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

Page concordance

< >
Scan Original
111 87
112 88
113 89
114 90
115 91
116 92
117 93
118 94
119 95
120 96
121 97
122 98
123 99
124 100
125 101
126 102
127 103
128 104
129 105
130 106
131 107
132 108
133 109
134 110
135 111
136 112
137 113
138 114
139 115
140 116
< >
page |< < (64) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div202" type="section" level="1" n="95">
          <pb o="64" file="0088" n="88" rhead=""/>
        </div>
        <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>
          </p>
        </div>
      </text>
    </echo>
Impressum