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

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          <p>
            <s xml:id="echoid-s1757" xml:space="preserve">
              <pb o="47" file="059" n="59" rhead=""/>
            parallelorum circulorum in ſphæra auferunt, aut
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            per parallelorum polos tranſeunt, aut eundem v-
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            num parallelum tangunt.</s>
            <s xml:id="echoid-s1758" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1759" xml:space="preserve">IN ſphæra maximi circuli A B C, D B E, auferant ex paralleli: </s>
            <s xml:id="echoid-s1760" xml:space="preserve">A D C,
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            F G, circunferentias ſimiles A D, F G. </s>
            <s xml:id="echoid-s1761" xml:space="preserve">Dico maximos circulos A B C, D B E,
              <lb/>
              <figure xlink:label="fig-059-01" xlink:href="fig-059-01a" number="66">
                <image file="059-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/059-01"/>
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            aut tranſire per polos parallelorum A D C,
              <lb/>
            F G, aut vnum eundem parallelum tangere.
              <lb/>
            </s>
            <s xml:id="echoid-s1762" xml:space="preserve">Aut enim alter illorum, nempe A B C, tran-
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            ſit per polos parallelorum, atque ita oſten-
              <lb/>
            demus, alterum per eoſdem tranſire, aut nõ
              <lb/>
            tranſit quidẽ per polos parallelorũ, ſed alte
              <lb/>
            rũ tamen illorũ tangit, atq; </s>
            <s xml:id="echoid-s1763" xml:space="preserve">ita demonſtra-
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            bimus, alterum cundem tangere; </s>
            <s xml:id="echoid-s1764" xml:space="preserve">aut deniq; </s>
            <s xml:id="echoid-s1765" xml:space="preserve">
              <lb/>
            neque per polos parallelorum incedit, neq; </s>
            <s xml:id="echoid-s1766" xml:space="preserve">
              <lb/>
            alterum illorum tangit: </s>
            <s xml:id="echoid-s1767" xml:space="preserve">quo poſito conclu
              <lb/>
            demus circulos maximos datos aliquẽ aliũ
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            parallelum tangere datis parallelis minorẽ. </s>
            <s xml:id="echoid-s1768" xml:space="preserve">
              <lb/>
            Tranſeat enim primum A B C, per polos pa-
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            rallelorum. </s>
            <s xml:id="echoid-s1769" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s1770" xml:space="preserve">D B E, per eoſdem trã
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            ſire, hoc eſt, pũctum B, in quo ſe ſecant maximi circuli A B C, D B E, polum
              <lb/>
            eſſe parallelorum A D C, F G. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">Si namque B, non eſt eorum polus, ſit H, po-
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            lus ipſorum. </s>
            <s xml:id="echoid-s1772" xml:space="preserve">Et quia circulus A B C, ponitur tranſire per eorum polos, erit
              <lb/>
            H, in circunferentia A B C. </s>
            <s xml:id="echoid-s1773" xml:space="preserve">Per H, G, deſcribatur circulus maximus H G,
              <lb/>
              <note position="right" xlink:label="note-059-01" xlink:href="note-059-01a" xml:space="preserve">20. 1. huius.</note>
              <note position="right" xlink:label="note-059-02" xlink:href="note-059-02a" xml:space="preserve">10. huius.</note>
            ſecans A D C. </s>
            <s xml:id="echoid-s1774" xml:space="preserve">in I. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">Eruntq́; </s>
            <s xml:id="echoid-s1776" xml:space="preserve">arcus A I, F G, ſimiles, cum intercipiantur in-
              <lb/>
            ter maximos circulos A H, H I, per polum H, deſcriptos: </s>
            <s xml:id="echoid-s1777" xml:space="preserve">Ponitur autem
              <lb/>
            & </s>
            <s xml:id="echoid-s1778" xml:space="preserve">arcus A D, eidem arcui F G, ſimilis. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">Similes ergo ſunt arcus A I, A D;
              <lb/>
            </s>
            <s xml:id="echoid-s1780" xml:space="preserve">atque adeo cum ſint eiuſdem circuli, inter ſe æquales erunt, totum & </s>
            <s xml:id="echoid-s1781" xml:space="preserve">pars. </s>
            <s xml:id="echoid-s1782" xml:space="preserve">
              <lb/>
            Quod eſt abſurdum. </s>
            <s xml:id="echoid-s1783" xml:space="preserve">Non ergo aliud punctum, præter B, polus erit parallelo-
              <lb/>
            rum, ſi alter circulorum A B C, D B E, nempe A B C, per illorum polos du
              <lb/>
            citur, Quare vterque circulus maximus A B C, D B E, per polum B, paralle
              <lb/>
            lorum tranſit, ſi vnusipſorum tranſit.</s>
            <s xml:id="echoid-s1784" xml:space="preserve"/>
          </p>
          <figure number="67">
            <image file="059-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/059-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s1785" xml:space="preserve">SED iam duo maximi circuli A B C, D E F,
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            auferant rurſum ex parallelis A D C, B E,
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            circunferentias ſimiles A D, B E, & </s>
            <s xml:id="echoid-s1786" xml:space="preserve">neuter
              <lb/>
            illorum tranſeat per parallelorum polos,
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            ſed alter, nempe A B C, vnum eorum, puta
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            B E, tangat in B. </s>
            <s xml:id="echoid-s1787" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s1788" xml:space="preserve">circulum D E F,
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            eundem B E, tangere in E. </s>
            <s xml:id="echoid-s1789" xml:space="preserve">Si enim non tan
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            git, ſed ſecat, deſcribatur per E, punctũ in
              <lb/>
            parallelo B E, datũ maximus circulus G E H,
              <lb/>
              <note position="right" xlink:label="note-059-03" xlink:href="note-059-03a" xml:space="preserve">14. huius.</note>
            tangens parallelum B E, in E; </s>
            <s xml:id="echoid-s1790" xml:space="preserve">eruntq́; </s>
            <s xml:id="echoid-s1791" xml:space="preserve">ſemi
              <lb/>
            circuli, quorum alter ex E, per G, ducitur,
              <lb/>
            alter vero ex B, per A, tranſit, non coeun-
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            tes, vt conſtat ex figura propoſ. </s>
            <s xml:id="echoid-s1792" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1793" xml:space="preserve">huius libri, & </s>
            <s xml:id="echoid-s1794" xml:space="preserve">ex demonſtratis ibidem.
              <lb/>
            </s>
            <s xml:id="echoid-s1795" xml:space="preserve">
              <note position="right" xlink:label="note-059-04" xlink:href="note-059-04a" xml:space="preserve">13. huius.</note>
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