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

Page concordance

< >
Scan Original
381 369
382 370
383 371
384 372
385 373
386 374
387 375
388 376
389 377
390 378
391 379
392 380
393 381
394 382
395 383
396 384
397 385
398 386
399 387
400 388
401 389
402 390
403 391
404 392
405 393
406 394
407 395
408 396
409 397
410 398
< >
page |< < (385) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1038" type="section" level="1" n="522">
          <p style="it">
            <s xml:id="echoid-s13141" xml:space="preserve">
              <pb o="385" file="397" n="397" rhead=""/>
            duos quidem maiores quadrante, & </s>
            <s xml:id="echoid-s13142" xml:space="preserve">vnum quadranti æqualem: </s>
            <s xml:id="echoid-s13143" xml:space="preserve">Sed poſſunt eſſe duo
              <lb/>
            quidem quadrante maiores, reliquus verò quadrante minor. </s>
            <s xml:id="echoid-s13144" xml:space="preserve">Sint enim duo ſemicir-
              <lb/>
            culi in ſuperficie ſphæra continentes angulos _A, C,_ obtuſos. </s>
            <s xml:id="echoid-s13145" xml:space="preserve">Si igitur accipiantur
              <lb/>
            duo arcus æquales _AB, AD,_ quorum vterque
              <lb/>
              <figure xlink:label="fig-397-01" xlink:href="fig-397-01a" number="238">
                <image file="397-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/397-01"/>
              </figure>
            maior ſit ſesqusaltero quadrante, ita vt ambo
              <lb/>
            ſimul tres quadrantes ſuperent; </s>
            <s xml:id="echoid-s13146" xml:space="preserve">deſeribatur
              <lb/>
            autem per puncta _B, D,_ arcus circuli maximi
              <lb/>
              <note position="right" xlink:label="note-397-01" xlink:href="note-397-01a" xml:space="preserve">20. 1 Theod.</note>
            _BD;_ </s>
            <s xml:id="echoid-s13147" xml:space="preserve">erit hic arcus _BD,_ quadrante minor. </s>
            <s xml:id="echoid-s13148" xml:space="preserve">Cum
              <lb/>
            enim tres arcus _AB, AD, BD,_ integro circu-
              <lb/>
              <note position="right" xlink:label="note-397-02" xlink:href="note-397-02a" xml:space="preserve">4. huius.</note>
            lo minores ſint, ponatur autem duo arcus _AB,_
              <lb/>
            _AD,_ tribus quadrantibus maiores; </s>
            <s xml:id="echoid-s13149" xml:space="preserve">erit neceſ-
              <lb/>
            ſario tertius arcus _BD,_ minor quadrãte: </s>
            <s xml:id="echoid-s13150" xml:space="preserve">Alias,
              <lb/>
            ſi quadrans eſſet, aut maior quadrante, ſupe-
              <lb/>
            rarent tres arcus trianguli _ABC,_ integrum
              <lb/>
            circulum. </s>
            <s xml:id="echoid-s13151" xml:space="preserve">Quoniam igitur duo anguli _B,_ & </s>
            <s xml:id="echoid-s13152" xml:space="preserve">_D,_ in triangulo _ABD,_ obtuſi ſunt,
              <lb/>
              <note position="right" xlink:label="note-397-03" xlink:href="note-397-03a" xml:space="preserve">25. huius.</note>
            necnon & </s>
            <s xml:id="echoid-s13153" xml:space="preserve">tertius angulus _A,_ obtuſus quoque, ex bypotheſi; </s>
            <s xml:id="echoid-s13154" xml:space="preserve">erunt omnes tres anguli
              <lb/>
            _A, B, D,_ obtuſi; </s>
            <s xml:id="echoid-s13155" xml:space="preserve">& </s>
            <s xml:id="echoid-s13156" xml:space="preserve">tamen neque omnes arcus ſunt quadrante maiores; </s>
            <s xml:id="echoid-s13157" xml:space="preserve">neque duo
              <lb/>
            tantum, & </s>
            <s xml:id="echoid-s13158" xml:space="preserve">tertius quadrans; </s>
            <s xml:id="echoid-s13159" xml:space="preserve">ſed duo quidem _AB, AD,_ quadrante maiores ſunt,
              <lb/>
            at tertius arcus _BD,_ quadrante minor, vt oſtendimus.</s>
            <s xml:id="echoid-s13160" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1040" type="section" level="1" n="523">
          <head xml:id="echoid-head558" xml:space="preserve">THEOR. 26. PROPOS. 28.</head>
          <p>
            <s xml:id="echoid-s13161" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cuius
              <lb/>
            omnes arcus ſint quadrante minores, reliqui duo
              <lb/>
            anguli acuti ſunt. </s>
            <s xml:id="echoid-s13162" xml:space="preserve">Et ſi reliqui duo anguli ſint acu-
              <lb/>
            ti, erunt ſinguli arcus quadrante minores.</s>
            <s xml:id="echoid-s13163" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13164" xml:space="preserve">IN triangulo ſphærico ABC, ſit angulus B, rectus, & </s>
            <s xml:id="echoid-s13165" xml:space="preserve">ſinguli arcus qua-
              <lb/>
            drante minores. </s>
            <s xml:id="echoid-s13166" xml:space="preserve">Dico reliquos angulos A, C, eſſe acutos. </s>
            <s xml:id="echoid-s13167" xml:space="preserve">Producantur enim
              <lb/>
            arcus BA, BC, vt ſint quadrantes BD, BE; </s>
            <s xml:id="echoid-s13168" xml:space="preserve">& </s>
            <s xml:id="echoid-s13169" xml:space="preserve">per puncta C, D, arcus maxi-
              <lb/>
            mi circuli ducatur CD, necnon per puncta A, E, ar-
              <lb/>
              <note position="right" xlink:label="note-397-04" xlink:href="note-397-04a" xml:space="preserve">20. 1 Theod.</note>
              <figure xlink:label="fig-397-02" xlink:href="fig-397-02a" number="239">
                <image file="397-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/397-02"/>
              </figure>
            cus circuli maximi AE. </s>
            <s xml:id="echoid-s13170" xml:space="preserve">Et quoniam quadrans BD,
              <lb/>
            ob angulum rectum B, per polos arcus BC, tranſit,
              <lb/>
              <note position="right" xlink:label="note-397-05" xlink:href="note-397-05a" xml:space="preserve">13. 1. Theod.
                <lb/>
              Coroll. 16.</note>
            abeſtq; </s>
            <s xml:id="echoid-s13171" xml:space="preserve">polus circuli maximi quadrate circuli maxi-
              <lb/>
            mi ab eo, erit D, polus arcus BC. </s>
            <s xml:id="echoid-s13172" xml:space="preserve">Igitur erit angu-
              <lb/>
              <note position="right" xlink:label="note-397-06" xlink:href="note-397-06a" xml:space="preserve">1. Theod.</note>
            lus BCD, rectus; </s>
            <s xml:id="echoid-s13173" xml:space="preserve">ac propterea angulus ACB, acu-
              <lb/>
              <note position="right" xlink:label="note-397-07" xlink:href="note-397-07a" xml:space="preserve">15. 1 Theod.</note>
            tus. </s>
            <s xml:id="echoid-s13174" xml:space="preserve">Eodem modo, quia quadrans BE, ob angulum
              <lb/>
            rectum B, per polos arcus AB, tranſit, abeſtq́; </s>
            <s xml:id="echoid-s13175" xml:space="preserve">polus
              <lb/>
              <note position="right" xlink:label="note-397-08" xlink:href="note-397-08a" xml:space="preserve">13. 1 Theod.</note>
            circuli maximi quadrante maximi circuli ab eo, erit
              <lb/>
              <note position="right" xlink:label="note-397-09" xlink:href="note-397-09a" xml:space="preserve">Coroll. 16.</note>
            E, polus arcus AB, Igitur angulus EAB, rectus erit;
              <lb/>
            </s>
            <s xml:id="echoid-s13176" xml:space="preserve">
              <note position="right" xlink:label="note-397-10" xlink:href="note-397-10a" xml:space="preserve">1. Theod.</note>
            ac proinde BAC, acutus.</s>
            <s xml:id="echoid-s13177" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">15. 1 Theod.</note>
          <p>
            <s xml:id="echoid-s13178" xml:space="preserve">SED iam in eodem triangulo ABC, angulus B, rectus ſit, & </s>
            <s xml:id="echoid-s13179" xml:space="preserve">reliqui A,
              <lb/>
            C, acuti. </s>
            <s xml:id="echoid-s13180" xml:space="preserve">Dico ſingulos arcus eſſe quadrante minores. </s>
            <s xml:id="echoid-s13181" xml:space="preserve">Fiant enim recti angu-
              <lb/>
            li BCD, BAE. </s>
            <s xml:id="echoid-s13182" xml:space="preserve">Quia igitur vterque angulus B, BCD, rectus eſt, erit vter-
              <lb/>
              <note position="right" xlink:label="note-397-12" xlink:href="note-397-12a" xml:space="preserve">25. huius.</note>
            que arcus BD, CD, quadrans. </s>
            <s xml:id="echoid-s13183" xml:space="preserve">Arcus igitur BA, quadrante minor eſt. </s>
            <s xml:id="echoid-s13184" xml:space="preserve">Eo-
              <lb/>
            dem modo arcus BC, minor erit quadrante; </s>
            <s xml:id="echoid-s13185" xml:space="preserve">propterea quòd & </s>
            <s xml:id="echoid-s13186" xml:space="preserve">arcus BE, AE,
              <lb/>
              <note position="right" xlink:label="note-397-13" xlink:href="note-397-13a" xml:space="preserve">25. huius.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum