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

Table of figures

< >
< >
page |< < (462) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1311" type="section" level="1" n="607">
          <p>
            <s xml:id="echoid-s16401" xml:space="preserve">
              <pb o="462" file="474" n="474" rhead=""/>
            ſtrauimus, omnes eius tres anguli noti fient, ac proinde & </s>
            <s xml:id="echoid-s16402" xml:space="preserve">reliqui duorum re-
              <lb/>
            ctorum ABC, ACB, necnon & </s>
            <s xml:id="echoid-s16403" xml:space="preserve">angulus A, cum angulo D, ſit æqualis.</s>
            <s xml:id="echoid-s16404" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">13. huius.</note>
          <p>
            <s xml:id="echoid-s16405" xml:space="preserve">SIT tertio arcus quidem AB, quandrante minor, at AC, maior. </s>
            <s xml:id="echoid-s16406" xml:space="preserve">Produ-
              <lb/>
            cto arcu AB, vt fiat quadrans AD, & </s>
            <s xml:id="echoid-s16407" xml:space="preserve">reſecto quadrante AE, ex AC, vt in
              <lb/>
            prima harum figurarum, ducatur per D, E, arcus circuli maximi DE, ſecans
              <lb/>
            arcum BC, in F. </s>
            <s xml:id="echoid-s16408" xml:space="preserve">Eruntq́; </s>
            <s xml:id="echoid-s16409" xml:space="preserve">anguli D, E, recti, ob quadrantes AD, AE. </s>
            <s xml:id="echoid-s16410" xml:space="preserve">Quia
              <lb/>
              <note position="left" xlink:label="note-474-02" xlink:href="note-474-02a" xml:space="preserve">25. huius.</note>
            ergo duo maximi circuli BC, DE, ſecant ſe-
              <lb/>
              <figure xlink:label="fig-474-01" xlink:href="fig-474-01a" number="343">
                <image file="474-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/474-01"/>
              </figure>
            ſe in F, & </s>
            <s xml:id="echoid-s16411" xml:space="preserve">à punctis B, C, arcus BC, ad arcum
              <lb/>
            DE, ducti ſunt arcus perpendiculares BD,
              <lb/>
              <note position="left" xlink:label="note-474-03" xlink:href="note-474-03a" xml:space="preserve">40. huius.</note>
            CE; </s>
            <s xml:id="echoid-s16412" xml:space="preserve">erit, vt ſinus arcus BF, ad ſinum arcus
              <lb/>
            BD, ita ſinus arcus CF, ad ſinum arcus CE:
              <lb/>
            </s>
            <s xml:id="echoid-s16413" xml:space="preserve">Et permutando, vt ſinus arcus BF, ad ſinum
              <lb/>
            arcus CF, ita ſinus arcus BD, ad ſinum ar-
              <lb/>
            cus CE. </s>
            <s xml:id="echoid-s16414" xml:space="preserve">Eſt autem proportio ſinus arcus BD,
              <lb/>
            ad ſinũ arcus CE, cognita, quod arcus BD,
              <lb/>
            CE, dati ſint, cũ ſint complemẽta datorũ ar-
              <lb/>
            cuũ AB, AC. </s>
            <s xml:id="echoid-s16415" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s16416" xml:space="preserve">proportio ſinus arcus
              <lb/>
            BF, ad ſinũ arcus CF, cognita erit, vtpote in
              <lb/>
            ſinubus complementorum arcuum AB, AC,
              <lb/>
            datorum: </s>
            <s xml:id="echoid-s16417" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s16418" xml:space="preserve">eorundem arcuum BF, CF,
              <lb/>
            aggregatum datum eſt, (nimirũ totus arcus BC.) </s>
            <s xml:id="echoid-s16419" xml:space="preserve">& </s>
            <s xml:id="echoid-s16420" xml:space="preserve">minus ſemicirculo; </s>
            <s xml:id="echoid-s16421" xml:space="preserve">quod
              <lb/>
            latus quodlibet trianguli ſphærici ſemicirculo ſit minus. </s>
            <s xml:id="echoid-s16422" xml:space="preserve">Igitur vterque arcus
              <lb/>
              <note position="left" xlink:label="note-474-04" xlink:href="note-474-04a" xml:space="preserve">2. huius.</note>
            BF, CF, cognitus erit. </s>
            <s xml:id="echoid-s16423" xml:space="preserve">Quoniam ergo in triangulo BFD, cuius angulus D,
              <lb/>
              <note position="left" xlink:label="note-474-05" xlink:href="note-474-05a" xml:space="preserve">6. triang.
                <lb/>
              rectil.</note>
            rectus, datus eſt arcus BF, angulo recto oppoſitus, cum arcu BD, qui com-
              <lb/>
              <note position="left" xlink:label="note-474-06" xlink:href="note-474-06a" xml:space="preserve">Schol. 53.
                <lb/>
              vel 43. huiꝰ.</note>
            plementum eſt arcus AB, dati; </s>
            <s xml:id="echoid-s16424" xml:space="preserve">notus erit quoque tertius arcus DF. </s>
            <s xml:id="echoid-s16425" xml:space="preserve">Simili
              <lb/>
            modo, quia in triangulo CFE, rectum habente angulum E, datus eſt arcus
              <lb/>
            CF, angulo recto oppoſitus, & </s>
            <s xml:id="echoid-s16426" xml:space="preserve">arcus CE, complementum ſcilicet arcus AC;
              <lb/>
            </s>
            <s xml:id="echoid-s16427" xml:space="preserve">reperietur quoque tertius arcus EF: </s>
            <s xml:id="echoid-s16428" xml:space="preserve">qui additus arcui DF, inuento, notum
              <lb/>
              <note position="left" xlink:label="note-474-07" xlink:href="note-474-07a" xml:space="preserve">Schol. 53.
                <lb/>
              vel 43. huiꝰ.</note>
            efficiet totum arcum DE, anguli A; </s>
            <s xml:id="echoid-s16429" xml:space="preserve">proptereaq́; </s>
            <s xml:id="echoid-s16430" xml:space="preserve">angulus A, notus erit. </s>
            <s xml:id="echoid-s16431" xml:space="preserve">Rur-
              <lb/>
            ſus in triangulo priori BFD, cuius angulus D, rectus, quoniam datus eſt ar-
              <lb/>
            cus BF, recto angulo oppoſitus, & </s>
            <s xml:id="echoid-s16432" xml:space="preserve">arcus BD, complementum nimirum da-
              <lb/>
              <note position="left" xlink:label="note-474-08" xlink:href="note-474-08a" xml:space="preserve">Schol. 51.
                <lb/>
              vel 45. huiꝰ.</note>
            ti arcus AB:
              <lb/>
            </s>
            <s xml:id="echoid-s16433" xml:space="preserve">
              <note position="left" xlink:label="note-474-09" xlink:href="note-474-09a" xml:space="preserve">Schol. 44.
                <lb/>
              vel 48. huiꝰ</note>
            AVT quia duo arcus BD, DF, circa rectum angu-
              <lb/>
            lum dati ſunt:
              <lb/>
            </s>
            <s xml:id="echoid-s16434" xml:space="preserve">VEL certe, quia datus eſt arcus BF, recto angulo
              <lb/>
              <note position="left" xlink:label="note-474-10" xlink:href="note-474-10a" xml:space="preserve">Schol. 55.
                <lb/>
              vel 41. huiꝰ</note>
            oppoſitus, cum arcu DF;
              <lb/>
            </s>
            <s xml:id="echoid-s16435" xml:space="preserve">notus efficietur quoque angulus DBF, ex ſcholijs in margine adductis; </s>
            <s xml:id="echoid-s16436" xml:space="preserve">atque
              <lb/>
            adeo & </s>
            <s xml:id="echoid-s16437" xml:space="preserve">reliquus duorum rectorum ABC, notus erit. </s>
            <s xml:id="echoid-s16438" xml:space="preserve">Pari ratione, cum in po
              <lb/>
            ſteriori triangulo CFE, cuius angulus E, rectus, datus ſit arcus CF, recto an-
              <lb/>
              <note position="left" xlink:label="note-474-11" xlink:href="note-474-11a" xml:space="preserve">Schol. 51.
                <lb/>
              vel 45. huiꝰ.</note>
            gulo oppoſitus, cum arcu CE, complemento videlicet arcus AC, dati;
              <lb/>
            </s>
            <s xml:id="echoid-s16439" xml:space="preserve">VEL cum duo arcus CE, EF, circa angulum re-
              <lb/>
              <note position="left" xlink:label="note-474-12" xlink:href="note-474-12a" xml:space="preserve">Schol. 44.
                <lb/>
              vel 48. huiꝰ</note>
            ctum dati ſint:
              <lb/>
            </s>
            <s xml:id="echoid-s16440" xml:space="preserve">VEL certe, cum datus ſit arcus CF, recto angulo
              <lb/>
              <note position="left" xlink:label="note-474-13" xlink:href="note-474-13a" xml:space="preserve">Schol. 55.
                <lb/>
              vel 41. huiꝰ.</note>
            oppoſitus, cum arcu EF;
              <lb/>
            </s>
            <s xml:id="echoid-s16441" xml:space="preserve">dabitur etiam angulus C, per ſcholia in margine deſcripta. </s>
            <s xml:id="echoid-s16442" xml:space="preserve">Atque ita omnes
              <lb/>
            tres anguli ABC, noti facti ſunt.</s>
            <s xml:id="echoid-s16443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16444" xml:space="preserve">SIT quarto arcus AB, quadrans, & </s>
            <s xml:id="echoid-s16445" xml:space="preserve">AC, minor, vt in poſteriore proxi-
              <lb/>
            marum figurarum. </s>
            <s xml:id="echoid-s16446" xml:space="preserve">Producto arcu AC, vt fiat quadrans AD, ducatur per </s>
          </p>
        </div>
      </text>
    </echo>
Impressum