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

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          <pb o="403" file="415" n="415" rhead=""/>
        </div>
        <div xml:id="echoid-div1103" type="section" level="1" n="542">
          <head xml:id="echoid-head577" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s13909" xml:space="preserve">IISDEM poſitis, proportio ſinus vnius arcuum eductorum ad
              <lb/>
            ſinum ſegmenti eiuſdem arcus inter punctum eductionis, & </s>
            <s xml:id="echoid-s13910" xml:space="preserve">arcum
              <lb/>
            reflexum, componitur ex proportione ſinus arcus reflexi à termino
              <lb/>
            dictiarcus ad ſinum ſegmenti eiuſdem arcus reflexi inter alterum ar-
              <lb/>
            cum eductum, & </s>
            <s xml:id="echoid-s13911" xml:space="preserve">alterum arcum reflexum, & </s>
            <s xml:id="echoid-s13912" xml:space="preserve">ex proportione ſi-
              <lb/>
            nus ſegmenti alterius arcus reflexi inter terminum alterius arcus
              <lb/>
            educti, & </s>
            <s xml:id="echoid-s13913" xml:space="preserve">priorem arcum reflexum ad ſinum totius poſterioris ar-
              <lb/>
            cus reflexi.</s>
            <s xml:id="echoid-s13914" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13915" xml:space="preserve">HOC eſt, proportio ſinus arcus AB, ad ſinum arcus AE, componitur ex pr@-
              <lb/>
            portione ſinus arcus BD, ad ſinum arcus DF, & </s>
            <s xml:id="echoid-s13916" xml:space="preserve">ex proportione ſinus arcus CF, ad
              <lb/>
            ſinum arcus
              <emph style="sc">Ce</emph>
            . </s>
            <s xml:id="echoid-s13917" xml:space="preserve">Ductis enim ex punctis B, E,
              <emph style="sc">F</emph>
            , ad planum circuli AC, tribus per-
              <lb/>
            pendicularibus BG, EH, FI; </s>
            <s xml:id="echoid-s13918" xml:space="preserve">quoniam duo circuli
              <lb/>
              <figure xlink:label="fig-415-01" xlink:href="fig-415-01a" number="263">
                <image file="415-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/415-01"/>
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            AB, AC, ſe mutuo ſecant in
              <emph style="sc">A</emph>
            , & </s>
            <s xml:id="echoid-s13919" xml:space="preserve">ex punctis
              <emph style="sc">B</emph>
            ,
              <lb/>
            E, in planum circuli AC, demiſſæ ſunt perpendicu-
              <lb/>
            lares
              <emph style="sc">BG</emph>
            , EH; </s>
            <s xml:id="echoid-s13920" xml:space="preserve">erit, vt ſinus arcus
              <emph style="sc">AB</emph>
            , ad ſinum
              <lb/>
              <note position="right" xlink:label="note-415-01" xlink:href="note-415-01a" xml:space="preserve">Schol. 40.
                <lb/>
              huius. &
                <lb/>
              permutan-
                <lb/>
              do.</note>
            arcus AE, ita recta
              <emph style="sc">BG</emph>
            , ad rectam EH: </s>
            <s xml:id="echoid-s13921" xml:space="preserve">Item quiæ
              <lb/>
            duo circuli
              <emph style="sc">B</emph>
            D, AC, ſe interſecant in D, & </s>
            <s xml:id="echoid-s13922" xml:space="preserve">ex
              <lb/>
            punctis
              <emph style="sc">B, F,</emph>
            in planũ circuli AC, deductæ ſunt per-
              <lb/>
            pendiculares
              <emph style="sc">BG</emph>
            , FI; </s>
            <s xml:id="echoid-s13923" xml:space="preserve">erit pari ratione, vt ſinus
              <lb/>
            arcus
              <emph style="sc">Db</emph>
            , ad ſinum arcus
              <emph style="sc">Df</emph>
            , ita recta
              <emph style="sc">B</emph>
            G, ad re-
              <lb/>
            ctam
              <emph style="sc">FI</emph>
            : </s>
            <s xml:id="echoid-s13924" xml:space="preserve">Denique quoniam duo circuli AC, CE, ſe in C, interſecant, & </s>
            <s xml:id="echoid-s13925" xml:space="preserve">ex pun-
              <lb/>
            ctis F, E, in planum circuli AC, demiſſæ ſunt perpendiculares
              <emph style="sc">F</emph>
            I, EH; </s>
            <s xml:id="echoid-s13926" xml:space="preserve">erit eadem
              <lb/>
            argumentatione, vt ſinus arcus CF, ad ſinum arcus CE, ita recta FI, ad rectam
              <lb/>
            EH. </s>
            <s xml:id="echoid-s13927" xml:space="preserve">Componitur autem proportio rectæ
              <emph style="sc">BG</emph>
            , ad rectam EH, (poſita media lineæ
              <lb/>
              <emph style="sc">F</emph>
            I.) </s>
            <s xml:id="echoid-s13928" xml:space="preserve">ex proportione rectæ
              <emph style="sc">BG</emph>
            , ad rectam FI, & </s>
            <s xml:id="echoid-s13929" xml:space="preserve">exproportione rectæ FI, ad rectam
              <lb/>
            EH. </s>
            <s xml:id="echoid-s13930" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s13931" xml:space="preserve">proportio ſinus arcus
              <emph style="sc">Ab</emph>
            , ad ſinum arcus AE, (quæ eadem eſt, quæ
              <lb/>
              <emph style="sc">BG</emph>
            , ad EH.) </s>
            <s xml:id="echoid-s13932" xml:space="preserve">componetur ex proportione ſinus arcus BD, ad ſinum arcus DF, (quæ
              <lb/>
            @adem eſt, quæ BG, ad FI,) & </s>
            <s xml:id="echoid-s13933" xml:space="preserve">ex proportione ſinus arcus CF, ad ſinum arcus CE,
              <lb/>
            (quæ cadem eſt, quæ FI, ad EH.) </s>
            <s xml:id="echoid-s13934" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s13935" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1105" type="section" level="1" n="543">
          <head xml:id="echoid-head578" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s13936" xml:space="preserve">IISDEM poſitis, proportio ſinus vnius arcuum eductorum ad
              <lb/>
            ſinum ſegmenti eiuſdem arcus inter eius terminum, & </s>
            <s xml:id="echoid-s13937" xml:space="preserve">arcum refle-
              <lb/>
            xum, componitur ex proportione ſinus ſegmenti alterius arcus edu-
              <lb/>
            cti inter punctum eductionis, & </s>
            <s xml:id="echoid-s13938" xml:space="preserve">arcum reflexum ad ſinum reliqui
              <lb/>
            ſegmenti, & </s>
            <s xml:id="echoid-s13939" xml:space="preserve">ex proportione ſinus ſegmenti arcus reflexi à termino
              <lb/>
            poſterioris arcus educti inter terminum, & </s>
            <s xml:id="echoid-s13940" xml:space="preserve">alterum arcum reflexum
              <lb/>
            ad ſinum reliqui ſegmenti eiuſdem arcus reflexi.</s>
            <s xml:id="echoid-s13941" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13942" xml:space="preserve">HOC eſt, (repetita figura primi theorematis) proportio ſinus arcus AC, ad ſi-
              <lb/>
            num arcus CD, componitur exproportione ſinus arcus AE, ad ſinum arcus
              <emph style="sc">Eb</emph>
            , &</s>
            <s xml:id="echoid-s13943" xml:space="preserve"/>
          </p>
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