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

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            <s xml:id="echoid-s13943" xml:space="preserve">
              <pb o="404" file="416" n="416" rhead=""/>
            ex proportione ſinus arcus
              <emph style="sc">BF</emph>
            , ad ſinum arcus FD. </s>
            <s xml:id="echoid-s13944" xml:space="preserve">Quoniam enim duo circuli AC,
              <lb/>
              <emph style="sc">Ce</emph>
            , ſe interſecant in C, & </s>
            <s xml:id="echoid-s13945" xml:space="preserve">ex punctis A, D, demißæ ſunt perpendiculares AH, DI,
              <lb/>
            ad planum circuli CE; </s>
            <s xml:id="echoid-s13946" xml:space="preserve">erit, vt ſinus arcus CA, ad ſinum arcus CD, ita recta AH,
              <lb/>
              <note position="left" xlink:label="note-416-01" xlink:href="note-416-01a" xml:space="preserve">Schol. 40.
                <lb/>
              huius. &
                <lb/>
              permutan-
                <lb/>
              do.</note>
            ad rectam DI: </s>
            <s xml:id="echoid-s13947" xml:space="preserve">Item quoniam duo circuli
              <emph style="sc">Ab</emph>
            , CE, ſe mutuo
              <lb/>
            ſecant in E, & </s>
            <s xml:id="echoid-s13948" xml:space="preserve">expunctis
              <emph style="sc">A, B</emph>
            , in planum circuli CE, dedu-
              <lb/>
              <figure xlink:label="fig-416-01" xlink:href="fig-416-01a" number="264">
                <image file="416-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/416-01"/>
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            ctæ ſunt perpendiculares AH, BG; </s>
            <s xml:id="echoid-s13949" xml:space="preserve">erit ſimili modo, vt ſinus
              <lb/>
            arcus EA, ad ſinum arcus
              <emph style="sc">Eb</emph>
            , ita recta AH, ad rectam
              <emph style="sc">BG</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s13950" xml:space="preserve">Denique quia duo circuli BD, CE, ſe mutuo ſecant in F, & </s>
            <s xml:id="echoid-s13951" xml:space="preserve">
              <lb/>
            ex punctis
              <emph style="sc">B</emph>
            , D, ad planum circuli CE, ductæ ſunt perpendi-
              <lb/>
            culares
              <emph style="sc">BG</emph>
            , DI; </s>
            <s xml:id="echoid-s13952" xml:space="preserve">erit eadem ratione, vt ſinus arcus
              <emph style="sc">FB</emph>
            , ad ſi-
              <lb/>
            num arcus FD, ita recta
              <emph style="sc">BG</emph>
            , ad rectam DI. </s>
            <s xml:id="echoid-s13953" xml:space="preserve">Componitur au-
              <lb/>
            tem proportio rectæ AH, ad rectam DI, (poſita media lineæ
              <lb/>
              <emph style="sc">BG</emph>
            ) ex proportione rectæ AH, ad rectam
              <emph style="sc">BG</emph>
            , & </s>
            <s xml:id="echoid-s13954" xml:space="preserve">ex propor
              <lb/>
            tione rectæ
              <emph style="sc">BG</emph>
            , ad rectam DI. </s>
            <s xml:id="echoid-s13955" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s13956" xml:space="preserve">proportio ſinus ar-
              <lb/>
            cus AC, ad ſinum arcus CD, (quæ eadem eſt, quæ AH, ad
              <lb/>
            DI.) </s>
            <s xml:id="echoid-s13957" xml:space="preserve">componetur ex proportione ſinus arcus AE, ad ſinum ar-
              <lb/>
            cus
              <emph style="sc">EB</emph>
            , (quæ eadem eſt, quæ AH, ad
              <emph style="sc">BG</emph>
            .) </s>
            <s xml:id="echoid-s13958" xml:space="preserve">& </s>
            <s xml:id="echoid-s13959" xml:space="preserve">ex proportione ſinus arcus
              <emph style="sc">BF</emph>
            , ad
              <lb/>
            ſinum arcus FD, (quæ eadem eſt, quæ
              <emph style="sc">BG</emph>
            , ad DI.) </s>
            <s xml:id="echoid-s13960" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s13961" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1107" type="section" level="1" n="544">
          <head xml:id="echoid-head579" xml:space="preserve">IIII.</head>
          <p>
            <s xml:id="echoid-s13962" xml:space="preserve">IISDEM poſitis, proportio ſinus ſegmenti vnius arcuum re-
              <lb/>
            flexorum inter terminum arcus educti, & </s>
            <s xml:id="echoid-s13963" xml:space="preserve">alterum arcum reflexum
              <lb/>
            ad ſinum reliqui ſegmenti, componitur ex proportione ſinus ſegmen
              <lb/>
            ti vnius arcuum eductorum inter eundem terminum, & </s>
            <s xml:id="echoid-s13964" xml:space="preserve">alterum ar-
              <lb/>
            cum reflexum ad ſinum reliqui ſegmenti, & </s>
            <s xml:id="echoid-s13965" xml:space="preserve">ex proportione ſinus al-
              <lb/>
            terius arcus educti ad ſinum ſegmenti illius inter terminum, & </s>
            <s xml:id="echoid-s13966" xml:space="preserve">ar-
              <lb/>
            cum reflexum.</s>
            <s xml:id="echoid-s13967" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s13968" xml:space="preserve">HOC eſt, (repetita eadem figura primi theorematis) proportio ſinus arcus BF,
              <lb/>
            ad ſinum arcus FD, componitur ex proportione ſinus arcus
              <emph style="sc">B</emph>
            E, ad ſinum arcus EA,
              <lb/>
            & </s>
            <s xml:id="echoid-s13969" xml:space="preserve">ex proportione ſinus arcus AC, ad ſinum arcus CD. </s>
            <s xml:id="echoid-s13970" xml:space="preserve">Cum enim duo circuli BD,
              <lb/>
            CE, ſe mutuo ſecent in F, & </s>
            <s xml:id="echoid-s13971" xml:space="preserve">ex BD, ad planum circuli CE, perpendiculares BG,
              <lb/>
            DI, ſint demiſſæ; </s>
            <s xml:id="echoid-s13972" xml:space="preserve">erit, vt ſinus arcus FB, ad ſinum arcus FD, ita recta BG, ad re-
              <lb/>
              <note position="left" xlink:label="note-416-02" xlink:href="note-416-02a" xml:space="preserve">Schol. 40.
                <lb/>
              huius. &
                <lb/>
              permutan.
                <lb/>
              do.</note>
            ctam DI: </s>
            <s xml:id="echoid-s13973" xml:space="preserve">Quia item duo circuli BA, CE, ſe mutuo ſecantin E, & </s>
            <s xml:id="echoid-s13974" xml:space="preserve">ex punctis B, A,
              <lb/>
            ad circulum CE, perpendiculares ductæ ſunt BG, AH; </s>
            <s xml:id="echoid-s13975" xml:space="preserve">erit quoque, vt ſinus arcus
              <lb/>
            EB, ad ſinum arcus
              <emph style="sc">E</emph>
            A, ita recta BG, ad rectam AH: </s>
            <s xml:id="echoid-s13976" xml:space="preserve">Denique quia duo circuli
              <lb/>
            AC, CE, ſeſe in C, ſecant, & </s>
            <s xml:id="echoid-s13977" xml:space="preserve">ex punctis A, D, ad planum circuli CE, demiſſæ
              <lb/>
            ſunt perpendiculares AH, DI; </s>
            <s xml:id="echoid-s13978" xml:space="preserve">erit ſimiliter, vt ſinus arcus CA, ad ſinum arcus
              <lb/>
            CD, ita recta AH, ad rectam DI. </s>
            <s xml:id="echoid-s13979" xml:space="preserve">Proportio autem rectæ BG, ad rectam DI,
              <lb/>
            (poſita media linea AH) componitur exproportione rectæ BG, ad rectam AH, & </s>
            <s xml:id="echoid-s13980" xml:space="preserve">
              <lb/>
            ex proportione rectæ AH, ad rectam DI. </s>
            <s xml:id="echoid-s13981" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s13982" xml:space="preserve">proportio ſinus arcus BF, ad
              <lb/>
            ſinum arcus FD, (quæ eadem eſt, quæ BG, ad DI.) </s>
            <s xml:id="echoid-s13983" xml:space="preserve">componetur ex proportione ſi-
              <lb/>
            nus arcus BE, ad ſinum arcus EA, (quæ eadem eſt, quæ BG, ad AH.) </s>
            <s xml:id="echoid-s13984" xml:space="preserve">& </s>
            <s xml:id="echoid-s13985" xml:space="preserve">ex pro-
              <lb/>
            portione ſinus arcus AC, ad ſinum arcus CD, (quæ eadem eſt, quæ AH, ad DI.)
              <lb/>
            </s>
            <s xml:id="echoid-s13986" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s13987" xml:space="preserve"/>
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