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

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        <div xml:id="echoid-div150" type="section" level="1" n="82">
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            <s xml:id="echoid-s1333" xml:space="preserve">
              <pb o="36" file="048" n="48" rhead=""/>
            ca ſuperficie tangat, obliquus erit ad alios circulos, quos ſecat, paral
              <lb/>
            lelos ei, quem tangit.</s>
            <s xml:id="echoid-s1334" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1335" xml:space="preserve">_IN_ eadem figura maximus circulus _A B,_ tangat circulum _A G,_ ſecet autem circu
              <lb/>
              <figure xlink:label="fig-048-01" xlink:href="fig-048-01a" number="54">
                <image file="048-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/048-01"/>
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            lum _C D,_ ipſi _A G,_ parallelum. </s>
            <s xml:id="echoid-s1336" xml:space="preserve">Dico circulum
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            _A B,_ obliquum eſſe ad circulum _C D._ </s>
            <s xml:id="echoid-s1337" xml:space="preserve">Quoniã
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            enim maximus circulus A B, tangens circulum
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            _A G,_ non tranſit per ipſius polos, (Si namque per
              <lb/>
              <note position="left" xlink:label="note-048-01" xlink:href="note-048-01a" xml:space="preserve">15. 1. huius.</note>
            ipſius polos duceretur, ſecaret ipſum bifariam,
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            non autem tangeret.) </s>
            <s xml:id="echoid-s1338" xml:space="preserve">atque adeo neque per po
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            los circuli _CD;_ </s>
            <s xml:id="echoid-s1339" xml:space="preserve">(habent enim paralleli circuli
              <lb/>
              <note position="left" xlink:label="note-048-02" xlink:href="note-048-02a" xml:space="preserve">1. huius.</note>
            _A G, C D,_ eoſdem polos) non ſecabit maximus
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            circulus _A B,_ circulum _C D,_ ad angulos rectos:
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            </s>
            <s xml:id="echoid-s1340" xml:space="preserve">Aliàs tranſiret per eius polos. </s>
            <s xml:id="echoid-s1341" xml:space="preserve">Igitur obliquus
              <lb/>
              <note position="left" xlink:label="note-048-03" xlink:href="note-048-03a" xml:space="preserve">13. 1. huius.</note>
            eſt ad circulum _C D._ </s>
            <s xml:id="echoid-s1342" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s1343" xml:space="preserve"/>
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        <div xml:id="echoid-div153" type="section" level="1" n="83">
          <head xml:id="echoid-head95" xml:space="preserve">THEOR. 9. PROPOS. 9.</head>
          <note position="left" xml:space="preserve">12.</note>
          <p>
            <s xml:id="echoid-s1344" xml:space="preserve">SI in ſphæra duo circuli ſe mutuo ſecent, ma-
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            ximus circulus per eorum polos ductus ſecabit bi
              <lb/>
            fariam ſegmenta ipſorum circulorum.</s>
            <s xml:id="echoid-s1345" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1346" xml:space="preserve">IN ſphæra ſe mutuo ſecent duo circuli A B C D, E D F B, in punctis B,
              <lb/>
            D, & </s>
            <s xml:id="echoid-s1347" xml:space="preserve">per eorum polos deſcribatur maxim us circulus A F C E, ſecans circu-
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              <note position="left" xlink:label="note-048-05" xlink:href="note-048-05a" xml:space="preserve">10. 1. huius.</note>
            los dictos in punctis A, C, E, F. </s>
            <s xml:id="echoid-s1348" xml:space="preserve">Dico circulum A F C E, ſecare bifariã ſeg-
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              <figure xlink:label="fig-048-02" xlink:href="fig-048-02a" number="55">
                <image file="048-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/048-02"/>
              </figure>
            menta B A D, B C D, B E D, B F D. </s>
            <s xml:id="echoid-s1349" xml:space="preserve">Quo-
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            niam enim circulus maximus A F C E, cir-
              <lb/>
              <note position="left" xlink:label="note-048-06" xlink:href="note-048-06a" xml:space="preserve">15. 1. huius.</note>
            culos A B C D, E D F B, ſecat bifariam, & </s>
            <s xml:id="echoid-s1350" xml:space="preserve">
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            ad angulos rectos, quòd per eorum polos du
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            ctus ſit, erunt communes ſectiones A C, E F,
              <lb/>
            quas cum ipſis facit, diametri ipſorum ſecan
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            tes ſeſe in G. </s>
            <s xml:id="echoid-s1351" xml:space="preserve">Secabunt enim ſe mutuo rectę
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            A C, E F, cum in eodẽ plano circuli A F C E,
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            exiſtant, ſitq́; </s>
            <s xml:id="echoid-s1352" xml:space="preserve">punctum E, inter puncta A,
              <lb/>
            & </s>
            <s xml:id="echoid-s1353" xml:space="preserve">C; </s>
            <s xml:id="echoid-s1354" xml:space="preserve">atque punctum E, inter eadem pun-
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            cta. </s>
            <s xml:id="echoid-s1355" xml:space="preserve">Connectantur rectæ B G, D G: </s>
            <s xml:id="echoid-s1356" xml:space="preserve">Eruntq́;
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            </s>
            <s xml:id="echoid-s1357" xml:space="preserve">tria puncta B, G, D, in vtroque plano circu
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            lorum A B C D, EDFB; </s>
            <s xml:id="echoid-s1358" xml:space="preserve">atque adeo in cõ
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            muni eorum ſectione: </s>
            <s xml:id="echoid-s1359" xml:space="preserve">Eſt autem communis
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            eorum ſectio linea recta. </s>
            <s xml:id="echoid-s1360" xml:space="preserve">Igitur recta erit B G D. </s>
            <s xml:id="echoid-s1361" xml:space="preserve">Et quoniam circulus A F C E,
              <lb/>
              <note position="left" xlink:label="note-048-07" xlink:href="note-048-07a" xml:space="preserve">3. vndee.</note>
            oſtenſus eſt ſecare ad angulos rectos vtrumque circulum A B C D, E D F B,
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            crit viciſsim vterque rectus ad circulum AFCE; </s>
            <s xml:id="echoid-s1362" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s1363" xml:space="preserve">B D, com-
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            munis eorum ſectio ad eundem perpendicularis erit. </s>
            <s xml:id="echoid-s1364" xml:space="preserve">Recti igitur erunt angu
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              <note position="left" xlink:label="note-048-08" xlink:href="note-048-08a" xml:space="preserve">19. vndec.</note>
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