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

Table of Notes

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            <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"/>
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            _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>
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        <div xml:id="echoid-div903" type="section" level="1" n="473">
          <head xml:id="echoid-head505" xml:space="preserve">FINIS TRIANGVLORVM
            <lb/>
          RECTILINEORVM.</head>
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