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

Table of contents

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[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)
[501.] THEOR 12. PROPOS. 14.
Page: 379 (367)
[502.] THEOR. 13. PROPOS. 15.
Page: 380 (368)
[503.] THEOR. 14. PROP. 16.
Page: 381 (369)
[504.] THEOR. 15. PROP. 17.
Page: 381 (369)
[505.] THEOR. 16. PROP. 18.
Page: 382 (370)
[506.] THEOR. 17. PROPOS. 19.
Page: 382 (370)
[507.] THEOR. 18. PROPOS. 20.
Page: 384 (372)
[508.] THEOR. 19. PROPOS. 21.
Page: 384 (372)
[509.] SCHOLIVM
Page: 385 (373)
[510.] THEOR. 20. PROPOS. 22.
Page: 386 (374)
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            <s xml:id="echoid-s17128" xml:space="preserve">
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            datus arcus AB, non quadrans. </s>
            <s xml:id="echoid-s17129" xml:space="preserve">Ducatur ex angulo A, ad arcum BC, datis
              <lb/>
            angulis adiacentẽ arcus perpendicularis AD:
              <lb/>
            </s>
            <s xml:id="echoid-s17130" xml:space="preserve">
              <note position="left" xlink:label="note-488-01" xlink:href="note-488-01a" xml:space="preserve">57. huius.</note>
            qui intra triangulum cadet, ſi vterque angu-
              <lb/>
              <figure xlink:label="fig-488-01" xlink:href="fig-488-01a" number="351">
                <image file="488-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/488-01"/>
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            lorum B, C, datorum fuerit acutus, vel obtu-
              <lb/>
            ſus; </s>
            <s xml:id="echoid-s17131" xml:space="preserve">extra vero, ſi vnus fuerit acutus, & </s>
            <s xml:id="echoid-s17132" xml:space="preserve">obtu
              <lb/>
            ſus alter. </s>
            <s xml:id="echoid-s17133" xml:space="preserve">Quia ergo in triangulo ABD, re-
              <lb/>
            ctum habẽte angulum D, datus eſt arcus AB,
              <lb/>
            angulo recto oppoſitus, cum angulo non re-
              <lb/>
            cto B; </s>
            <s xml:id="echoid-s17134" xml:space="preserve">notus fiet arcus AD, circa angulum
              <lb/>
              <note position="left" xlink:label="note-488-02" xlink:href="note-488-02a" xml:space="preserve">Schol. 41.
                <lb/>
              huius.</note>
            rectum dato angulo B, oppoſitus. </s>
            <s xml:id="echoid-s17135" xml:space="preserve">Hinc in
              <lb/>
            eodem triangulo ABD, quoniam datus eſt
              <lb/>
              <note position="left" xlink:label="note-488-03" xlink:href="note-488-03a" xml:space="preserve">Schol. 43.
                <lb/>
              vel 53. huiꝰ.</note>
            arcus AB, recto angulo oppoſitus, cum arcu
              <lb/>
            AD, circa angulum rectum:
              <lb/>
            </s>
            <s xml:id="echoid-s17136" xml:space="preserve">VEL, quia datus eſt arcus AB, angulo recto op-
              <lb/>
              <note position="left" xlink:label="note-488-04" xlink:href="note-488-04a" xml:space="preserve">Schol. 45.
                <lb/>
              huius.</note>
            poſitus, & </s>
            <s xml:id="echoid-s17137" xml:space="preserve">præterea angulus B, non rectus:
              <lb/>
            </s>
            <s xml:id="echoid-s17138" xml:space="preserve">VEL denique, quoniam datus eſt arcus AD, circa
              <lb/>
              <note position="left" xlink:label="note-488-05" xlink:href="note-488-05a" xml:space="preserve">Schol. 49.
                <lb/>
              vel 44. huiꝰ.</note>
            rectum angulum, cum angulo B, non recto ei oppoſito;
              <lb/>
            </s>
            <s xml:id="echoid-s17139" xml:space="preserve">conſtatq́; </s>
            <s xml:id="echoid-s17140" xml:space="preserve">præterea ſpecies arcus BD. </s>
            <s xml:id="echoid-s17141" xml:space="preserve">Nam ſi AB, da-
              <lb/>
            tus fuerit minor quadrante; </s>
            <s xml:id="echoid-s17142" xml:space="preserve">ſi quidem & </s>
            <s xml:id="echoid-s17143" xml:space="preserve">AD, inuentus
              <lb/>
            ſit minor, erit quoque BD, minor; </s>
            <s xml:id="echoid-s17144" xml:space="preserve">ſi autem maior, ma-
              <lb/>
              <note position="left" xlink:label="note-488-06" xlink:href="note-488-06a" xml:space="preserve">36. huius.</note>
            ior. </s>
            <s xml:id="echoid-s17145" xml:space="preserve">Si vero AB, datus fuerit quadrante maior; </s>
            <s xml:id="echoid-s17146" xml:space="preserve">ſi qui-
              <lb/>
            dem & </s>
            <s xml:id="echoid-s17147" xml:space="preserve">AD, inuentus ſit maior, erit BD, minor; </s>
            <s xml:id="echoid-s17148" xml:space="preserve">ſi ve-
              <lb/>
            ro AD, ſit minor, erit BD, maior;
              <lb/>
            </s>
            <s xml:id="echoid-s17149" xml:space="preserve">reperietur quoque, ex ſcholijs in margine citatis, alter arcus BD, circa an-
              <lb/>
            gulum rectum. </s>
            <s xml:id="echoid-s17150" xml:space="preserve">Hinc rurſus in eodem triangulo ABD, quoniam datus eſt ar-
              <lb/>
              <note position="left" xlink:label="note-488-07" xlink:href="note-488-07a" xml:space="preserve">Schol. 41.
                <lb/>
              vel 55. huiꝰ.</note>
            cus AB, recto angulo oppoſitus, & </s>
            <s xml:id="echoid-s17151" xml:space="preserve">præterea arcus BD, circa angulũ rectum:
              <lb/>
            </s>
            <s xml:id="echoid-s17152" xml:space="preserve">AVT, quia datus eſt vterque arcus AD, BD, cir-
              <lb/>
              <note position="left" xlink:label="note-488-08" xlink:href="note-488-08a" xml:space="preserve">Schol. 44.
                <lb/>
              vel 48. huiꝰ.</note>
            ca angulum rectum:
              <lb/>
            </s>
            <s xml:id="echoid-s17153" xml:space="preserve">VEL, quia datus eſt arcus AB, recto angulo oppo
              <lb/>
              <note position="left" xlink:label="note-488-09" xlink:href="note-488-09a" xml:space="preserve">Schol. 45.
                <lb/>
              vel 51. huiꝰ.</note>
            ſitus, cum arcu AD, circa angulum rectum:
              <lb/>
            </s>
            <s xml:id="echoid-s17154" xml:space="preserve">VEL, quia datus eſt arcus AD, circa rectum angu-
              <lb/>
              <note position="left" xlink:label="note-488-10" xlink:href="note-488-10a" xml:space="preserve">Schol. 56.
                <lb/>
              vel 42. huiꝰ.</note>
            lum, & </s>
            <s xml:id="echoid-s17155" xml:space="preserve">inſuper angulus non rectus B, ei oppoſitus; </s>
            <s xml:id="echoid-s17156" xml:space="preserve">con
              <lb/>
            ſtatq́; </s>
            <s xml:id="echoid-s17157" xml:space="preserve">præterea ſpecies anguli BAD. </s>
            <s xml:id="echoid-s17158" xml:space="preserve">Nam ſi BD, arcus
              <lb/>
            inuentus ſit quadrante maior, erit angulus BAD, ob-
              <lb/>
              <note position="left" xlink:label="note-488-11" xlink:href="note-488-11a" xml:space="preserve">34. huius.</note>
            tuſus; </s>
            <s xml:id="echoid-s17159" xml:space="preserve">ſi vero minor, acutus.
              <lb/>
            </s>
            <s xml:id="echoid-s17160" xml:space="preserve">VEL denique, quia datus eſt arcus AD, angulo
              <lb/>
              <note position="left" xlink:label="note-488-12" xlink:href="note-488-12a" xml:space="preserve">Schol. 47.
                <lb/>
              huius.</note>
            recto oppoſitus, cum angulo non recto B;
              <lb/>
            </s>
            <s xml:id="echoid-s17161" xml:space="preserve">notus fiet quoq; </s>
            <s xml:id="echoid-s17162" xml:space="preserve">angulus non rectus BAD, ex ſcholijs in margine appoſitis.</s>
            <s xml:id="echoid-s17163" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17164" xml:space="preserve">DEINDE in triangulo ACD, rectum habente angulum D, quoniam
              <lb/>
            datus eſt arcus AD, circa rectum angulum, cum angulo C, oppoſito; </s>
            <s xml:id="echoid-s17165" xml:space="preserve">(Nam
              <lb/>
            quando perpendicularis arcus AD, extra triangulum cadit, dabitur angulus
              <lb/>
            ACD, ſi datus angulus ACB, ex duobus rectis ſubducatur.) </s>
            <s xml:id="echoid-s17166" xml:space="preserve">poniturq; </s>
            <s xml:id="echoid-s17167" xml:space="preserve">præ-
              <lb/>
            terea conſtare ſpecies arcus AC, qui in propoſito triangulo ABC, alteri da-
              <lb/>
            to angulo B, opponitur, in hoc vero triangulo ACD, recto angulo D, op-
              <lb/>
            poſitus eſt; </s>
            <s xml:id="echoid-s17168" xml:space="preserve">notus quoque euadet arcus AC; </s>
            <s xml:id="echoid-s17169" xml:space="preserve">qui vnus eſt reliquorum arcuum,
              <lb/>
              <note position="left" xlink:label="note-488-13" xlink:href="note-488-13a" xml:space="preserve">Schol. 41.
                <lb/>
              vel 54. huiꝰ.</note>
            qui inueſtigandi proponuntur in triangulo ABC. </s>
            <s xml:id="echoid-s17170" xml:space="preserve">Hinc quia in eodem trian
              <lb/>
            gulo ACD, datus eſt arcus AC, recto angulo oppoſitus, & </s>
            <s xml:id="echoid-s17171" xml:space="preserve">arcus AD, circa
              <lb/>
              <note position="left" xlink:label="note-488-14" xlink:href="note-488-14a" xml:space="preserve">Schol. 43.
                <lb/>
              vel 53. huiꝰ.</note>
            rectum angulum:</s>
            <s xml:id="echoid-s17172" xml:space="preserve"/>
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