Clavius, Christoph, Geometria practica

Page concordance

< >
Scan Original
241 211
242 212
243 213
244 214
245 215
246 216
247 217
248 218
249 219
250 220
251 221
252 222
253 223
254 224
255 225
256 226
257 227
258 228
259 229
260 230
261 231
262 232
263 233
264 234
265 235
266 236
267 237
268 238
269 239
270 240
< >
page |< < (293) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div838" type="section" level="1" n="291">
          <p>
            <s xml:id="echoid-s13894" xml:space="preserve">
              <pb o="293" file="323" n="323" rhead="LIBER SEPTIMVS."/>
            rectæ B E, G H, ipſi A D, æquidiſtantes, eritque G H, ęqualis
              <note symbol="a" position="right" xlink:label="note-323-01" xlink:href="note-323-01a" xml:space="preserve">34. primi.</note>
            A D. </s>
            <s xml:id="echoid-s13895" xml:space="preserve"> Quoniamigitur rectangulum BCFE, duplum eſt trianguli ABC; </s>
            <s xml:id="echoid-s13896" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-323-02" xlink:href="note-323-02a" xml:space="preserve">41. primi.</note>
            duplum rectanguli BEHG: </s>
            <s xml:id="echoid-s13897" xml:space="preserve">erit rectangulum BEHG, quod continetur ſub per-
              <lb/>
              <note symbol="c" position="right" xlink:label="note-323-03" xlink:href="note-323-03a" xml:space="preserve">36. primi.</note>
            pendiculari GH, vel AD, & </s>
            <s xml:id="echoid-s13898" xml:space="preserve">dimidio baſis BG, æquale triangulo ABC.</s>
            <s xml:id="echoid-s13899" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13900" xml:space="preserve">
              <emph style="sc">Secetvr</emph>
            iam perpendicularis AD, vel G H, bifariam in I, agaturque per I,
              <lb/>
            ipſi BC, parallela KL. </s>
            <s xml:id="echoid-s13901" xml:space="preserve">Dico triangulum idem ABC, æquale quoque eſſe rectã-
              <lb/>
            gulo BCLK, in 1. </s>
            <s xml:id="echoid-s13902" xml:space="preserve">& </s>
            <s xml:id="echoid-s13903" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13904" xml:space="preserve">figura, Item rectangulo BCLM, in 3. </s>
            <s xml:id="echoid-s13905" xml:space="preserve">figura, comprehen-
              <lb/>
            ſo nimirum ſub ID, vel IG, ſemiſſe perpendicularis AD, vel HG. </s>
            <s xml:id="echoid-s13906" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-323-04" xlink:href="note-323-04a" xml:space="preserve">41. primi.</note>
            enim triangulum ABC, dimidium eſt rectanguli E C, eiuſdemque dimidium et-
              <lb/>
            iam eſt rectangulum BL; </s>
            <s xml:id="echoid-s13907" xml:space="preserve"> quod rectangula BL, LE, ſuper æquales baſes
              <note symbol="e" position="right" xlink:label="note-323-05" xlink:href="note-323-05a" xml:space="preserve">36. primi.</note>
            lia ſint: </s>
            <s xml:id="echoid-s13908" xml:space="preserve">æqualia inter ſe erunt triangulum A B C, & </s>
            <s xml:id="echoid-s13909" xml:space="preserve">rectangulum B L. </s>
            <s xml:id="echoid-s13910" xml:space="preserve"> Et
              <note symbol="f" position="right" xlink:label="note-323-06" xlink:href="note-323-06a" xml:space="preserve">41. primi.</note>
            rectangulum B F, contentum ſub perpendiculari A D, vel B E, & </s>
            <s xml:id="echoid-s13911" xml:space="preserve">baſe trianguli
              <lb/>
            BC, duplum eſt trianguli ABC; </s>
            <s xml:id="echoid-s13912" xml:space="preserve">erit triangulum ſemiſsiillius rectanguli ęquale.
              <lb/>
            </s>
            <s xml:id="echoid-s13913" xml:space="preserve">Area igitur cuiuslibet trianguli æqualis eſt, &</s>
            <s xml:id="echoid-s13914" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13915" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s13916" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div842" type="section" level="1" n="292">
          <head xml:id="echoid-head319" xml:space="preserve">PROBL. 2. PROPOS. 2.</head>
          <note position="right" xml:space="preserve">Regularis fi-
            <lb/>
          gura quæcun-
            <lb/>
          que cuirectã-
            <lb/>
          gulo @qualis
            <lb/>
          ſit.</note>
          <p>
            <s xml:id="echoid-s13917" xml:space="preserve">AREA cuiuslibet figuræ regularis æqualis eſt rectangulo contento ſub
              <lb/>
            perpendiculari à centro figuræ ad vnum latus ducta, & </s>
            <s xml:id="echoid-s13918" xml:space="preserve">ſub dimidia-
              <lb/>
            to ambitu eiuſdem figuræ.</s>
            <s xml:id="echoid-s13919" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13920" xml:space="preserve">
              <emph style="sc">Sit</emph>
            figura regularis quæcunque ABCDEF, & </s>
            <s xml:id="echoid-s13921" xml:space="preserve">centrum eius punctum G, à
              <lb/>
            quo ducatur GH, perpendicularis ad vnum latus, nempe ad AB: </s>
            <s xml:id="echoid-s13922" xml:space="preserve">Sit quoq; </s>
            <s xml:id="echoid-s13923" xml:space="preserve">re-
              <lb/>
            ctangulum I K L M, contentum ſub I K, quæ æqualis ſit perpendiculari G H, & </s>
            <s xml:id="echoid-s13924" xml:space="preserve">
              <lb/>
            ſub KL, recta, quæ æqualis ponatur dimidiæ parti ambitus figuræ ABCDEF. </s>
            <s xml:id="echoid-s13925" xml:space="preserve">Di-
              <lb/>
              <figure xlink:label="fig-323-01" xlink:href="fig-323-01a" number="214">
                <image file="323-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/323-01"/>
              </figure>
            co huic rectangulo æqualem eſſe figuram regularem ABCDEF. </s>
            <s xml:id="echoid-s13926" xml:space="preserve">Ducantur enim
              <lb/>
            ex G, ad ſingulos angulos lineæ rectæ, vt tota figura in triangula reſoluatur, quæ
              <lb/>
            omnia æqualia inter ſe erunt, vt in corollario propoſ. </s>
            <s xml:id="echoid-s13927" xml:space="preserve">8. </s>
            <s xml:id="echoid-s13928" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13929" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13930" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s13931" xml:space="preserve">demonſtra-
              <lb/>
            tum eſt à nobis: </s>
            <s xml:id="echoid-s13932" xml:space="preserve">propterea quòd omnia latera triangulorum à puncto G, ex-
              <lb/>
            euntia ſint inter ſe æqualia, habeantq; </s>
            <s xml:id="echoid-s13933" xml:space="preserve">baſes æquales, nempè latera figuræ regu-
              <lb/>
            laris. </s>
            <s xml:id="echoid-s13934" xml:space="preserve"> Hinc enim effi citur, omnes angulos ad G, æquales eſſe, ac proinde, ex
              <note symbol="g" position="right" xlink:label="note-323-08" xlink:href="note-323-08a" xml:space="preserve">8. primi.</note>
            cto corollario, triangula ipſa inter ſe quo que eſſe æqualia. </s>
            <s xml:id="echoid-s13935" xml:space="preserve"> Quoniam igitur
              <note symbol="h" position="right" xlink:label="note-323-09" xlink:href="note-323-09a" xml:space="preserve">1. hui{us}.</note>
            ctangulum contentum ſub GH, perpendiculari, & </s>
            <s xml:id="echoid-s13936" xml:space="preserve">medietate baſis AB, æquale
              <lb/>
            eſt triangulo ABG, ſi ſumantur tot huiuſmodi rectangula, in quot triangula di-
              <lb/>
            uiſa eſt figura regularis, erunt omnia ſimul figuræ ABCDEF, ęqualia; </s>
            <s xml:id="echoid-s13937" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum