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

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          <head xml:id="echoid-head285" xml:space="preserve">THEOR. 10. PROPOS. 18.</head>
          <p>
            <s xml:id="echoid-s7749" xml:space="preserve">QVAM proportionem habet ſinus comple
              <lb/>
              <note position="right" xlink:label="note-203-01" xlink:href="note-203-01a" xml:space="preserve">Quam pro
                <lb/>
              portionem
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              habeat ſinꝰ
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              totus ad :5
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              genté, & ſe
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              cantem cu-
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              iuſuis arcꝰ.</note>
            menti arcus cuiuſuis ad ſinum rectum eiuſdem ar
              <lb/>
            cus, eam habet ſinus totus ad tangentem eiuſdem
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            arcus: </s>
            <s xml:id="echoid-s7750" xml:space="preserve">Item quam proportionem habet ſinus re-
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            ctus cuiuſlibet arcus ad ſinum complementi eiuſ-
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            dem arcus, eam habet ſinus totus ad tangentem
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            eiuſdem complementi. </s>
            <s xml:id="echoid-s7751" xml:space="preserve">Sinus autem totus medio
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            loco proportionalis eſt inter ſinum complementi
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            cuiuſuis arcus, & </s>
            <s xml:id="echoid-s7752" xml:space="preserve">ſecantem eiuſdem aicus: </s>
            <s xml:id="echoid-s7753" xml:space="preserve">Item
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            inter ſinum rectum cuiuſlibet arcus, & </s>
            <s xml:id="echoid-s7754" xml:space="preserve">ſecantem
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            complementi eiuſdem arcus. </s>
            <s xml:id="echoid-s7755" xml:space="preserve">Sinus denique idem
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            totus medius proportionalis eſt inter tangentem
              <lb/>
            arcus cuiuſuis, & </s>
            <s xml:id="echoid-s7756" xml:space="preserve">tangentem complementi eiuſ-
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            dem arcus.</s>
            <s xml:id="echoid-s7757" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7758" xml:space="preserve">IN quadrante ABC, ſit DF, ſinus arcus CD; </s>
            <s xml:id="echoid-s7759" xml:space="preserve">& </s>
            <s xml:id="echoid-s7760" xml:space="preserve">CE, eiuſdem tangens
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            inter ſemidiametrum AC, & </s>
            <s xml:id="echoid-s7761" xml:space="preserve">ſecantem AE: </s>
            <s xml:id="echoid-s7762" xml:space="preserve">Item BG, tangens arcus BD, qui
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            complementum eſt arcus CD. </s>
            <s xml:id="echoid-s7763" xml:space="preserve">Dico ita eſſe ſinum complementi arcus CD, ad
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            ſinum rectum eiuſdé arcus, vt eſt ſinus totus AC,
              <lb/>
              <figure xlink:label="fig-203-01" xlink:href="fig-203-01a" number="150">
                <image file="203-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/203-01"/>
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            ad tangentem CE, &</s>
            <s xml:id="echoid-s7764" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7765" xml:space="preserve">Quoniam enim, vt in ex-
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            poſitione definitionum dictum eſt, AF, æqualis
              <lb/>
            eſt ſinui complementi arcus CD, cum ſit æqualis
              <lb/>
            ſinui recto arcus BD, qui complementum eſt arcus
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            CD; </s>
            <s xml:id="echoid-s7766" xml:space="preserve">ſuntq́; </s>
            <s xml:id="echoid-s7767" xml:space="preserve">triangula AFD, ACE, æquiangula,
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            ob rectos angulos F, C, & </s>
            <s xml:id="echoid-s7768" xml:space="preserve">communem angulum
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            A: </s>
            <s xml:id="echoid-s7769" xml:space="preserve">erit vt AF, ſinus complementi arcus CD, ad
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              <note position="right" xlink:label="note-203-02" xlink:href="note-203-02a" xml:space="preserve">4. ſexti.</note>
            FD, ſinum rectum eiuſdem arcus CD, ita AC, ſi-
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            nus totus ad CE, tangentem eiuſdem arcus. </s>
            <s xml:id="echoid-s7770" xml:space="preserve">quod
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            eſt primum.</s>
            <s xml:id="echoid-s7771" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7772" xml:space="preserve">DEINDE eadem ratione erit, vt AF, ſinus
              <lb/>
            rectus arcus BD, ad FD, ſinũ complementi eiuſdem arcus BD, ita AC, ſinus
              <lb/>
            totus ad CE, tangentem eiuſdem complementi arcus BD. </s>
            <s xml:id="echoid-s7773" xml:space="preserve">quod eſt ſecundum.</s>
            <s xml:id="echoid-s7774" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7775" xml:space="preserve">TERTIO in eiſdem triangulis erit, vt AF, ſinus complementi arcus
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            CD, ad AD, ſinum totum, ita AC, ſinus totus ad AE, ſecantem </s>
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