            <s xml:id="echoid-s2247" xml:space="preserve">ſemper in-
              <lb/>
            ter ſe magis recedentes, & </s>
            <s xml:id="echoid-s2248" xml:space="preserve">in infinitum productæ ad interuallum
              <lb/>
            perueniunt maius quocunque dato interuallo.</s>
            <s xml:id="echoid-s2249" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2250" xml:space="preserve">SInt duæ Hyperbolæ ABC, DBE per eundem verticem B ſimul adſcriptę,
              <lb/>
            quarum rectumlatus ſit idem BF, tranſuerſum verò Hyperbolæ ABC
              <lb/>
            ſit minor recta BH, & </s>
            <s xml:id="echoid-s2251" xml:space="preserve">regula HF; </s>
            <s xml:id="echoid-s2252" xml:space="preserve">Hyperbolæ autem DBE ſit maior recta
              <lb/>
            BG eiuſque regula ſit GF: </s>
            <s xml:id="echoid-s2253" xml:space="preserve">dico primùm has inter ſe ſimul eſſe non coeuntes.</s>
            <s xml:id="echoid-s2254" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2255" xml:space="preserve">Cum enim Hyperbole DBE, maius habens trãſuerſum latus, inſcripta
              <note symbol="a" position="left" xlink:label="note-0088-02" xlink:href="note-0088-02a" xml:space="preserve">4. Corol.
                <lb/>
              19. huius.</note>
            Hyperbolæ ABC, patet ipſas, licet in infinitum producantur, nunquam in-
              <lb/>
            ter ſe conuenire, vnde erunt ſimul non coeuntes.</s>
            <s xml:id="echoid-s2256" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2257" xml:space="preserve">Iam dico ipſas eſſe ſimul ſemper recedentes. </s>
            <s xml:id="echoid-s2258" xml:space="preserve">Applicatis enim duabus
              <lb/>
            quibuſcunque rectis CEILM, PONQR, iungatur quoque FN rectam MI
              <lb/>
            ſecans in S. </s>
            <s xml:id="echoid-s2259" xml:space="preserve">Cum ſit LS minor LI habebit ML ad L S maiorem rationem
              <lb/>
            quàm ML ad LI, & </s>
            <s xml:id="echoid-s2260" xml:space="preserve">componendo MS ad SL, ſiue RN ad NQ, hoc eſt
              <note symbol="b" position="left" xlink:label="note-0088-03" xlink:href="note-0088-03a" xml:space="preserve">4. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            dratum PN ad NO, habebit maiorem rationem, quàm MI ad IL, hoc
              <note symbol="c" position="left" xlink:label="note-0088-04" xlink:href="note-0088-04a" xml:space="preserve">ibidem.</note>
            quàm quadratum CI ad IE, ſiue applicata PN ad NO maiorem habebit ra-
              <lb/>
            tionem quàm applicata CI ad IE: </s>
            <s xml:id="echoid-s2261" xml:space="preserve">ſi ergo fiat vt PN ad NO, ita CI ad IT,
              <lb/>
            habebit CI ad IT maiorem rationem quàm CI ad IE, ergo IT erit minor IE,
              <lb/>
            ideoque CT maior CE: </s>
            <s xml:id="echoid-s2262" xml:space="preserve">cumque ſit PN ad NO vt CI ad IT, erit per conuer-
              <lb/>
            ſionem rationis, & </s>
            <s xml:id="echoid-s2263" xml:space="preserve">permutando PN ad CI vt PO ad CT, ſed eſt PN
              <note symbol="d" position="left" xlink:label="note-0088-05" xlink:href="note-0088-05a" xml:space="preserve">32. h.</note>
            CI; </s>
            <s xml:id="echoid-s2264" xml:space="preserve">quare PO maior erit ipſa CT, eſtque CT maior CE, ergo PO </s>
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