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

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          <p>
            <s xml:id="echoid-s13754" xml:space="preserve">
              <pb o="399" file="411" n="411" rhead=""/>
            eirculi AECF, perpendiculares BP, GQ. </s>
            <s xml:id="echoid-s13755" xml:space="preserve">Et quoniam rectæ BP, GQ, ca-
              <lb/>
            dunt in communes ſectiones circulorum IBK, LGM, cum circulo AECF,
              <lb/>
              <note position="right" xlink:label="note-411-01" xlink:href="note-411-01a" xml:space="preserve">38. vndec.
                <lb/>
              11. 1. Theod.</note>
            quem bifariam ſecãtin punctis I, K; </s>
            <s xml:id="echoid-s13756" xml:space="preserve">L, M, hoc eſt, cadũtin diametros circulorũ
              <lb/>
            maximorum IBK, LGM;
              <lb/>
            </s>
            <s xml:id="echoid-s13757" xml:space="preserve">
              <figure xlink:label="fig-411-01" xlink:href="fig-411-01a" number="259">
                <image file="411-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/411-01"/>
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            (quòd horum circulorum
              <lb/>
              <note position="right" xlink:label="note-411-02" xlink:href="note-411-02a" xml:space="preserve">15. 1. Theod.</note>
            plana recta ſint ad planum
              <lb/>
            circuli AECF,) ac proin-
              <lb/>
            de rectos angulos faciunt
              <lb/>
            cum diametris circulorum
              <lb/>
            IBK, LGM, ex defin. </s>
            <s xml:id="echoid-s13758" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s13759" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13760" xml:space="preserve">11. </s>
            <s xml:id="echoid-s13761" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s13762" xml:space="preserve">erit quoque
              <lb/>
            tam BP, ſinus rectus arcuũ
              <lb/>
            BI, BK, quam GQ, ſinus
              <lb/>
            rectus arcuum GL, GM,
              <lb/>
            ex definitione ſinus recti. </s>
            <s xml:id="echoid-s13763" xml:space="preserve">
              <lb/>
            Ducantur in plano circuli
              <lb/>
            AECF, rectæ NP, OQ; </s>
            <s xml:id="echoid-s13764" xml:space="preserve">
              <lb/>
            eruntq; </s>
            <s xml:id="echoid-s13765" xml:space="preserve">per defin. </s>
            <s xml:id="echoid-s13766" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13767" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13768" xml:space="preserve">11. </s>
            <s xml:id="echoid-s13769" xml:space="preserve">
              <lb/>
            Eucl. </s>
            <s xml:id="echoid-s13770" xml:space="preserve">anguli P, Q, recti, in
              <lb/>
            triangulis NBP, OGQ. </s>
            <s xml:id="echoid-s13771" xml:space="preserve">
              <lb/>
            Quia verò tam rectæ BN,
              <lb/>
              <note position="right" xlink:label="note-411-03" xlink:href="note-411-03a" xml:space="preserve">28. primi.</note>
            GO, parallelę ſunt, propter
              <lb/>
            angulos rectos ANB, AOG,
              <lb/>
            quam rectæ BP, GQ, cum hæ perpendiculares ſint ad planũ circuli AECF;
              <lb/>
            </s>
            <s xml:id="echoid-s13772" xml:space="preserve">
              <note position="right" xlink:label="note-411-04" xlink:href="note-411-04a" xml:space="preserve">6. vndee.</note>
            erunt quoque anguli B, G, æquales in eisdem triangulis NBP, OGQ.
              <lb/>
            </s>
            <s xml:id="echoid-s13773" xml:space="preserve">
              <note position="right" xlink:label="note-411-05" xlink:href="note-411-05a" xml:space="preserve">10. vndee.</note>
            AEquiangula igitur ſunt triangula NBP, OGQ; </s>
            <s xml:id="echoid-s13774" xml:space="preserve">atque adeò erit, vt NB,
              <lb/>
              <note position="right" xlink:label="note-411-06" xlink:href="note-411-06a" xml:space="preserve">32. primi.</note>
            ſinus arcus AB, vel CB, ad BP, ſinum arcus BI, vel BK, ita OG, ſinus ar-
              <lb/>
              <note position="right" xlink:label="note-411-07" xlink:href="note-411-07a" xml:space="preserve">4. ſexti.</note>
            cus AG, vel CG, ad GQ, ſinum arcus GL, vel GM, quomodocunque ar-
              <lb/>
            cus ſumantur, cum cuilibet ſinui duo arcus ſemicirculũ conficientes reſpon-
              <lb/>
            deant. </s>
            <s xml:id="echoid-s13775" xml:space="preserve">Hcc eſt, erit, vt ſinus arcus AB, ad ſinum arcus BI, ita ſinus arcus AG,
              <lb/>
            ad ſinum arcus GL. </s>
            <s xml:id="echoid-s13776" xml:space="preserve">Item vt ſinus arcus AB, ad ſinum arcus BK, ita ſinus ar-
              <lb/>
            cus AG, ad ſinum arcus GM. </s>
            <s xml:id="echoid-s13777" xml:space="preserve">Item vt ſinus arcus CB, ad ſinum arcus BI, ita
              <lb/>
            ſinus arcus CG, ad ſinum arcus GL. </s>
            <s xml:id="echoid-s13778" xml:space="preserve">Item vt ſinus arcus CB, ad ſinum arcus
              <lb/>
            BK, ita ſinus arcus CG, ad ſinum arcus GM. </s>
            <s xml:id="echoid-s13779" xml:space="preserve">Item vt ſinus arcus AB, ad
              <lb/>
            ſinum arcus BI, ita ſinus arcus CG, ad ſinum arcus GM, &</s>
            <s xml:id="echoid-s13780" xml:space="preserve">c.</s>
            <s xml:id="echoid-s13781" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13782" xml:space="preserve">DEINDE ſumatur vnum punctum, puta B, in ſemicirculo ABC, & </s>
            <s xml:id="echoid-s13783" xml:space="preserve">al-
              <lb/>
            terum, nempe D, in altero ſemicirculo CDA, eiuſdem circuli, ducanturq́ue
              <lb/>
            per puncta B, D, & </s>
            <s xml:id="echoid-s13784" xml:space="preserve">polum circuli AECF, qui ſit H, duo arcus circulorum
              <lb/>
              <note position="right" xlink:label="note-411-08" xlink:href="note-411-08a" xml:space="preserve">20. 1 Theod.</note>
            maximorum IBK, DFS; </s>
            <s xml:id="echoid-s13785" xml:space="preserve">eruntq́ue anguli recti F, I, S, K. </s>
            <s xml:id="echoid-s13786" xml:space="preserve">Dico rurſus, vt eſt ſi-
              <lb/>
              <note position="right" xlink:label="note-411-09" xlink:href="note-411-09a" xml:space="preserve">15. 1. Theod.</note>
            nus arcus AB, vel CB, ad ſinum arcus BI, vel BK, ita eſſe ſinum arcus AD,
              <lb/>
            vel CD, ad ſinum arcus DF, vel arcus, qui cum arcu FD, ſemicirculum per-
              <lb/>
            ficit ã puncto D, vſque ad punctum S, ſemicirculi AEC. </s>
            <s xml:id="echoid-s13787" xml:space="preserve">Nam arcus ab F, per
              <lb/>
            D, vſque ad S, ſemicirculus eſt, cum circuli AECF, DFS, ſe mutuo bifa-
              <lb/>
              <note position="right" xlink:label="note-411-10" xlink:href="note-411-10a" xml:space="preserve">11. 1. Theod.</note>
            riam ſecentin F, S. </s>
            <s xml:id="echoid-s13788" xml:space="preserve">Sumatur enim arcui AD, arcus AG, æqualis, & </s>
            <s xml:id="echoid-s13789" xml:space="preserve">per G,
              <lb/>
              <note position="right" xlink:label="note-411-11" xlink:href="note-411-11a" xml:space="preserve">1. huius.</note>
            & </s>
            <s xml:id="echoid-s13790" xml:space="preserve">polum circuli AECF, nempe per H, arcus maximi circuli ducatur LGM;
              <lb/>
            </s>
            <s xml:id="echoid-s13791" xml:space="preserve">
              <note position="right" xlink:label="note-411-12" xlink:href="note-411-12a" xml:space="preserve">20. 1 Theod.</note>
            eruntq́ue anguli L, M, recti. </s>
            <s xml:id="echoid-s13792" xml:space="preserve">Quoniam igitur duo anguli A, L, trianguli AGL,
              <lb/>
              <note position="right" xlink:label="note-411-13" xlink:href="note-411-13a" xml:space="preserve">15. 1. Theod.</note>
            duobus angulis A, F, trianguli ADF, æquales ſunt, (ſunt enim duo anguli
              <lb/>
            A, ad verticem æquales, & </s>
            <s xml:id="echoid-s13793" xml:space="preserve">anguli L, F, recti.) </s>
            <s xml:id="echoid-s13794" xml:space="preserve">ſuntq́ue latera AG, AD, rectos
              <lb/>
              <note position="right" xlink:label="note-411-14" xlink:href="note-411-14a" xml:space="preserve">6. huius.</note>
            </s>
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