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

Table of contents

< >
[471.] PROBL. 9. PROPOS. 13.
Page: 343 (331)
[472.] SCHOLIVM.
Page: 346 (334)
[473.] FINIS TRIANGVLORVM RECTILINEORVM.
Page: 346 (334)
[474.] CHRISTOPHORI CLAVII BAMBERGENSIS ESOCIETATE IESV TRIANGVLA SPHÆRICA.
Page: 349
[475.] CHRISTOPHORI CLAVII BAMBERGENSIS E SOCIETATE IESV TRIANGVLA SPHÆRICA. PRÆFATIO.
Page: 351 (339)
[476.] DEFINITIONES. I.
Page: 352 (340)
[477.] II.
Page: 368 (356)
[478.] III.
Page: 368 (356)
[479.] IIII.
Page: 368 (356)
[480.] V.
Page: 369 (357)
[481.] VI.
Page: 369 (357)
[482.] VII.
Page: 369 (357)
[483.] VIII.
Page: 370 (358)
[484.] IX.
Page: 370 (358)
[485.] PROBLEMA I. PROPOSITIO I.
Page: 370 (358)
[486.] THEOR. 1. PROPOS. 2.
Page: 370 (358)
[487.] THEOR. 2. PROPOS. 3. IN omni triangulo ſphærico, duo latera reli-quo ſunt maiora, quomodocunque aſſumpta.
Page: 371 (359)
[488.] THEOR. 3. PROPOS. 4.
Page: 372 (360)
[489.] THEOR. 4. PROPOS. 5.
Page: 372 (360)
[490.] COROLLARIVM.
Page: 373 (361)
[491.] THEOR. 5. PROPOS. 6.
Page: 373 (361)
[492.] THEOR. 6. PROPOS. 7.
Page: 373 (361)
[493.] THEOR. 7. PROPOS. 8.
Page: 374 (362)
[494.] COROLLARIVM.
Page: 375 (363)
[495.] THEOR. 8. PROPOS. 9.
Page: 375 (363)
[496.] COROLLARIVM.
Page: 375 (363)
[497.] PROBL. 2. PROPOS. 10.
Page: 376 (364)
[498.] THEOR. 9. PROPOS. 11.
Page: 376 (364)
[499.] THEOR. 10. PROPOS. 12.
Page: 377 (365)
[500.] THEOR. 11. PROPOS. 13.
Page: 379 (367)
< >
page |< < (455) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1293" type="section" level="1" n="601">
          <p>
            <s xml:id="echoid-s16118" xml:space="preserve">
              <pb o="455" file="467" n="467" rhead=""/>
            crũt ſinus arcuum circa reliquum angulum vnius
              <lb/>
            ſinubus arcuum circa reliquum angulum alterius
              <lb/>
            proportionales, homologiq́; </s>
            <s xml:id="echoid-s16119" xml:space="preserve">erunt ſinus arcuum
              <lb/>
            æquales angulos ſubtendentium. </s>
            <s xml:id="echoid-s16120" xml:space="preserve">Et ſi vnus angu-
              <lb/>
            lus vnius vniangulo alterius ſit æqualis, ſinusq́; </s>
            <s xml:id="echoid-s16121" xml:space="preserve">ar-
              <lb/>
            cuum circa alium angulum vnius ſinubus arcuum
              <lb/>
            circa alium angulum alterius proportionales, ita
              <lb/>
            vt ſinus arcuum æquales angulos ſubtendentium
              <lb/>
            ſint homologi: </s>
            <s xml:id="echoid-s16122" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s16123" xml:space="preserve">anguli arcubus reliquo-
              <lb/>
            rum ſinuum homologorum oppoſiti inter ſe æ-
              <lb/>
            quales, vel æquales duobus rectis.</s>
            <s xml:id="echoid-s16124" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16125" xml:space="preserve">SINT in duobus triangulis ſphæricis ABC, DEF, duo anguli inter ſe
              <lb/>
            æquales B, E, necnon duo C, F. </s>
            <s xml:id="echoid-s16126" xml:space="preserve">Dico ita eſſe ſinum arcus AB, ad ſinum arcus
              <lb/>
            AC, vt eſt ſinus arcus DE, ad ſinum arcus DF. </s>
            <s xml:id="echoid-s16127" xml:space="preserve">Quia enim eſt, vt ſinus arcus
              <lb/>
            AB, ad ſinum anguli C, ita ſinus arcus AC, ad ſinum
              <lb/>
              <note position="right" xlink:label="note-467-01" xlink:href="note-467-01a" xml:space="preserve">41. huius.</note>
            anguli B; </s>
            <s xml:id="echoid-s16128" xml:space="preserve">erit permutando, vt ſinus arcus AB, ad ſi-
              <lb/>
              <figure xlink:label="fig-467-01" xlink:href="fig-467-01a" number="335">
                <image file="467-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/467-01"/>
              </figure>
            num arcus AC, ita ſinus anguli C, ad ſinum anguli B,
              <lb/>
            hoc eſt, ita ſinus anguli F, ad ſinum anguli E, cum hi
              <lb/>
            anguli illis ponantur æquales. </s>
            <s xml:id="echoid-s16129" xml:space="preserve">Item quia eſt, vt ſi-
              <lb/>
            nus arcus DE, ad ſinum anguli F, ita ſinus arcus DF,
              <lb/>
              <note position="right" xlink:label="note-467-02" xlink:href="note-467-02a" xml:space="preserve">41. huius.</note>
            ad ſinum anguli E; </s>
            <s xml:id="echoid-s16130" xml:space="preserve">erit permutando, vt ſinus arcus
              <lb/>
            DE, ad ſinum arcus DF, ita ſinus anguli F, ad ſinum
              <lb/>
            anguli E. </s>
            <s xml:id="echoid-s16131" xml:space="preserve">Oſtenſum autem eſt, ita etiam eſſe ſinum
              <lb/>
            arcus AB, ad ſinum arcus AC, vt eſt ſinus anguli F,
              <lb/>
            ad ſinum anguli E. </s>
            <s xml:id="echoid-s16132" xml:space="preserve">Igitur erit, vt ſinus arcus AB, ad
              <lb/>
            ſinum arcus AC, ita ſinus arcus DE, ad ſinum arcus DF. </s>
            <s xml:id="echoid-s16133" xml:space="preserve">Quod eſt propoſitũ.</s>
            <s xml:id="echoid-s16134" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16135" xml:space="preserve">SED ſint iam anguli B, E, æquales, & </s>
            <s xml:id="echoid-s16136" xml:space="preserve">ita ſit ſinus arcus AB, ad ſinus ar-
              <lb/>
            cus AC, vt eſt ſinus arcus DE, ad ſinum arcus DF. </s>
            <s xml:id="echoid-s16137" xml:space="preserve">Dico angulos quoq; </s>
            <s xml:id="echoid-s16138" xml:space="preserve">C,
              <lb/>
            F, æquales eſſe, vel certe duobus rectis æquales. </s>
            <s xml:id="echoid-s16139" xml:space="preserve">Oſtendemus enim, vt prius,
              <lb/>
            ita eſſe ſinum arcus AB, ad ſinum arcus AC, vt eſt ſinus anguli C, ad ſinum
              <lb/>
              <note position="right" xlink:label="note-467-03" xlink:href="note-467-03a" xml:space="preserve">41. huius.
                <lb/>
              Et permu-
                <lb/>
              tando.</note>
            anguli B. </s>
            <s xml:id="echoid-s16140" xml:space="preserve">Item ita eſſe ſinum arcus DE, ad ſinum arcus DF, vt eſt ſinus angu-
              <lb/>
            li F, ad ſinum anguli E. </s>
            <s xml:id="echoid-s16141" xml:space="preserve">Quare cum ponatur, vt ſinus arcus AB, ad ſinum ar-
              <lb/>
            cus AC, ita ſinus arcus DE, ad ſinum arcus DF; </s>
            <s xml:id="echoid-s16142" xml:space="preserve">erit, vt ſinus anguli C, ad ſi-
              <lb/>
            num anguli B, ita ſinus anguli F, ad ſinum anguli E: </s>
            <s xml:id="echoid-s16143" xml:space="preserve">Et conuertendo, vt ſinus
              <lb/>
            anguli B, ad ſinum anguli C, ita ſinus anguli E, ad ſinum anguli F. </s>
            <s xml:id="echoid-s16144" xml:space="preserve">Cum ergo
              <lb/>
            ſinus æqualium angulorum B, E, æquales ſint, erunt & </s>
            <s xml:id="echoid-s16145" xml:space="preserve">ſinus angulorum C,
              <lb/>
              <note position="right" xlink:label="note-467-04" xlink:href="note-467-04a" xml:space="preserve">14. quinti.</note>
            F, æquales; </s>
            <s xml:id="echoid-s16146" xml:space="preserve">ac proinde vel anguli C, F, æquales erunt, vel duobus rectis æqua-
              <lb/>
            les. </s>
            <s xml:id="echoid-s16147" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s16148" xml:space="preserve">Itaque ſi duo triangula ſphærica duos angulos,
              <lb/>
            &</s>
            <s xml:id="echoid-s16149" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16150" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s16151" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum