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

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            <s xml:id="echoid-s6574" xml:space="preserve">
              <pb o="176" file="188" n="188" rhead=""/>
            recta BC, ex hypotheſi. </s>
            <s xml:id="echoid-s6575" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s6576" xml:space="preserve">AE, maior erit, quã EC. </s>
            <s xml:id="echoid-s6577" xml:space="preserve">Diuiſa ergo AC, bi-
              <lb/>
            fariã in F, erit punctũ F, in maiori ſegmento AE. </s>
            <s xml:id="echoid-s6578" xml:space="preserve">Ducta autẽ recta DF; </s>
            <s xml:id="echoid-s6579" xml:space="preserve">quoniã
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            latera AF, FD, trianguli AFD, lateribus CF, FD, trianguli CFD, baſisq́;
              <lb/>
            </s>
            <s xml:id="echoid-s6580" xml:space="preserve">AD, baſi CD, oſtenſa eſt æqualis; </s>
            <s xml:id="echoid-s6581" xml:space="preserve">erit angulus AFD, angulo CFD, æqua-
              <lb/>
              <note position="left" xlink:label="note-188-01" xlink:href="note-188-01a" xml:space="preserve">8. primi.</note>
            lis; </s>
            <s xml:id="echoid-s6582" xml:space="preserve">ac proinde vterq; </s>
            <s xml:id="echoid-s6583" xml:space="preserve">rectus erit. </s>
            <s xml:id="echoid-s6584" xml:space="preserve">Cum ergo in triangulo DEF, duo anguli
              <lb/>
            E, F, duobus rectis ſint minores, erit angulus E, acutus, ac proinde reliquus
              <lb/>
              <note position="left" xlink:label="note-188-02" xlink:href="note-188-02a" xml:space="preserve">17. primi.</note>
            CED, obtuſus. </s>
            <s xml:id="echoid-s6585" xml:space="preserve">Quare cum in triangulo CDE, duo anguli C, E, ſint duo-
              <lb/>
            bus rectis minores, erit angulus C, acutus. </s>
            <s xml:id="echoid-s6586" xml:space="preserve">Eſt igitur in triangulo DEF, la-
              <lb/>
            tus DE, maius latere DF, & </s>
            <s xml:id="echoid-s6587" xml:space="preserve">in triangulo CDE, minus latere CD. </s>
            <s xml:id="echoid-s6588" xml:space="preserve">Quocir-
              <lb/>
              <note position="left" xlink:label="note-188-03" xlink:href="note-188-03a" xml:space="preserve">19. primi.</note>
            ca arcus circuli ex D, centro per E, deſcriptus ſecabit rectam DF, productam
              <lb/>
            in H, rectam autem CD, infra punctum C, in G. </s>
            <s xml:id="echoid-s6589" xml:space="preserve">Quoniam vero ſector DHE,
              <lb/>
            ad triangulum DEC, maiorem proportionem habet, quam triangulũ DFE,
              <lb/>
              <note position="left" xlink:label="note-188-04" xlink:href="note-188-04a" xml:space="preserve">8, quinti.</note>
              <figure xlink:label="fig-188-01" xlink:href="fig-188-01a" number="138">
                <image file="188-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/188-01"/>
              </figure>
            adidem triangulum DEC: </s>
            <s xml:id="echoid-s6590" xml:space="preserve">Item ſector idem DHE, ad ſectorem DEG, ma-
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            iorem proportionem habet, quam ad triangulum DEC; </s>
            <s xml:id="echoid-s6591" xml:space="preserve">habebit multò ma-
              <lb/>
            iorem proportionem ſector DHE, ad ſectorem DEG, quam triangulum
              <lb/>
            DFE, ad triangulum DEC. </s>
            <s xml:id="echoid-s6592" xml:space="preserve">Eſt autem, vt ſector DHE, ad ſectorem DEG,
              <lb/>
              <note position="left" xlink:label="note-188-05" xlink:href="note-188-05a" xml:space="preserve">Coroll. 1.
                <lb/>
              propoſ. 33.
                <lb/>
              lib. 6.</note>
            ita angulus HDE, ad angulum EDG. </s>
            <s xml:id="echoid-s6593" xml:space="preserve">Maior ergo quoq; </s>
            <s xml:id="echoid-s6594" xml:space="preserve">erit proportio an-
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            guli HDE, ad angulum EDG, quam trianguli DFE, ad triangulum DEC:
              <lb/>
            </s>
            <s xml:id="echoid-s6595" xml:space="preserve">
              <note position="left" xlink:label="note-188-06" xlink:href="note-188-06a" xml:space="preserve">1. ſexti.</note>
            Sed vt triangulum DFE, ad triangulum DEC, ita eſt recta FE, ad rectam
              <lb/>
            EC. </s>
            <s xml:id="echoid-s6596" xml:space="preserve">Eſt igitur maior quoq; </s>
            <s xml:id="echoid-s6597" xml:space="preserve">proportio anguli HDE, ad angulum EDG,
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            quæ rectę FE, ad rectam EC. </s>
            <s xml:id="echoid-s6598" xml:space="preserve">Etcomponendo, maior etiam erit proportio
              <lb/>
              <note position="left" xlink:label="note-188-07" xlink:href="note-188-07a" xml:space="preserve">28. quinti.</note>
            anguli HDG, ad angulum EDG, quam rectæ FC, ad rectam EC. </s>
            <s xml:id="echoid-s6599" xml:space="preserve">Quia igi-
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              <note position="right" xlink:label="note-188-08" xlink:href="note-188-08a" xml:space="preserve">
                <lb/>
              Anguli # Rectæ.
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              ADC. # AC.
                <lb/>
              HDG. # FC.
                <lb/>
              EDG. # EC.
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              </note>
            tur eſt, vt angulus ADC, ad angulum HDG, ita
              <lb/>
            recta AC, ad rectã FC: </s>
            <s xml:id="echoid-s6600" xml:space="preserve">(vtrobiq; </s>
            <s xml:id="echoid-s6601" xml:space="preserve">enim eſt proportio
              <lb/>
            dupla) Angulus autem HDG, ad angulum EDG,
              <lb/>
            maiorem habet proportionem, quam recta FC, ad
              <lb/>
            rectam EC, vt oſtendimus; </s>
            <s xml:id="echoid-s6602" xml:space="preserve">erit ex æquo maior quo-
              <lb/>
              <note position="left" xlink:label="note-188-09" xlink:href="note-188-09a" xml:space="preserve">31. quinti.</note>
            que proportio anguli ADC, ad angulum EDG,
              <lb/>
            quam rectæ AC, ad rectam EC, vt in hac formula
              <lb/>
            apparet. </s>
            <s xml:id="echoid-s6603" xml:space="preserve">Diuidendo ergo erit quoq; </s>
            <s xml:id="echoid-s6604" xml:space="preserve">maior proportio anguli ADE, ad angu-
              <lb/>
              <note position="left" xlink:label="note-188-10" xlink:href="note-188-10a" xml:space="preserve">29. quinti.</note>
            lum EDG, quam rectæ AE, ad rectam EC. </s>
            <s xml:id="echoid-s6605" xml:space="preserve">Atqui vt angulus ADE, ad an-
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            gulum EDG, ita eſt arcus AB, ad arcum BC; </s>
            <s xml:id="echoid-s6606" xml:space="preserve">Et vt recta AE, ad rectam EC,
              <lb/>
              <note position="left" xlink:label="note-188-11" xlink:href="note-188-11a" xml:space="preserve">33. ſexti.</note>
            ita eſt chorda AB, ad chordam BC. </s>
            <s xml:id="echoid-s6607" xml:space="preserve">Igitur maior erit etiam proportio arcus
              <lb/>
              <note position="left" xlink:label="note-188-12" xlink:href="note-188-12a" xml:space="preserve">3. ſexti.</note>
            AB, ad arcum BC, quam chordæ AB, ad chordam BC. </s>
            <s xml:id="echoid-s6608" xml:space="preserve">In circulo ergo ſum-
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            ptis duobus arcubus inæqualibus, &</s>
            <s xml:id="echoid-s6609" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6610" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s6611" xml:space="preserve"/>
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