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

Table of figures

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            <s xml:id="echoid-s16047" xml:space="preserve">
              <pb o="453" file="465" n="465" rhead=""/>
            nus verſus anguli A, ſeu arcus DL, ad
              <emph style="sc">K</emph>
            T, differentiam inter ſinus verſos
              <lb/>
            BR, BQ, arcuum BC,
              <emph style="sc">Bk</emph>
            ; </s>
            <s xml:id="echoid-s16048" xml:space="preserve">ſi modo triangula
              <emph style="sc">Sk</emph>
            T, XAV, æquiangula eſſe
              <lb/>
            concludamus, hac argumétatio-
              <lb/>
              <figure xlink:label="fig-465-01" xlink:href="fig-465-01a" number="332">
                <image file="465-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/465-01"/>
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            ne. </s>
            <s xml:id="echoid-s16049" xml:space="preserve">Angulus
              <emph style="sc">Y</emph>
            IX, æqualis eſt
              <lb/>
            interno & </s>
            <s xml:id="echoid-s16050" xml:space="preserve">oppoſito
              <emph style="sc">K</emph>
            ST. </s>
            <s xml:id="echoid-s16051" xml:space="preserve">Igitur
              <lb/>
              <note position="right" xlink:label="note-465-01" xlink:href="note-465-01a" xml:space="preserve">29. primi.</note>
            in triangulis rectangulis
              <emph style="sc">Sk</emph>
            T,
              <lb/>
              <emph style="sc">IXy</emph>
            , reliquus angulus
              <emph style="sc">Sk</emph>
            T, re-
              <lb/>
            liquo angulo
              <emph style="sc">IXy</emph>
            , hoc eſt, an-
              <lb/>
            gulo interno, & </s>
            <s xml:id="echoid-s16052" xml:space="preserve">oppoſito XAV,
              <lb/>
            (cum parallelæ ſint AV, GH.)
              <lb/>
            </s>
            <s xml:id="echoid-s16053" xml:space="preserve">æqualis erit; </s>
            <s xml:id="echoid-s16054" xml:space="preserve">ac proinde triãgula
              <lb/>
            rectangula
              <emph style="sc">Sk</emph>
            T, XAV, æquian-
              <lb/>
            gula erunt. </s>
            <s xml:id="echoid-s16055" xml:space="preserve">Quapropter In omni triangulo ſphærico, cuius duo arcus ſint
              <lb/>
            inæquales, &</s>
            <s xml:id="echoid-s16056" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16057" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s16058" xml:space="preserve"/>
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        <div xml:id="echoid-div1288" type="section" level="1" n="599">
          <head xml:id="echoid-head634" xml:space="preserve">SCHOLIVM. I.</head>
          <p style="it">
            <s xml:id="echoid-s16059" xml:space="preserve">FX omnibus quindecim caſibus buius demonſtrationis liquet, arcum BC, angus
              <lb/>
            lo A, ſub arcubus inæqualibus comprehenſo oppoſitum ſemper maiorem eſſe arcu BK,
              <lb/>
            hoc eſt, d'fferentia arcuum inæqualium. </s>
            <s xml:id="echoid-s16060" xml:space="preserve">In omnibus enim figuris arcus BC, per de-
              <lb/>
            fin. </s>
            <s xml:id="echoid-s16061" xml:space="preserve">poli, arcui BO, (vel arcui BG, quando BC, quadrans eſt, vt in caſu 2. </s>
            <s xml:id="echoid-s16062" xml:space="preserve">5. </s>
            <s xml:id="echoid-s16063" xml:space="preserve">8. </s>
            <s xml:id="echoid-s16064" xml:space="preserve">11.
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            </s>
            <s xml:id="echoid-s16065" xml:space="preserve">& </s>
            <s xml:id="echoid-s16066" xml:space="preserve">14.) </s>
            <s xml:id="echoid-s16067" xml:space="preserve">æqualis eſt. </s>
            <s xml:id="echoid-s16068" xml:space="preserve">Conſtat autem arcum BO, (vel arcum BH, in dictis quinque
              <lb/>
            caſibus) maiorem eſſe arcu BK: </s>
            <s xml:id="echoid-s16069" xml:space="preserve">quod tamen ita eſſe, facile ſequens quoque theore-
              <lb/>
            ma demonſtrabit.</s>
            <s xml:id="echoid-s16070" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16071" xml:space="preserve">IN omni triangulo ſphærico, cuius duo arcus ſint inæquales; </s>
            <s xml:id="echoid-s16072" xml:space="preserve">ar-
              <lb/>
            cus reliquus maior eſt arcu, quo inæquales arcus inter ſe differunt.</s>
            <s xml:id="echoid-s16073" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16074" xml:space="preserve">IN triangulo enim
              <emph style="sc">ABC</emph>
            , ſit arcus AB, maior arcu
              <lb/>
            AC, & </s>
            <s xml:id="echoid-s16075" xml:space="preserve">ex polo A, ad interuallum AC, arcus circuli de-
              <lb/>
              <figure xlink:label="fig-465-02" xlink:href="fig-465-02a" number="333">
                <image file="465-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/465-02"/>
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            ſcribatur CD. </s>
            <s xml:id="echoid-s16076" xml:space="preserve">Erit ergo arcus AD, arcui AC, per
              <lb/>
            deſin. </s>
            <s xml:id="echoid-s16077" xml:space="preserve">poli, æqualis, atque adeo arcus BD, differentia
              <lb/>
            arcuum inæqualium AB, AC. </s>
            <s xml:id="echoid-s16078" xml:space="preserve">Dico arcum BC, arcu
              <lb/>
            BD, maiorem eſſe. </s>
            <s xml:id="echoid-s16079" xml:space="preserve">Quoniam enim duo arcus
              <emph style="sc">Ac</emph>
            , CB,
              <lb/>
            ſimul maiores ſunt arcu AB; </s>
            <s xml:id="echoid-s16080" xml:space="preserve">ablatis æqualibus arcubus
              <lb/>
              <note position="right" xlink:label="note-465-02" xlink:href="note-465-02a" xml:space="preserve">3. huius.</note>
            AC, AD, reliquus quoq; </s>
            <s xml:id="echoid-s16081" xml:space="preserve">CB, reliquo BD, maior erit.
              <lb/>
            </s>
            <s xml:id="echoid-s16082" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s16083" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16084" xml:space="preserve">ITAQVE in omni ſphærico triangulo, cuius duo arcus inæquales ſint, ſinus ver
              <lb/>
              <note position="right" xlink:label="note-465-03" xlink:href="note-465-03a" xml:space="preserve">In triangu
                <lb/>
              lo ſphęrico
                <lb/>
              duorum ar
                <lb/>
              cuum inæ-
                <lb/>
              qualium,
                <lb/>
              ſinus uer-
                <lb/>
              ſuster@j ar
                <lb/>
              cus ma@or
                <lb/>
              eſt ſinu ver
                <lb/>
              ſo differen
                <lb/>
              tię arcuum
                <lb/>
              inæqualiũ.</note>
            ſus reliqui arcus ſemper maior eſt ſinu verſo differentiæ arcuum inæqualium. </s>
            <s xml:id="echoid-s16085" xml:space="preserve">Cum
              <lb/>
            enim arcus ille reliquus oſtenſus ſit maior, quam ea differentia, maior autem arcus
              <lb/>
            habeat ſemper maiorem ſinum verſum, vt ex tractatione ſinuum conſtat, perſpicuum
              <lb/>
            fit, reliqui arcus ſinum verſum maiorem eſſe ſinu verſo differentiæ arcuum inæ-
              <lb/>
            qualium.</s>
            <s xml:id="echoid-s16086" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16087" xml:space="preserve">HOC idcirco dixerim, vt rationem videas, quare in praxipropoſ. </s>
            <s xml:id="echoid-s16088" xml:space="preserve">64. </s>
            <s xml:id="echoid-s16089" xml:space="preserve">differentia
              <lb/>
            inter ſinus verſos, quorum vnus reliquo tertio arcui, alter vero differentiæ inæqua-
              <lb/>
            lium arcuum debetur, adijcienda præcipiatur ſinui verſo differentiæ arcuum inæqua
              <lb/>
            lium, vt componatur ſinus verſus reliqui tertij arcus, nunquam autem detrahenda à
              <lb/>
            ſinu verſo dictæ differentiæ, vt ſinus verſus reliqui arcus relinquatur.</s>
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