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

Table of figures

< >
< >
page |< < (395) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1076" type="section" level="1" n="533">
          <p>
            <s xml:id="echoid-s13602" xml:space="preserve">
              <pb o="395" file="407" n="407" rhead=""/>
            @rcus AC, quadrante maior: </s>
            <s xml:id="echoid-s13603" xml:space="preserve">quæ omnia abſurdo ſunt, eum arcus AC, po-
              <lb/>
              <note position="right" xlink:label="note-407-01" xlink:href="note-407-01a" xml:space="preserve">35. huius</note>
            natur quadrante minor. </s>
            <s xml:id="echoid-s13604" xml:space="preserve">Erit ergo vel vterque arcus AB, BC, minor quadran
              <lb/>
            te, vel maior.</s>
            <s xml:id="echoid-s13605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13606" xml:space="preserve">TERTIO ſit arcus AC, maior quadrante. </s>
            <s xml:id="echoid-s13607" xml:space="preserve">Dico alterum reliquorum
              <lb/>
            AB, BC, quadrante quidem eſſe maiorem, alterum verò minorem. </s>
            <s xml:id="echoid-s13608" xml:space="preserve">Si enim
              <lb/>
            non eſt alter maior, & </s>
            <s xml:id="echoid-s13609" xml:space="preserve">alter minor quadrante, erit vel vterque quadrans,
              <lb/>
            vel alter ſaltem quadrans, & </s>
            <s xml:id="echoid-s13610" xml:space="preserve">alter non, ac proinde & </s>
            <s xml:id="echoid-s13611" xml:space="preserve">arcus AC, quadrans;
              <lb/>
            </s>
            <s xml:id="echoid-s13612" xml:space="preserve">
              <note position="right" xlink:label="note-407-02" xlink:href="note-407-02a" xml:space="preserve">35. huius.</note>
            vel vterque minor quadrante, aut maior, atque adeo arcus AC, quadrante
              <lb/>
              <note position="right" xlink:label="note-407-03" xlink:href="note-407-03a" xml:space="preserve">35. huius.</note>
            minor: </s>
            <s xml:id="echoid-s13613" xml:space="preserve">quæ omnia ſunt abſurda, cum arcus AC, maior ponatur, quam qua-
              <lb/>
            drans. </s>
            <s xml:id="echoid-s13614" xml:space="preserve">Erit ergo alter arcuum AB, BC, quadrante quidem maior, alter ve-
              <lb/>
            ro minor. </s>
            <s xml:id="echoid-s13615" xml:space="preserve">Quocirca in omni triangulo ſphærico rectangulo, &</s>
            <s xml:id="echoid-s13616" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13617" xml:space="preserve">Quod de-
              <lb/>
            monſtrandum erat.</s>
            <s xml:id="echoid-s13618" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1080" type="section" level="1" n="534">
          <head xml:id="echoid-head569" xml:space="preserve">THEOR. 35. PROPOS. 37.</head>
          <p>
            <s xml:id="echoid-s13619" xml:space="preserve">IN omni triangulo ſphærico, ſi vterque reli-
              <lb/>
            quorum angulorum, vel alter ſaltem fuerit rectus,
              <lb/>
            erit arcus rectum angulum ſubtendens, quadrans:
              <lb/>
            </s>
            <s xml:id="echoid-s13620" xml:space="preserve">ſi verò vterque reliquorum angulorum minor fue-
              <lb/>
            rit recto, vel maior, erit arcus ſubtendens angulum
              <lb/>
            rectum quadrante minor: </s>
            <s xml:id="echoid-s13621" xml:space="preserve">ſi deniq; </s>
            <s xml:id="echoid-s13622" xml:space="preserve">alter reliquo-
              <lb/>
            rum fuerit maior recto, & </s>
            <s xml:id="echoid-s13623" xml:space="preserve">alter minor, erit arcus
              <lb/>
            angulum rectum ſubtendens, quadrante maior.</s>
            <s xml:id="echoid-s13624" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13625" xml:space="preserve">IN triangulo ſphærico ABC, cuius angulus B, rectus, ſit primum vter-
              <lb/>
            que angulorum A, C, vel alter ſaltem, nempe C, rectus. </s>
            <s xml:id="echoid-s13626" xml:space="preserve">Dico arcum AC, qui
              <lb/>
            rectum angulum B, ſubtendit, eſſe quadrantem. </s>
            <s xml:id="echoid-s13627" xml:space="preserve">Si enim vterque angulus A,
              <lb/>
            C, rectus eſt, vel C, tantum, erit triangulum ABC,
              <lb/>
              <figure xlink:label="fig-407-01" xlink:href="fig-407-01a" number="256">
                <image file="407-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/407-01"/>
              </figure>
            rectangulũ habens angulum C, rectum: </s>
            <s xml:id="echoid-s13628" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s13629" xml:space="preserve">
              <lb/>
            angulus B, rectus. </s>
            <s xml:id="echoid-s13630" xml:space="preserve">Igitur arcus AC, quadrans erit.</s>
            <s xml:id="echoid-s13631" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">34. huius.</note>
          <p>
            <s xml:id="echoid-s13632" xml:space="preserve">DEINDE ſit vterque angulus A, C, vel minor
              <lb/>
            recto, vel maior. </s>
            <s xml:id="echoid-s13633" xml:space="preserve">Dico arcum AC, quadrante eſſe
              <lb/>
            minorem. </s>
            <s xml:id="echoid-s13634" xml:space="preserve">Si namque vterque angulus A, C, eſt mi-
              <lb/>
              <note position="right" xlink:label="note-407-05" xlink:href="note-407-05a" xml:space="preserve">34. huius.</note>
            nor recto, erit tam arcus BC, quam AB, minor qua-
              <lb/>
            drante; </s>
            <s xml:id="echoid-s13635" xml:space="preserve">ſi verò vterque angulus A, C, maior eſt re-
              <lb/>
              <note position="right" xlink:label="note-407-06" xlink:href="note-407-06a" xml:space="preserve">34. huius.</note>
            cto, erit tam arcus BC, quam AB, quadrante maior.
              <lb/>
            </s>
            <s xml:id="echoid-s13636" xml:space="preserve">Quare cum in triangulo ABc, angulus B, rectus
              <lb/>
            ſit, & </s>
            <s xml:id="echoid-s13637" xml:space="preserve">vterque arcus AB, BC, vel minor, vel maior quadrante, erit ſemper
              <lb/>
            arcus AC, quadrante minor.</s>
            <s xml:id="echoid-s13638" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">35. huius.</note>
          <p>
            <s xml:id="echoid-s13639" xml:space="preserve">TERTIO ſit angulus A, maior recto, & </s>
            <s xml:id="echoid-s13640" xml:space="preserve">C, minor. </s>
            <s xml:id="echoid-s13641" xml:space="preserve">Dico arcum AC, eſ-
              <lb/>
            ſe quadrante maiorem. </s>
            <s xml:id="echoid-s13642" xml:space="preserve">Cum enim angulus A, obtuſus ſit, erit arcus BC,
              <lb/>
              <note position="right" xlink:label="note-407-08" xlink:href="note-407-08a" xml:space="preserve">34. huius.</note>
            maior quadrante: </s>
            <s xml:id="echoid-s13643" xml:space="preserve">Et cum angulus C, acutus ſit, erit arcus AB, quadrante mi-
              <lb/>
              <note position="right" xlink:label="note-407-09" xlink:href="note-407-09a" xml:space="preserve">34. huius.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum