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

Page concordance

< >
Scan Original
441 429
442 430
443 431
444 432
445 433
446 434
447 435
448 436
449 437
450 438
451 439
452 440
453 441
454 442
455 443
456 444
457 445
458 446
459 447
460 448
461 449
462 450
463 451
464 452
465 453
466 454
467 455
468 456
469 457
470 458
< >
page |< < (431) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1213" type="section" level="1" n="575">
          <pb o="431" file="443" n="443" rhead=""/>
        </div>
        <div xml:id="echoid-div1215" type="section" level="1" n="576">
          <head xml:id="echoid-head611" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s15118" xml:space="preserve">INFERTVR ex theoremate hoc ſequens problema: </s>
            <s xml:id="echoid-s15119" xml:space="preserve">quod licet demonſtratum
              <lb/>
            quoque ſit problemate 2. </s>
            <s xml:id="echoid-s15120" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15121" xml:space="preserve">44. </s>
            <s xml:id="echoid-s15122" xml:space="preserve">facilius tamen hic abſoluitur, cumin aurea re-
              <lb/>
            gula ſinus to tus primum obtineat locum.</s>
            <s xml:id="echoid-s15123" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15124" xml:space="preserve">IN triangulo ſphærico rectangulo, datis duobus arcubus circa
              <lb/>
            angulum rectum, vtrumlibet angulorum non rectorum, vnà cum
              <lb/>
            arcu reliquo, qui angulo recto opponitur, indagare.</s>
            <s xml:id="echoid-s15125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15126" xml:space="preserve">IN triangulo ABC, cuius angulus C, rectus,
              <lb/>
              <figure xlink:label="fig-443-01" xlink:href="fig-443-01a" number="299">
                <image file="443-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/443-01"/>
              </figure>
            ſint dati duo arcus AC, CB. </s>
            <s xml:id="echoid-s15127" xml:space="preserve">Dico vtrumuis angulo-
              <lb/>
            rum A, B, & </s>
            <s xml:id="echoid-s15128" xml:space="preserve">arcum AB, quoque dari. </s>
            <s xml:id="echoid-s15129" xml:space="preserve">Nam cum ſit,
              <lb/>
            vt ſinus totus ad ſinum arcus AC, ita tangens comple-
              <lb/>
              <note position="right" xlink:label="note-443-01" xlink:href="note-443-01a" xml:space="preserve">48. huius.</note>
            menti arcus CB, ad tangentem complementi anguli
              <lb/>
            A. </s>
            <s xml:id="echoid-s15130" xml:space="preserve">Item vt ſinus totus ad ſinum arcus CB, ita tan-
              <lb/>
            gens complementi arcus AC, ad tangentem complemen
              <lb/>
            ti anguli B:</s>
            <s xml:id="echoid-s15131" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15132" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum vtrius vis arcuum circa angulum re-
              <lb/>
              <note position="right" xlink:label="note-443-02" xlink:href="note-443-02a" xml:space="preserve">Praxis.</note>
            ctum, ita tangens complementi alterius arcus circa rectum angulum ad
              <lb/>
            aliud, reperietur tangens complementi anguli huic poſterioriarcui oppo-
              <lb/>
            ſiti. </s>
            <s xml:id="echoid-s15133" xml:space="preserve">Ex datis quoque duobus arcubus circa angulum rectum cognoſcetur
              <lb/>
            & </s>
            <s xml:id="echoid-s15134" xml:space="preserve">tertius arcus angulo recto oppoſitus, vt in problemate propoſ. </s>
            <s xml:id="echoid-s15135" xml:space="preserve">43. </s>
            <s xml:id="echoid-s15136" xml:space="preserve">oſten
              <lb/>
            dimus. </s>
            <s xml:id="echoid-s15137" xml:space="preserve">Vel certe ex dato vtrolibet arcu, & </s>
            <s xml:id="echoid-s15138" xml:space="preserve">angulo, qui ei opponitur, in-
              <lb/>
            uento, vt in problemate 3. </s>
            <s xml:id="echoid-s15139" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15140" xml:space="preserve">41. </s>
            <s xml:id="echoid-s15141" xml:space="preserve">traditum eſt.</s>
            <s xml:id="echoid-s15142" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15143" xml:space="preserve">VTRVM autem angulus quæſitus ſit acutus, obtuſusve, docebit arcus ei oppo-
              <lb/>
            ſitus. </s>
            <s xml:id="echoid-s15144" xml:space="preserve">Hic enim ſi minor fuerit quadrante, erit angulus ei oppoſitus, acutus; </s>
            <s xml:id="echoid-s15145" xml:space="preserve">ſi vero
              <lb/>
              <note position="right" xlink:label="note-443-03" xlink:href="note-443-03a" xml:space="preserve">34. huius.</note>
            maior, obtuſus.</s>
            <s xml:id="echoid-s15146" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1219" type="section" level="1" n="577">
          <head xml:id="echoid-head612" xml:space="preserve">THEOR. 47. PROPOS. 49.</head>
          <p>
            <s xml:id="echoid-s15147" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cu-
              <lb/>
            ius omnes arcus ſint minores quadrante: </s>
            <s xml:id="echoid-s15148" xml:space="preserve">ſinus to-
              <lb/>
            tus ad tangentem vtriusvis arcuum circa angulum
              <lb/>
            rectum eandem proportionem habet, quam tan-
              <lb/>
            gens complementi anguli oppoſiti ad ſinum alte-
              <lb/>
            rius arcus circa rectum angulum.</s>
            <s xml:id="echoid-s15149" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15150" xml:space="preserve">IN ſphærico triangulo ADE, cuius arcus omnes quadrante minores, ſit
              <lb/>
            angulus D, rectus. </s>
            <s xml:id="echoid-s15151" xml:space="preserve">Dico ita eſſe ſinum totum ad tangentem arcus DE, vt </s>
          </p>
        </div>
      </text>
    </echo>
Impressum