Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

Page concordance

< >
Scan Original
241 229
242 230
243 231
244 232
245 233
246 234
247 235
248 236
249 237
250 238
251 239
252 240
253 241
254 242
255 243
256
257
258 246
259 247
260 248
261 249
262 250
263 251
264 252
265 253
266 254
267 255
268 256
269 257
270 258
< >
page |< < (334) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div891" type="section" level="1" n="471">
          <pb o="334" file="346" n="346" rhead=""/>
          <note position="right" xml:space="preserve">
            <lb/>
          AC. # AC. # AD. # # AD.
            <lb/>
          20. # 100000. # 12? # fit # 60000.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s11035" xml:space="preserve">Eſt ergo angulus C, grad. </s>
            <s xml:id="echoid-s11036" xml:space="preserve">36. </s>
            <s xml:id="echoid-s11037" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11038" xml:space="preserve">52. </s>
            <s xml:id="echoid-s11039" xml:space="preserve">& </s>
            <s xml:id="echoid-s11040" xml:space="preserve">proinde reliquus duorum rectorum
              <lb/>
            BAC, grad. </s>
            <s xml:id="echoid-s11041" xml:space="preserve">30. </s>
            <s xml:id="echoid-s11042" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11043" xml:space="preserve">31. </s>
            <s xml:id="echoid-s11044" xml:space="preserve">Latus BC, inuenietur 11. </s>
            <s xml:id="echoid-s11045" xml:space="preserve">vt prius. </s>
            <s xml:id="echoid-s11046" xml:space="preserve">Igitur, Datis
              <lb/>
            duobus lateribus trianguli non rectanguli, &</s>
            <s xml:id="echoid-s11047" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11048" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s11049" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div900" type="section" level="1" n="472">
          <head xml:id="echoid-head504" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">Quãdo da-
            <lb/>
          tus angu-
            <lb/>
          lus eſt acu-
            <lb/>
          tus, cur cõ-
            <lb/>
          ſtare de-
            <lb/>
          beat, num
            <lb/>
          alter angu
            <lb/>
          lus ſit acu-
            <lb/>
          tus, vel ob-
            <lb/>
          tuſus.</note>
          <p>
            <s xml:id="echoid-s11050" xml:space="preserve">QVOD _autem nihil certi colligi poſsit, quando datus angulus vni datorum la-_
              <lb/>
            _terum oppoſitus acutus eſt, niſi prius cognitum ſit, num angulus alteri dato la-_
              <lb/>
            _teri oppoſitus ſit acutus, obtuſusue, vt in propoſ. </s>
            <s xml:id="echoid-s11051" xml:space="preserve">diximus, ita per ſpicuum faciemus._
              <lb/>
            </s>
            <s xml:id="echoid-s11052" xml:space="preserve">_Sint in triangulo_
              <emph style="sc">Abc</emph>
            , _data latera_
              <emph style="sc">Ab</emph>
            ,
              <emph style="sc">A</emph>
            C, _vna cum angulo acuto_
              <emph style="sc">B</emph>
            . </s>
            <s xml:id="echoid-s11053" xml:space="preserve">_Du-_
              <lb/>
            _cta ex_ A, _ad_
              <emph style="sc">B</emph>
            C, _perpendiculari_ AD, _ignorabitur, num ea cadat extra trian-_
              <lb/>
              <figure xlink:label="fig-346-01" xlink:href="fig-346-01a" number="192">
                <image file="346-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/346-01"/>
              </figure>
            _gulum, an intra, niſi ſciatur, angulum alterum_ ACB, _eſſe_
              <lb/>
            _obtuſum, acutumue. </s>
            <s xml:id="echoid-s11054" xml:space="preserve">Sumpta quoque recta_ DE, _ex altera_
              <lb/>
            _parte perpendicularis_
              <emph style="sc">A</emph>
            D, _ipſi_ DC, _æqualis, ductaq́; </s>
            <s xml:id="echoid-s11055" xml:space="preserve">recta_
              <lb/>
              <note position="left" xlink:label="note-346-03" xlink:href="note-346-03a" xml:space="preserve">4. primi.</note>
              <emph style="sc">AE</emph>
            ; </s>
            <s xml:id="echoid-s11056" xml:space="preserve">_erit_
              <emph style="sc">Ae</emph>
            , _ipſi_
              <emph style="sc">A</emph>
            C, _æqualis: </s>
            <s xml:id="echoid-s11057" xml:space="preserve">propterea quòd latera_
              <lb/>
            DC,
              <emph style="sc">Da</emph>
            , _lateribus_
              <emph style="sc">De</emph>
            ,
              <emph style="sc">Da</emph>
            , _æqualia ſunt, angulosq́; </s>
            <s xml:id="echoid-s11058" xml:space="preserve">com_
              <lb/>
            _prehendunt æquales, vtpote rectos. </s>
            <s xml:id="echoid-s11059" xml:space="preserve">Itaque etiamſinota ſint_
              <lb/>
            _latera_
              <emph style="sc">Ab</emph>
            , AC, _vel_ AB, AE, _& </s>
            <s xml:id="echoid-s11060" xml:space="preserve">angulus acutus_ B, _non_
              <lb/>
            _tamen idcirco reliquum latus notum erit, aut reliqui an-_
              <lb/>
            _guli; </s>
            <s xml:id="echoid-s11061" xml:space="preserve">cum reliquum latus poſsit eſſe vel_
              <emph style="sc">B</emph>
            C, _vel_
              <emph style="sc">B</emph>
            E; </s>
            <s xml:id="echoid-s11062" xml:space="preserve">_ac_
              <lb/>
            _propterea reliqui anguli vel_ BCA,
              <emph style="sc">B</emph>
            AC, _vel_
              <emph style="sc">B</emph>
            EA,
              <lb/>
              <emph style="sc">B</emph>
            AE: </s>
            <s xml:id="echoid-s11063" xml:space="preserve">_niſi prius conſtet, angulum_
              <emph style="sc">B</emph>
            CA, _obtuſum eſſe, vel acutum._ </s>
            <s xml:id="echoid-s11064" xml:space="preserve">H_oc enim co-_
              <lb/>
            _gnito, ſciemus, quando perpendicularis_ AD, _extra triangulum cadit, & </s>
            <s xml:id="echoid-s11065" xml:space="preserve">quando_
              <lb/>
            _intra; </s>
            <s xml:id="echoid-s11066" xml:space="preserve">&</s>
            <s xml:id="echoid-s11067" xml:space="preserve">c._</s>
            <s xml:id="echoid-s11068" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11069" xml:space="preserve">EX _quibus conſtat, Nicolaum Copernicum, alioquin diligentißimum, hallucina-_
              <lb/>
              <note position="left" xlink:label="note-346-04" xlink:href="note-346-04a" xml:space="preserve">Error Nico
                <lb/>
              lai Coper-
                <lb/>
              nici,</note>
            _tum fuiſſe lb._ </s>
            <s xml:id="echoid-s11070" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11071" xml:space="preserve">_Reuo lutionum propoſ._ </s>
            <s xml:id="echoid-s11072" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11073" xml:space="preserve">_triangulorum rectilineorum, dum ſimplici-_
              <lb/>
            _ter proponit: </s>
            <s xml:id="echoid-s11074" xml:space="preserve">Si duo latera trianguli data ſint, & </s>
            <s xml:id="echoid-s11075" xml:space="preserve">angulus vni eorum oppoſitus datus_
              <lb/>
            _etiam, reliquum latus, & </s>
            <s xml:id="echoid-s11076" xml:space="preserve">reliquos angulos dari poſſe. </s>
            <s xml:id="echoid-s11077" xml:space="preserve">Hoc etenim fieri non poteſt, vt_
              <lb/>
            _demonſtrauimus, quando datus angulus eſt acutus, niſi conſtet, num angulus alteri_
              <lb/>
            _laterum daterum oppoſitus ſit acutus, an obtuſus._</s>
            <s xml:id="echoid-s11078" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div903" type="section" level="1" n="473">
          <head xml:id="echoid-head505" xml:space="preserve">FINIS TRIANGVLORVM
            <lb/>
          RECTILINEORVM.</head>
          <figure number="193">
            <image file="346-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/346-02"/>
          </figure>
        </div>
      </text>
    </echo>
Impressum