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

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            <s xml:id="echoid-s16363" xml:space="preserve">
              <pb o="461" file="473" n="473" rhead=""/>
            autem, vt produceretur verſus maiorem arcum, qui hic ſit AC. </s>
            <s xml:id="echoid-s16364" xml:space="preserve">Erunt au-
              <lb/>
              <note position="right" xlink:label="note-473-01" xlink:href="note-473-01a" xml:space="preserve">comprehe
                <unsure/>
                <lb/>
              dẽtes ſunt
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              inæquales.</note>
            tem anguli D, E, recti, ob quadrantes AD, AE. </s>
            <s xml:id="echoid-s16365" xml:space="preserve">Quoniam igitur duo maximi
              <lb/>
            circuli BF, DF, ſe interſecant in F, & </s>
            <s xml:id="echoid-s16366" xml:space="preserve">à pun-
              <lb/>
              <figure xlink:label="fig-473-01" xlink:href="fig-473-01a" number="341">
                <image file="473-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/473-01"/>
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            ctis B, C, arcus BF, ad arcum DF, demiſsi
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            ſunt perpendiculares arcus BD, CE; </s>
            <s xml:id="echoid-s16367" xml:space="preserve">erit, vt
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            ſinus arcus BF, ad ſinum arcus BD, ita ſinus
              <lb/>
              <note position="right" xlink:label="note-473-02" xlink:href="note-473-02a" xml:space="preserve">40. huius.</note>
            arcus CF, ad ſinum arcus CE: </s>
            <s xml:id="echoid-s16368" xml:space="preserve">Et permutan
              <lb/>
            do, vt ſinus arcus BF, ad ſinum arcus CF, ita
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            ſinus arcus BD, ad ſinum arcus CE. </s>
            <s xml:id="echoid-s16369" xml:space="preserve">Eſt au-
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            tem proportio ſinus arcus BD, ad ſinum ar-
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            cus CE, data, quòd arcus BD, CE, dati ſint,
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            vtpotè complementa datorum arcuum AB,
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            AC. </s>
            <s xml:id="echoid-s16370" xml:space="preserve">Igitur proportio ſinus arcus BF, ad ſi-
              <lb/>
            num arcus CF, data quoque erit, nempe in
              <lb/>
            ſinubus complementorum, arcuum datorum
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            AB, AC: </s>
            <s xml:id="echoid-s16371" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s16372" xml:space="preserve">eorundem arcuum BF, CF,
              <lb/>
            quorum ſinguli ſemicirculo minores ſunt, differentia data eſt, nempe arcus
              <lb/>
              <note position="right" xlink:label="note-473-03" xlink:href="note-473-03a" xml:space="preserve">2. huius.</note>
            BC. </s>
            <s xml:id="echoid-s16373" xml:space="preserve">Vterque ergo arcus BF, CF, notus reddetur. </s>
            <s xml:id="echoid-s16374" xml:space="preserve">Itaque quoniam in trian
              <lb/>
              <note position="right" xlink:label="note-473-04" xlink:href="note-473-04a" xml:space="preserve">7. triãg. re-
                <lb/>
              ctil.</note>
            gulo BFD, habente angulum D, rectum, datus eſt arcus BF, recto angulo op-
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            poſitus cum arcu BD, complemento videlicet arcus AB, dati; </s>
            <s xml:id="echoid-s16375" xml:space="preserve">cognitus erit
              <lb/>
              <note position="right" xlink:label="note-473-05" xlink:href="note-473-05a" xml:space="preserve">Schol. 53.
                <lb/>
              vel 43. huiꝰ.</note>
            & </s>
            <s xml:id="echoid-s16376" xml:space="preserve">tertius arcus DF. </s>
            <s xml:id="echoid-s16377" xml:space="preserve">Eadem ratione, cum in triangulo CFE, angulum ha-
              <lb/>
            bente rectum E, datus ſit arcus CF, angulo recto oppoſitus, cum arcu CE,
              <lb/>
            complemento nimirum arcus dati AC; </s>
            <s xml:id="echoid-s16378" xml:space="preserve">cognoſcetur, etiã tertius arcus EF: </s>
            <s xml:id="echoid-s16379" xml:space="preserve">qui
              <lb/>
              <note position="right" xlink:label="note-473-06" xlink:href="note-473-06a" xml:space="preserve">Schol. 53.
                <lb/>
              vel 43. huiꝰ.</note>
            ſubtractus ex inuento arcu DF, notum reddet arcum reliquum DE, anguli A;
              <lb/>
            </s>
            <s xml:id="echoid-s16380" xml:space="preserve">ac proinde angulus A, cognitus erit. </s>
            <s xml:id="echoid-s16381" xml:space="preserve">Rurſus in triangulo priore BFD, cuius
              <lb/>
              <note position="right" xlink:label="note-473-07" xlink:href="note-473-07a" xml:space="preserve">Schol. 51.
                <lb/>
              vel 45. huiꝰ.</note>
            angulus D, rectus, cum datus ſit arcus BF, recto angulo oppoſitus, cum arcu
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            BD, complemento videlicet arcus dati AB:
              <lb/>
            </s>
            <s xml:id="echoid-s16382" xml:space="preserve">VEL, cum duo arcus BD, DF, circa angulum re-
              <lb/>
              <note position="right" xlink:label="note-473-08" xlink:href="note-473-08a" xml:space="preserve">Schol. 44.
                <lb/>
              vel 48. huiꝰ.</note>
            ctum dati ſint:
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            </s>
            <s xml:id="echoid-s16383" xml:space="preserve">AVT denique, cum datus ſit arcus BF, recto angu-
              <lb/>
              <note position="right" xlink:label="note-473-09" xlink:href="note-473-09a" xml:space="preserve">Schol. 55.
                <lb/>
              vel 41. huiꝰ.</note>
            lo oppoſitus, & </s>
            <s xml:id="echoid-s16384" xml:space="preserve">arcus DF;
              <lb/>
            </s>
            <s xml:id="echoid-s16385" xml:space="preserve">inuenietur quoque, ex ſcholijs in margine citatis, angulus DBF: </s>
            <s xml:id="echoid-s16386" xml:space="preserve">ideoque & </s>
            <s xml:id="echoid-s16387" xml:space="preserve">
              <lb/>
            reliquus duorum rectorum ABC, notus erit. </s>
            <s xml:id="echoid-s16388" xml:space="preserve">Eadem ratione, cum in poſte-
              <lb/>
              <note position="right" xlink:label="note-473-10" xlink:href="note-473-10a" xml:space="preserve">Schol. 51.
                <lb/>
              vel 45. huiꝰ.</note>
            riore triangulo CFE, angulum E, habente rectum, datus ſit arcus CF, angu-
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            lo recto oppoſitus, cum arcu CE, complemento nimirum arcus dati AC:
              <lb/>
            </s>
            <s xml:id="echoid-s16389" xml:space="preserve">VEL, cum duo arcus CE, EF, circa rectum angu-
              <lb/>
              <note position="right" xlink:label="note-473-11" xlink:href="note-473-11a" xml:space="preserve">Schol. 44.
                <lb/>
              vel 48. huiꝰ.</note>
            lum dati ſint:
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            </s>
            <s xml:id="echoid-s16390" xml:space="preserve">AVT denique, cum datus ſit arcus CF, recto angu-
              <lb/>
              <note position="right" xlink:label="note-473-12" xlink:href="note-473-12a" xml:space="preserve">Schol. 55.
                <lb/>
              vel 41. huiꝰ.</note>
            lo oppoſitus, & </s>
            <s xml:id="echoid-s16391" xml:space="preserve">inſuper arcus EF;
              <lb/>
            </s>
            <s xml:id="echoid-s16392" xml:space="preserve">cognoſcetur etiam, ex ſcholijs in margine poſitis, angu-
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              <figure xlink:label="fig-473-02" xlink:href="fig-473-02a" number="342">
                <image file="473-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/473-02"/>
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            lus ECF: </s>
            <s xml:id="echoid-s16393" xml:space="preserve">ideoq́ue & </s>
            <s xml:id="echoid-s16394" xml:space="preserve">angulus ACB, qui ei ad verticem
              <lb/>
              <note position="right" xlink:label="note-473-13" xlink:href="note-473-13a" xml:space="preserve">6. huius.</note>
            æqualis eſt, notus erit. </s>
            <s xml:id="echoid-s16395" xml:space="preserve">Tres ergo anguli trianguli ABC,
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            omnes noti facti ſunt.</s>
            <s xml:id="echoid-s16396" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16397" xml:space="preserve">SINT deinde duo arcus inæquales AB, AC, maio-
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            res quadrante. </s>
            <s xml:id="echoid-s16398" xml:space="preserve">Prodocantur, donec coeant in D. </s>
            <s xml:id="echoid-s16399" xml:space="preserve">Erunt
              <lb/>
            iu triangulo DBC, duo arcus DB, DC, quadrante mi-
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            nores, atq; </s>
            <s xml:id="echoid-s16400" xml:space="preserve">adeo noti, cum reliqui ſint ex arcubus ABD,
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            ACD, qui ſemicirculi ſunt. </s>
            <s xml:id="echoid-s16401" xml:space="preserve">Igitur, vt proxime demon-
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              <note position="right" xlink:label="note-473-14" xlink:href="note-473-14a" xml:space="preserve">11. 1 Theod.</note>
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