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

Page concordance

< >
Scan Original
131 107
132 108
133 109
134 110
135 111
136 112
137 113
138 114
139 115
140 116
141 117
142 118
143 119
144 120
145 121
146 122
147 123
148 124
149 125
150 126
151 127
152 128
153 129
154 130
155 131
156 132
157 133
158 134
159 135
160 136
< >
page |< < (125) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div406" type="section" level="1" n="171">
          <pb o="125" file="0149" n="149" rhead=""/>
        </div>
        <div xml:id="echoid-div408" type="section" level="1" n="172">
          <head xml:id="echoid-head177" xml:space="preserve">LEMMA XII. PROP. LXXX.</head>
          <p>
            <s xml:id="echoid-s4221" xml:space="preserve">Si fuerit rectangulum ABC, ęquale rectangulo DEF, ſitque AC
              <lb/>
            maior DF, erit BC minor EF.</s>
            <s xml:id="echoid-s4222" xml:space="preserve"/>
          </p>
          <figure number="115">
            <image file="0149-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0149-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s4223" xml:space="preserve">SI enim dicatur BC æqualem, vel maiorem
              <lb/>
            eſſe EF, cum ſit data AC maior DF, eſſet
              <lb/>
            omnino AB maior DE, & </s>
            <s xml:id="echoid-s4224" xml:space="preserve">BC dicitur æqualis,
              <lb/>
            vel maior EF, ergo rectangulum ABC eſſet om-
              <lb/>
            nino maius rectangulo DEF, ſed æquale poſi-
              <lb/>
            tum fuit. </s>
            <s xml:id="echoid-s4225" xml:space="preserve">Ergo patet propoſitum.</s>
            <s xml:id="echoid-s4226" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div409" type="section" level="1" n="173">
          <head xml:id="echoid-head178" xml:space="preserve">THEOR. XXXVIII. PROP. LXXXI.</head>
          <p>
            <s xml:id="echoid-s4227" xml:space="preserve">Si recta linea ad alterũ terminũ cuiuſdam applicatæ coni-ſectio-
              <lb/>
            nem, vel circulũ cõtingat, ipſa omnino ſecabit ſibi adſcriptã eiuſdẽ
              <lb/>
            nominis ſectionẽ circa eandẽ applicatam, & </s>
            <s xml:id="echoid-s4228" xml:space="preserve">cum æquali tranſuerſa
              <lb/>
            diametro, ſi ſectiones fuerint Hyperbolæ, vel Ellipſes, aut circuli.</s>
            <s xml:id="echoid-s4229" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4230" xml:space="preserve">ESto quæcunque coni-ſectio, vel circulus ABC, cuius diameter BD, yo
              <unsure/>
              <lb/>
            vna applicatarum ſit AC. </s>
            <s xml:id="echoid-s4231" xml:space="preserve">& </s>
            <s xml:id="echoid-s4232" xml:space="preserve">ad ipſius terminum A, ſit recta contingens
              <lb/>
            EAF, quæ diametro occurret in F; </s>
            <s xml:id="echoid-s4233" xml:space="preserve">& </s>
            <s xml:id="echoid-s4234" xml:space="preserve">ſumpto in diametri ſegmento
              <note symbol="a" position="right" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">24. 25.
                <lb/>
              pr. conic.</note>
            quolibet puncto G, cum diametro GD, & </s>
            <s xml:id="echoid-s4235" xml:space="preserve">applicata AC in qualibet figura,
              <lb/>
              <figure xlink:label="fig-0149-02" xlink:href="fig-0149-02a" number="116">
                <image file="0149-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0149-02"/>
              </figure>
            ſed etiam, pro Hyperbola in ſecunda, & </s>
            <s xml:id="echoid-s4236" xml:space="preserve">pro Ellipſi, vel circulo, in tertia,
              <lb/>
            cum dato tranſuerſo latere GM, quod æquale ſit tranſuerſo BL datæ ſectio-
              <lb/>
            nis, deſcribatur eiuſdem nomin@s ſectio AGC: </s>
            <s xml:id="echoid-s4237" xml:space="preserve">dico hanc omnino
              <note symbol="b" position="right" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">57. h.</note>
            contingente EAF.</s>
            <s xml:id="echoid-s4238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4239" xml:space="preserve">Ducatur enim per A recta IAH, quæ ſectionem continge
              <unsure/>
            t AGC, cum
              <lb/>
            eius diametro conueniat in H.</s>
            <s xml:id="echoid-s4240" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4241" xml:space="preserve">Iam in prima figura exhiben@ Parabolas, cum AF contingat </s>
          </p>
        </div>
      </text>
    </echo>
Impressum