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

List of thumbnails

< >
431
431 (419) 		432
432 (420)
433
433 (421) 		434
434 (422)
435
435 (423) 		436
436 (424)
437
437 (425) 		438
438 (426)
439
439 (427) 		440
440 (428)
< >
page |< < (419) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1158" type="section" level="1" n="559">
          <p>
            <s xml:id="echoid-s14602" xml:space="preserve">
              <pb o="419" file="431" n="431" rhead=""/>
            poſito, erit reliquus angulus C, obtuſus;</s>
            <s xml:id="echoid-s14603" xml:space="preserve">; ac proinde arcus AC, rectum angu-
              <lb/>
              <note position="right" xlink:label="note-431-01" xlink:href="note-431-01a" xml:space="preserve">33. huius.</note>
            lum B, ſubtendens quadrante quoque maior.
              <lb/>
            </s>
            <s xml:id="echoid-s14604" xml:space="preserve">
              <note position="right" xlink:label="note-431-02" xlink:href="note-431-02a" xml:space="preserve">37. huius.</note>
            Abſcindantur quadrantes AD, AE, & </s>
            <s xml:id="echoid-s14605" xml:space="preserve">per
              <lb/>
              <figure xlink:label="fig-431-01" xlink:href="fig-431-01a" number="284">
                <image file="431-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/431-01"/>
              </figure>
            puncta D, E, ducatur arcus DE, circuli ma-
              <lb/>
              <note position="right" xlink:label="note-431-03" xlink:href="note-431-03a" xml:space="preserve">20. 1 Theod.</note>
            ximi conueniens cum arcu BC, producto in
              <lb/>
            F; </s>
            <s xml:id="echoid-s14606" xml:space="preserve">Eritá; </s>
            <s xml:id="echoid-s14607" xml:space="preserve">vterque angulus D, E, rectus, ob
              <lb/>
              <note position="right" xlink:label="note-431-04" xlink:href="note-431-04a" xml:space="preserve">25. huius.</note>
            quadrantes AD, AE; </s>
            <s xml:id="echoid-s14608" xml:space="preserve">atque adeo, cum & </s>
            <s xml:id="echoid-s14609" xml:space="preserve">an-
              <lb/>
            gulus B, rectus ſit, quadrantes erunt arcus
              <lb/>
              <note position="right" xlink:label="note-431-05" xlink:href="note-431-05a" xml:space="preserve">25. huius.</note>
            BF, DF; </s>
            <s xml:id="echoid-s14610" xml:space="preserve">proptereaq́; </s>
            <s xml:id="echoid-s14611" xml:space="preserve">BD, arcus erit anguli
              <lb/>
            F. </s>
            <s xml:id="echoid-s14612" xml:space="preserve">Item arcus CF, complementum erit arcus
              <lb/>
              <note position="right" xlink:label="note-431-06" xlink:href="note-431-06a" xml:space="preserve">41. huius.</note>
            BC, & </s>
            <s xml:id="echoid-s14613" xml:space="preserve">arcus DB, EC, complementa arcuum
              <lb/>
            AB, AC, ob quadrantes BF, AD, AE. </s>
            <s xml:id="echoid-s14614" xml:space="preserve">Per-
              <lb/>
            ſpicuum eſt autem in triangulo CEF, ita eſ-
              <lb/>
            ſe ſinum arcus EC, id eſt, ſinum complemen-
              <lb/>
            ti arcus AC, ad ſinum anguli F, hoc eſt, ad ſi-
              <lb/>
            num arcus DB, hoc eſt, ad ſinum complementi arcus AB, vt eſt ſinus arcus
              <lb/>
            CF, nempe ſinus complementi arcus BC, ad ſinum anguli recti E, hoc eſt, ad
              <lb/>
            ſinum totum. </s>
            <s xml:id="echoid-s14615" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s14616" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14617" xml:space="preserve">POSTREMO ſit angulus A, obtuſus, & </s>
            <s xml:id="echoid-s14618" xml:space="preserve">adhuc arcus AB, quadrante
              <lb/>
            maior. </s>
            <s xml:id="echoid-s14619" xml:space="preserve">Fiat angulus rectus BAD, ſecetq́; </s>
            <s xml:id="echoid-s14620" xml:space="preserve">arcus AD, arcum BC, in D. </s>
            <s xml:id="echoid-s14621" xml:space="preserve">Ab-
              <lb/>
            ſcindatur quoque ex AB, quadrans AE, & </s>
            <s xml:id="echoid-s14622" xml:space="preserve">per puncta E, D, deſcribatur ar-
              <lb/>
              <note position="right" xlink:label="note-431-07" xlink:href="note-431-07a" xml:space="preserve">20. 1 Theod.</note>
            cus ED, circuli maximi ſecans arcum AC,
              <lb/>
            productum in F. </s>
            <s xml:id="echoid-s14623" xml:space="preserve">Et quia angulus B, ponitur
              <lb/>
              <figure xlink:label="fig-431-02" xlink:href="fig-431-02a" number="285">
                <image file="431-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/431-02"/>
              </figure>
            rectus, & </s>
            <s xml:id="echoid-s14624" xml:space="preserve">angulus BAD, rectus factus eſt, e-
              <lb/>
              <note position="right" xlink:label="note-431-08" xlink:href="note-431-08a" xml:space="preserve">25 huius.</note>
            runt arcus AD, BD, quadrantes. </s>
            <s xml:id="echoid-s14625" xml:space="preserve">Rurſus
              <lb/>
            quia arcus AD, AE, quadrantes ſunt, con-
              <lb/>
            tinentq́; </s>
            <s xml:id="echoid-s14626" xml:space="preserve">angulum rectum DAE, erit & </s>
            <s xml:id="echoid-s14627" xml:space="preserve">arcus
              <lb/>
            DE, quadrans, & </s>
            <s xml:id="echoid-s14628" xml:space="preserve">A, polus arcus ED; </s>
            <s xml:id="echoid-s14629" xml:space="preserve">atque
              <lb/>
              <note position="right" xlink:label="note-431-09" xlink:href="note-431-09a" xml:space="preserve">26. huius.</note>
            adeo angulus F, rectus erit Præterea quia
              <lb/>
              <note position="right" xlink:label="note-431-10" xlink:href="note-431-10a" xml:space="preserve">15. 1. Theo.</note>
            DB, DE, quadrantes ſunt oſtenſi, erit EB,
              <lb/>
            arcus anguli BDE, hoc eſt, anguli CDF, qui
              <lb/>
              <note position="right" xlink:label="note-431-11" xlink:href="note-431-11a" xml:space="preserve">6. huius.</note>
            illi ad verticem eſt æqualis. </s>
            <s xml:id="echoid-s14630" xml:space="preserve">Item cum A, po-
              <lb/>
            lus ſit arcus EF, erit arcus AF, quadrans,
              <lb/>
              <note position="right" xlink:label="note-431-12" xlink:href="note-431-12a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. Theod.</note>
            quòd arcus EF, quadrãte ſemper abſit à ſuo
              <lb/>
            polo. </s>
            <s xml:id="echoid-s14631" xml:space="preserve">Arcus item CF, complementum erit
              <lb/>
            arcus AC; </s>
            <s xml:id="echoid-s14632" xml:space="preserve">& </s>
            <s xml:id="echoid-s14633" xml:space="preserve">arcus EB, complementum arcus AB; </s>
            <s xml:id="echoid-s14634" xml:space="preserve">& </s>
            <s xml:id="echoid-s14635" xml:space="preserve">arcus CD, complemen
              <lb/>
            tum arcus BC, ob quadrantes AF, AE, BD. </s>
            <s xml:id="echoid-s14636" xml:space="preserve">Maniſeſtum eſt autem in trian
              <lb/>
            gulo CDF, ita eſſe ſinum arcus CF, id eſt, ſinum complementi arcus AC, ad
              <lb/>
              <note position="right" xlink:label="note-431-13" xlink:href="note-431-13a" xml:space="preserve">41. huius</note>
            ſinum anguli CDF, hoc eſt, ad ſinum arcus BE, ſiue complementi arcus AB,
              <lb/>
            vt eſt ſinus arcus CD, nempe ſinus complementi arcus BC, ad ſinum anguli
              <lb/>
            recti F, hoc eſt, ad ſinum totum. </s>
            <s xml:id="echoid-s14637" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s14638" xml:space="preserve">In omni ergo trian-
              <lb/>
            gulo ſphærico rectangulo, &</s>
            <s xml:id="echoid-s14639" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14640" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s14641" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1163" type="section" level="1" n="560">
          <head xml:id="echoid-head595" xml:space="preserve">SCHOLIVM. I.</head>
          <p style="it">
            <s xml:id="echoid-s14642" xml:space="preserve">SEQVENS problema ex hac propoſ. </s>
            <s xml:id="echoid-s14643" xml:space="preserve">colligemus hunc in modum.</s>
            <s xml:id="echoid-s14644" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14645" xml:space="preserve">IN triangulo ſphærico rectangulo, datis duobus arcubus qui-
              <lb/>
            buſlibet, inuenire tertium arcũ, & </s>
            <s xml:id="echoid-s14646" xml:space="preserve">reliquos duos angulos non rectos.</s>
            <s xml:id="echoid-s14647" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum