Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres
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            æqualis; </s>
            <s xml:id="echoid-s15941" xml:space="preserve">proptereaq́; </s>
            <s xml:id="echoid-s15942" xml:space="preserve">in triangulis rectangulis SkT, XAV, reliqui anguli
              <lb/>
              <emph style="sc">Sk</emph>
            T, XAV, æquales erunt.</s>
            <s xml:id="echoid-s15943" xml:space="preserve"/>
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            <s xml:id="echoid-s15944" xml:space="preserve">8. </s>
            <s xml:id="echoid-s15945" xml:space="preserve">SIT adhuc AC, quadrante maior, & </s>
            <s xml:id="echoid-s15946" xml:space="preserve">AB, minor quadrante, ſed BC,
              <lb/>
              <note position="left" xlink:label="note-462-01" xlink:href="note-462-01a" xml:space="preserve">3. caſus.</note>
            quadrans. </s>
            <s xml:id="echoid-s15947" xml:space="preserve">Completo circulo ABDGH, & </s>
            <s xml:id="echoid-s15948" xml:space="preserve">abſciſſo quadrante AL, ex AC,
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            deſcribantur ex polis A, B, ad in-
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            terualla quadrantum AL, BC,
              <lb/>
              <figure xlink:label="fig-462-01" xlink:href="fig-462-01a" number="325">
                <image file="462-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/462-01"/>
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            maximi circuli DEF,
              <emph style="sc">GEh</emph>
            :
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            </s>
            <s xml:id="echoid-s15949" xml:space="preserve">Item ex polo A, ad interuallum
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            AC, circulus nõ maximus
              <emph style="sc">K</emph>
            CN,
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            & </s>
            <s xml:id="echoid-s15950" xml:space="preserve">alia fiãt, vt in primo caſu. </s>
            <s xml:id="echoid-s15951" xml:space="preserve">De-
              <lb/>
            monſtrabitur, vt ibi, ita eſſe qua-
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            dratum ſinus totius, nimirum re
              <lb/>
            ctãgulum ſub DX, XA, ad re-
              <lb/>
            ctangulum ſub AV,
              <emph style="sc">K</emph>
            Y, ſinubus
              <lb/>
            rectis arcuum AB, AC, vt eſt
              <lb/>
            DZ, ſinus verſus arcus DL, ſiue anguli A, ad
              <emph style="sc">K</emph>
            T, differentiam ſinuum verſo-
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            rum BR, BQ, arcuum BC, BK: </s>
            <s xml:id="echoid-s15952" xml:space="preserve">ſi tamen triangula XAV,
              <emph style="sc">Sk</emph>
            T, oſtenda-
              <lb/>
            mus æquiangula eſſe, vtin ſeptimo caſu.</s>
            <s xml:id="echoid-s15953" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15954" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15955" xml:space="preserve">SIT rurſus AC, maior quadrante, & </s>
            <s xml:id="echoid-s15956" xml:space="preserve">AB, quadrante minor, ſed BC,
              <lb/>
              <note position="left" xlink:label="note-462-02" xlink:href="note-462-02a" xml:space="preserve">5. caſus.</note>
            maior etiam quadrante. </s>
            <s xml:id="echoid-s15957" xml:space="preserve">Completo circulo ABDGH, & </s>
            <s xml:id="echoid-s15958" xml:space="preserve">abſciſsis quadran-
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            tibus AL, BM, ex AC, BC, reliqua conſtruantur, vt in primo caſu. </s>
            <s xml:id="echoid-s15959" xml:space="preserve">Nam,
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            vtibi, ita hic demonſtrabitur, ita
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            eſſe quadratum ſinus totius, re-
              <lb/>
              <figure xlink:label="fig-462-02" xlink:href="fig-462-02a" number="326">
                <image file="462-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/462-02"/>
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            ctangulum videlicet ſub DX,
              <lb/>
            XA, ad rectangulum ſub AV,
              <lb/>
              <emph style="sc">K</emph>
            Y, ſinubus rectis arcuum AB,
              <lb/>
            AC, vt eſt DZ, ſinus verſus ar-
              <lb/>
            cus DL, ſiue anguli A, ad
              <emph style="sc">K</emph>
            T,
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            differentiam ſinuum verſorum
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            BR, BQ arcuum BC,
              <emph style="sc">Bk</emph>
            . </s>
            <s xml:id="echoid-s15960" xml:space="preserve">Sed
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            triangula XAV,
              <emph style="sc">Sk</emph>
            T, eſſe æ-
              <lb/>
            quiangula, ita confirmabitur.
              <lb/>
            </s>
            <s xml:id="echoid-s15961" xml:space="preserve">Angulus
              <emph style="sc">K</emph>
            ST, angulo ISR, æqualis eſt. </s>
            <s xml:id="echoid-s15962" xml:space="preserve">Igitur in rectangulis triangulis SKT,
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              <note position="left" xlink:label="note-462-03" xlink:href="note-462-03a" xml:space="preserve">15. primi.</note>
            SIR, & </s>
            <s xml:id="echoid-s15963" xml:space="preserve">reliqui anguli
              <emph style="sc">Sk</emph>
            T, SIR, æquales erunt; </s>
            <s xml:id="echoid-s15964" xml:space="preserve">ac proinde in triangulis
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            rectangulis
              <emph style="sc">Sk</emph>
            T, IXY, reliqui quoque anguli
              <emph style="sc">K</emph>
            ST, IXY, hoc eſt, AXV,
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            (cum hic ipſi IXY, ſit æqualis) inter ſe æquales erunt. </s>
            <s xml:id="echoid-s15965" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s15966" xml:space="preserve">reliqui angu-
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              <note position="left" xlink:label="note-462-04" xlink:href="note-462-04a" xml:space="preserve">15. primi.</note>
            li
              <emph style="sc">Sk</emph>
            T, XAV, in triangulis rectangulis
              <emph style="sc">Sk</emph>
            T, XAV, erunt æquales.</s>
            <s xml:id="echoid-s15967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15968" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15969" xml:space="preserve">SIT arcus AC, maior
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              <figure xlink:label="fig-462-03" xlink:href="fig-462-03a" number="327">
                <image file="462-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/462-03"/>
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              <note position="left" xlink:label="note-462-05" xlink:href="note-462-05a" xml:space="preserve">10. caſus.</note>
            quadrante, & </s>
            <s xml:id="echoid-s15970" xml:space="preserve">AB, quadrans, at
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            BC, quadrante minor. </s>
            <s xml:id="echoid-s15971" xml:space="preserve">Comple-
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            to circulo ABGF, abſciſſoq́ue
              <lb/>
            quadrante AL, ex AC, & </s>
            <s xml:id="echoid-s15972" xml:space="preserve">pro-
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            ducto BC, vt fiat quadrans BM,
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            deſcribãtur ex polis A, B, ad in-
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            terualla quadrantum AL, BM,
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            circuli maximi BLEF, AEMG,
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            incedetq́; </s>
            <s xml:id="echoid-s15973" xml:space="preserve">ille per punctum B, & </s>
            <s xml:id="echoid-s15974" xml:space="preserve">hic per punctum A, ob quadrantem AB; </s>
            <s xml:id="echoid-s15975" xml:space="preserve">pro-
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              <note position="left" xlink:label="note-462-06" xlink:href="note-462-06a" xml:space="preserve">Coroll. 16.</note>
            pterea quòd maximus circulus à polo abeſt quadrante maximi circuli. </s>
            <s xml:id="echoid-s15976" xml:space="preserve">Item
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              <note position="left" xlink:label="note-462-07" xlink:href="note-462-07a" xml:space="preserve">1. Theod.</note>
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