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

Page concordance

< >
Scan Original
211 29
212 30
213 31
214 32
215 33
216 34
217 35
218 36
219 37
220 38
221 39
222 40
223 41
224 42
225 43
226 44
227 45
228 46
229 47
230 48
231 49
232 50
233
234
235 51
236 52
237 53
238 54
239 55
240 56
< >
page |< < (50) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div674" type="section" level="1" n="269">
          <pb o="50" file="0232" n="232" rhead=""/>
        </div>
        <div xml:id="echoid-div676" type="section" level="1" n="270">
          <head xml:id="echoid-head279" xml:space="preserve">LEMMA XII. PROP. XXXIX.</head>
          <p>
            <s xml:id="echoid-s6498" xml:space="preserve">Si fuerit quodcunque quadrilaterum rectilineum A B C D, cu-
              <lb/>
            ius oppoſita latera A D, B C bifariam ſecta ſint in punctis F,
              <lb/>
            E, iunctaque ſit recta F E, in qua ſumptum ſit quodlibet pun-
              <lb/>
            ctum G, vel intra, vel extra quadrilaterum à quo ad terminos
              <lb/>
            alterius ęquidiſtantium veluti ad A, D, ductæ ſint G A, G D,
              <lb/>
            ac in triangulo A G D, ſit quædam H I ipſis A D, B C æquidi-
              <lb/>
            ſtans, & </s>
            <s xml:id="echoid-s6499" xml:space="preserve">E F ſecans in L. </s>
            <s xml:id="echoid-s6500" xml:space="preserve">Dico, ſi iungantur B H, C I, trian-
              <lb/>
            gula A B H, D C I inter ſe æqualia eſſe.</s>
            <s xml:id="echoid-s6501" xml:space="preserve"/>
          </p>
          <figure number="194">
            <image file="0232-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0232-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s6502" xml:space="preserve">NAm totum quadrilaterum A B E F, æquale eſt integro quadrilatero
              <lb/>
            D C E F (vtrunque enim diuiditur per diagonales A E, D E, in
              <lb/>
            duo triangula alterum alteri æquale, eò quod ſint ſuper æqualibus baſi-
              <lb/>
            bus, ac inter eaſdem parallelas) eadem ratione quadrilaterum A H L F
              <lb/>
            æquale eſt quadrilatero D I L F, & </s>
            <s xml:id="echoid-s6503" xml:space="preserve">quadrilaterum B E L H æquale qua-
              <lb/>
            drilatero C E L I, ergo, & </s>
            <s xml:id="echoid-s6504" xml:space="preserve">reliquum triangulum A B H reliquo triangulo
              <lb/>
            D C I eſt æquale. </s>
            <s xml:id="echoid-s6505" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s6506" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6507" xml:space="preserve">His itaque præoſtenſis, ad inueſtigationem MAXIMARVM, MI-
              <lb/>
            NIMARV MQVE portionum per idem datum punctum ex qualibet coni-
              <lb/>
            ſectione abſciſſarum accedamus, præmiſſo tamen, ſuper figurastertij Sche-
              <lb/>
            matiſmi, ſequenti Theoremate, vniuerſalem, ſimulque facilem methodum
              <lb/>
            exhibente, qua æquales portiones de eadem coni-ſectione abſcindi poſſunt.</s>
            <s xml:id="echoid-s6508" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum