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

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          <p>
            <s xml:id="echoid-s1033" xml:space="preserve">
              <pb o="28" file="040" n="40" rhead=""/>
            ab eo puncto ad circunferentiam circuli cuiuſpiam in ſphæra dati
              <lb/>
            cadant plures, quàm duæ rectæ lineę æquales, acceptum punctum
              <lb/>
            polus eſt ipſius circuli.</s>
            <s xml:id="echoid-s1034" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s1035" xml:space="preserve">_IN_ ſuperficie ſphæræ _A B C,_ acceptum ſit punctum _A,_ a quo ad circunferentiã
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            circuli _B C,_ cadant plures, quàm duæ, rectæ linæ æquales _A D, A E, A F._ </s>
            <s xml:id="echoid-s1036" xml:space="preserve">Dico
              <lb/>
              <figure xlink:label="fig-040-01" xlink:href="fig-040-01a" number="40">
                <image file="040-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/040-01"/>
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            _A,_ polum eſſe circuli _B C._ </s>
            <s xml:id="echoid-s1037" xml:space="preserve">Demittatur enim ex
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            _A,_ in planum circuli _B C,_ perpendicularis
              <lb/>
              <note position="left" xlink:label="note-040-01" xlink:href="note-040-01a" xml:space="preserve">11. valec.</note>
            _A G,_ iungãturq́; </s>
            <s xml:id="echoid-s1038" xml:space="preserve">rectæ _D G, E G, F G,_ eruntq́;
              <lb/>
            </s>
            <s xml:id="echoid-s1039" xml:space="preserve">ex 3. </s>
            <s xml:id="echoid-s1040" xml:space="preserve">defin. </s>
            <s xml:id="echoid-s1041" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1042" xml:space="preserve">I I. </s>
            <s xml:id="echoid-s1043" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1044" xml:space="preserve">omnes treas anguli ad
              <lb/>
            G, recti. </s>
            <s xml:id="echoid-s1045" xml:space="preserve">Quare tam quadratum ex _A D,_ qua-
              <lb/>
            dratis ex _A G, G D,_ quàm quadratum ex _A E,_
              <lb/>
              <note position="left" xlink:label="note-040-02" xlink:href="note-040-02a" xml:space="preserve">47. primi.</note>
            quadratis ex _A G, G E,_ & </s>
            <s xml:id="echoid-s1046" xml:space="preserve">quadratum ex _A F,_
              <lb/>
            quadratis ex _A G, G F,_ æquale erit. </s>
            <s xml:id="echoid-s1047" xml:space="preserve">Cum er-
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            go quadrata rectarum æqualiũ _A D, A E, A F._
              <lb/>
            </s>
            <s xml:id="echoid-s1048" xml:space="preserve">æqualia ſint, erunt & </s>
            <s xml:id="echoid-s1049" xml:space="preserve">quadrata ex _A G, G D,_
              <lb/>
            ſimul quadratis ex _A G, G E,_ ſimul, nec non
              <lb/>
            quadratis ex _A G, G F,_ ſimul æqualia; </s>
            <s xml:id="echoid-s1050" xml:space="preserve">dem-
              <lb/>
            ptoq́; </s>
            <s xml:id="echoid-s1051" xml:space="preserve">communi quadrato lineæ _A G,_ æqualia
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            erunt reliqua quadrata linearum _G D, G E,_
              <lb/>
            _G F,_ at que adeo & </s>
            <s xml:id="echoid-s1052" xml:space="preserve">rectæ _G D, G E, G F,_ æquales erunt, Igitur _G,_ centrum erit
              <lb/>
              <note position="left" xlink:label="note-040-03" xlink:href="note-040-03a" xml:space="preserve">9. tertij.</note>
            circuli _BC;_ </s>
            <s xml:id="echoid-s1053" xml:space="preserve">ac proinde recta _G A,_ quæ ex centro _G,_ ad circulum _B C,_ perpendi-
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            cularis eſt ducta, in polum circuli _B C,_ cadet. </s>
            <s xml:id="echoid-s1054" xml:space="preserve">Punctum ergo _A,_ polus eſt circuli
              <lb/>
              <note position="left" xlink:label="note-040-04" xlink:href="note-040-04a" xml:space="preserve">Schol. 8. hu
                <lb/>
              ius.</note>
            B C. </s>
            <s xml:id="echoid-s1055" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s1056" xml:space="preserve"/>
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        <div xml:id="echoid-div117" type="section" level="1" n="65">
          <head xml:id="echoid-head76" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s1057" xml:space="preserve">IN ſphæra circuli, à quorum polis rectæ ad eorum circunferen
              <lb/>
              <note position="left" xlink:label="note-040-05" xlink:href="note-040-05a" xml:space="preserve">34.</note>
            tias ductæ ſunt æquales, inter ſe ęquales ſunt. </s>
            <s xml:id="echoid-s1058" xml:space="preserve">Et circulorum ęqua-
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            lium ęquales ſunt rectę ab eorum polis ad circunferentias ductæ.</s>
            <s xml:id="echoid-s1059" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1060" xml:space="preserve">_IN_ ſphæra _A B C D E F,_ cuius centrum _G,_ ſint duo circuli _B F, C E,_ a quorum
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              <figure xlink:label="fig-040-02" xlink:href="fig-040-02a" number="41">
                <image file="040-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/040-02"/>
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            polis _A, D,_ rectæ _A F, D E,_ ad eorum circunfe
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            rentias ductæ ſint æquales. </s>
            <s xml:id="echoid-s1061" xml:space="preserve">Dico circulos _B F,_
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            _C E,_ æquales eſſe. </s>
            <s xml:id="echoid-s1062" xml:space="preserve">Ducantur ex polis _A, D,_ ad
              <lb/>
              <note position="left" xlink:label="note-040-06" xlink:href="note-040-06a" xml:space="preserve">21. vndec.</note>
            plana circulorum perpendiculares _A H, D I,_ quæ
              <lb/>
            cadent in eorum centra _H, I,_ & </s>
            <s xml:id="echoid-s1063" xml:space="preserve">inde productæ
              <lb/>
              <note position="left" xlink:label="note-040-07" xlink:href="note-040-07a" xml:space="preserve">9. huius.</note>
            in reliquos polos; </s>
            <s xml:id="echoid-s1064" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s1065" xml:space="preserve">in _G,_ centrum
              <lb/>
              <note position="left" xlink:label="note-040-08" xlink:href="note-040-08a" xml:space="preserve">10. huius.</note>
            ſphæræ. </s>
            <s xml:id="echoid-s1066" xml:space="preserve">Ductis igitur ſemidiametris ſphæræ _F G,_
              <lb/>
            _E G,_ & </s>
            <s xml:id="echoid-s1067" xml:space="preserve">ſemidiametris circulorũ _F H, E I,_ cum
              <lb/>
            latera _A G, G F,_ lateribus _D G, G E,_ ſint æqua
              <lb/>
              <note position="left" xlink:label="note-040-09" xlink:href="note-040-09a" xml:space="preserve">3. primi.</note>
            lia, & </s>
            <s xml:id="echoid-s1068" xml:space="preserve">baſis _A F,_ baſi _DE_ erunt anquli _A G F,_
              <lb/>
            _D G E,_ æquales. </s>
            <s xml:id="echoid-s1069" xml:space="preserve">Sunt autem anguli _H, I,_ ex
              <lb/>
            defin. </s>
            <s xml:id="echoid-s1070" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1071" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1072" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1073" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1074" xml:space="preserve">recti. </s>
            <s xml:id="echoid-s1075" xml:space="preserve">Triangula igitur
              <lb/>
            _F G H, E G I,_ duos angulos duobus angulis æ-
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            quales habent: </s>
            <s xml:id="echoid-s1076" xml:space="preserve">habent autem & </s>
            <s xml:id="echoid-s1077" xml:space="preserve">latus _F G,_ lateri _E G,_ quod recto angulo </s>
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