Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres
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            <s xml:id="echoid-s14057" xml:space="preserve">
              <pb o="407" file="419" n="419" rhead=""/>
            arcus
              <emph style="sc">BC</emph>
            , compoſita ex proportione ſinus arcus
              <emph style="sc">EF</emph>
            , ad ſinum arcus DE, & </s>
            <s xml:id="echoid-s14058" xml:space="preserve">ex
              <lb/>
            proportione ſinus totius quadrantis AD, ad ſinum arcus
              <emph style="sc">AB</emph>
            . </s>
            <s xml:id="echoid-s14059" xml:space="preserve">Eſt autem, (cum CF,
              <lb/>
            ſit complementum arcus
              <emph style="sc">BC</emph>
            .) </s>
            <s xml:id="echoid-s14060" xml:space="preserve">vt ſinus arcus CF, ad ſinum arcus
              <emph style="sc">CB</emph>
            , ita ſinus to-
              <lb/>
              <note position="right" xlink:label="note-419-01" xlink:href="note-419-01a" xml:space="preserve">18. Sinu@.</note>
            tus ad tangentem arcus
              <emph style="sc">BC</emph>
            : </s>
            <s xml:id="echoid-s14061" xml:space="preserve">Item, (cum DE, ſit cowplementum arcus EF.) </s>
            <s xml:id="echoid-s14062" xml:space="preserve">vt ſi-
              <lb/>
            nus arcus DE, ad ſinum arcus EF, ita ſinus totus ad tangentem arcus
              <emph style="sc">EF</emph>
            ; </s>
            <s xml:id="echoid-s14063" xml:space="preserve">& </s>
            <s xml:id="echoid-s14064" xml:space="preserve">con-
              <lb/>
            uertendo, vt ſinus arcus
              <emph style="sc">EF</emph>
            , ad ſinum arcus
              <emph style="sc">De</emph>
            , ita tangens arcus
              <emph style="sc">EF</emph>
            , ad ſinum
              <lb/>
            totum. </s>
            <s xml:id="echoid-s14065" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s14066" xml:space="preserve">proportio ſinus totius ad tangentem arcus
              <emph style="sc">BC</emph>
            , compoſita erit ex
              <lb/>
            proportione tangentis arcus
              <emph style="sc">EF</emph>
            , ad ſinũ totum, & </s>
            <s xml:id="echoid-s14067" xml:space="preserve">ex proportione ſinus totius qua-
              <lb/>
            drantis
              <emph style="sc">A</emph>
            D, ad ſinum arcus
              <emph style="sc">AB</emph>
            . </s>
            <s xml:id="echoid-s14068" xml:space="preserve">Cum ergo proportio tangentis arcus
              <emph style="sc">EF</emph>
            , ad ſi-
              <lb/>
            num arcus
              <emph style="sc">AB</emph>
            , componatur quoque ex proportione tangentis arcus
              <emph style="sc">EF</emph>
            , ad ſinum
              <lb/>
            totum, & </s>
            <s xml:id="echoid-s14069" xml:space="preserve">ex proportione ſinus totius ad ſinum arcus
              <emph style="sc">AB</emph>
            ; </s>
            <s xml:id="echoid-s14070" xml:space="preserve">quòd ſinus totus ſit me-
              <lb/>
            dius inter illam tangentem, & </s>
            <s xml:id="echoid-s14071" xml:space="preserve">hunc ſinum: </s>
            <s xml:id="echoid-s14072" xml:space="preserve">erit, vt ſinus totus ad tangentem arcus
              <lb/>
              <emph style="sc">BC</emph>
            , ita tangens arcus
              <emph style="sc">EF</emph>
            , ad ſinum arcus
              <emph style="sc">AB</emph>
            . </s>
            <s xml:id="echoid-s14073" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s14074" xml:space="preserve"/>
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        <div xml:id="echoid-div1115" type="section" level="1" n="548">
          <head xml:id="echoid-head583" xml:space="preserve">VIII.</head>
          <p>
            <s xml:id="echoid-s14075" xml:space="preserve">SI in ſphæræ ſuperficie duo maximi circuli ad angulos non rectos
              <lb/>
            ſe mutuo ſecent, & </s>
            <s xml:id="echoid-s14076" xml:space="preserve">à duobus punctis in vno aſſumptis ad alterum cir-
              <lb/>
            culum duo arcus perpendiculares ducantur: </s>
            <s xml:id="echoid-s14077" xml:space="preserve">Erit, vt ſinus arcus inter
              <lb/>
            punctum ſectionis, & </s>
            <s xml:id="echoid-s14078" xml:space="preserve">alterutrum punctorum ſumptorum ad ſecan-
              <lb/>
            tem complementi arcus per reliquum punctum aſſumptum ducti, ita
              <lb/>
            ſinus arcus inter punctum ſectionis, & </s>
            <s xml:id="echoid-s14079" xml:space="preserve">reliquum hoc punctum ſum-
              <lb/>
            ptum ad ſecantem complementi arcus per alterum illud punctum aſ-
              <lb/>
            ſumptum ducti.</s>
            <s xml:id="echoid-s14080" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14081" xml:space="preserve">IN proxima figura ſecent ſeſe duo maximi circuli AD, AE, in A, ad angulosno@
              <lb/>
            rectos, & </s>
            <s xml:id="echoid-s14082" xml:space="preserve">ex punctis C, E, ad AD, arcus perpendiculares ducantur CB, ED, pro-
              <lb/>
            ducanturq́;</s>
            <s xml:id="echoid-s14083" xml:space="preserve">, donec coeant in F. </s>
            <s xml:id="echoid-s14084" xml:space="preserve">Erunt BF, DF, quadrantes, ac propterea CF,
              <emph style="sc">EF</emph>
            ,
              <lb/>
              <note position="right" xlink:label="note-419-02" xlink:href="note-419-02a" xml:space="preserve">25. huius.</note>
            complementa arcuum
              <emph style="sc">BC</emph>
            ,
              <emph style="sc">De</emph>
            . </s>
            <s xml:id="echoid-s14085" xml:space="preserve">Dico ita eſſe ſinũ
              <lb/>
            arcus
              <emph style="sc">AE</emph>
            , ad ſecantem arcus CF, vt eſt ſinus ar-
              <lb/>
            cus AC, ad ſecantem arcus
              <emph style="sc">EF</emph>
            . </s>
            <s xml:id="echoid-s14086" xml:space="preserve">Quoniam enim à
              <lb/>
              <figure xlink:label="fig-419-01" xlink:href="fig-419-01a" number="268">
                <image file="419-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/419-01"/>
              </figure>
            puncto D, duo arcus educuntur
              <emph style="sc">Da</emph>
            , DF, à quo-
              <lb/>
            rum terminis
              <emph style="sc">A</emph>
            , F, duo alij ad ipſos reflectuntur
              <lb/>
              <emph style="sc">AE, FB</emph>
            , ſe interſecantes in C; </s>
            <s xml:id="echoid-s14087" xml:space="preserve">erit proportio ſi-
              <lb/>
            nus arcus
              <emph style="sc">AE</emph>
            , ad ſinum arcus
              <emph style="sc">AC</emph>
            , compoſita ex
              <lb/>
              <note position="right" xlink:label="note-419-03" xlink:href="note-419-03a" xml:space="preserve">Theorema
                <lb/>
              5. huius
                <lb/>
              ſcholij.</note>
            proportione ſinus arcus
              <emph style="sc">De</emph>
            , ad ſinum totum qua-
              <lb/>
            drantis DF, & </s>
            <s xml:id="echoid-s14088" xml:space="preserve">ex proportione ſinus totius qua-
              <lb/>
              <note position="right" xlink:label="note-419-04" xlink:href="note-419-04a" xml:space="preserve">18. Sinuũ.</note>
            drantis
              <emph style="sc">BF</emph>
            , ad ſinum arcus
              <emph style="sc">BC</emph>
            . </s>
            <s xml:id="echoid-s14089" xml:space="preserve">Eſt autem, vt
              <lb/>
            ſinus arcus
              <emph style="sc">De</emph>
            , ad ſinum totum quadrantis DF,
              <lb/>
            ita ſinus totus ad ſecantem arcus
              <emph style="sc">EF</emph>
            ; </s>
            <s xml:id="echoid-s14090" xml:space="preserve">propterea
              <lb/>
            quòd ſinus totus medio loco proportionalis eſt in-
              <lb/>
              <note position="right" xlink:label="note-419-05" xlink:href="note-419-05a" xml:space="preserve">18. Sinuú.</note>
            ter ſinum rectum arcus
              <emph style="sc">De</emph>
            , & </s>
            <s xml:id="echoid-s14091" xml:space="preserve">ſecantem arcus
              <emph style="sc">EF</emph>
            , qui complementum eſt arcus
              <emph style="sc">De</emph>
            :
              <lb/>
            </s>
            <s xml:id="echoid-s14092" xml:space="preserve">
              <emph style="sc">E</emph>
            ademq́; </s>
            <s xml:id="echoid-s14093" xml:space="preserve">ratione ita eſt ſecans arcus CF, ad ſinum totum, vt ſinus totus quadrantis
              <lb/>
              <emph style="sc">BF</emph>
            , ad ſinum arcus
              <emph style="sc">BC</emph>
            ; </s>
            <s xml:id="echoid-s14094" xml:space="preserve">quòd ſinus totus medio quoque loco ſit proportionalis inter
              <lb/>
            ſecantem arcus CF, qui complementum eſt arcus
              <emph style="sc">BC</emph>
            , & </s>
            <s xml:id="echoid-s14095" xml:space="preserve">ſinum rectum arcus
              <emph style="sc">BC</emph>
            . </s>
            <s xml:id="echoid-s14096" xml:space="preserve">
              <lb/>
            Igitur proportio ſinus arcus
              <emph style="sc">AE</emph>
            , ad ſinum arcus
              <emph style="sc">AC</emph>
            , componetur quoque ex pro-
              <lb/>
            portione ſecantis arcus CF, ad ſinum totum, & </s>
            <s xml:id="echoid-s14097" xml:space="preserve">exproportione ſinus totius ad </s>
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