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

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        <div xml:id="echoid-div195" type="section" level="1" n="98">
          <pb o="53" file="065" n="65" rhead=""/>
          <p>
            <s xml:id="echoid-s2027" xml:space="preserve">IN ſphæra parallelos A B, C D, E F, ſecet in H, O; </s>
            <s xml:id="echoid-s2028" xml:space="preserve">I, N; </s>
            <s xml:id="echoid-s2029" xml:space="preserve">K, M, non ta-
              <lb/>
            men per polos, circulus maximus GHIKLMNO, ſitque ſupra hemiſphæ-
              <lb/>
              <figure xlink:label="fig-065-01" xlink:href="fig-065-01a" number="75">
                <image file="065-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/065-01"/>
              </figure>
            rium G B L, polus conſpicuus P, occultus
              <lb/>
            autem Q Dico arcum O B H, maiorem eſſe,
              <lb/>
            quàm vt ſimilis ſit arcui N D I, & </s>
            <s xml:id="echoid-s2030" xml:space="preserve">N D I, ma
              <lb/>
            iorem, quàm vt ſimilis ſit arcui M F K. </s>
            <s xml:id="echoid-s2031" xml:space="preserve">Per
              <lb/>
            polum enim parallelorum P, & </s>
            <s xml:id="echoid-s2032" xml:space="preserve">puncta I, N,
              <lb/>
              <note position="right" xlink:label="note-065-01" xlink:href="note-065-01a" xml:space="preserve">20. 1. huius.</note>
            deſcribãtur duo circuli maximi P I, P N, ſe-
              <lb/>
            cantes parallelum A B, ſupra circulũ G I L N,
              <lb/>
            in R, S: </s>
            <s xml:id="echoid-s2033" xml:space="preserve">eritque arcus R B S, arcui I D N, ſi-
              <lb/>
              <note position="right" xlink:label="note-065-02" xlink:href="note-065-02a" xml:space="preserve">10. huius.</note>
            milis. </s>
            <s xml:id="echoid-s2034" xml:space="preserve">Cum ergo arcus O B H, maior ſit ar-
              <lb/>
            cu R B S, maior quoque erit, quam vt ſimilis
              <lb/>
            ſit arcui N D I. </s>
            <s xml:id="echoid-s2035" xml:space="preserve">Eodem modo oſtendemus
              <lb/>
            arcum N D I, maiorem eſſe, quàm vt ſimilis
              <lb/>
            ſit arcui M F K, ſi nimirum per polum P, & </s>
            <s xml:id="echoid-s2036" xml:space="preserve">
              <lb/>
            puncta K, M, duo alij circuli maximi deſcri-
              <lb/>
            bantur. </s>
            <s xml:id="echoid-s2037" xml:space="preserve">Igitur ſi in ſphæra maximus circulus parallelos aliquot, &</s>
            <s xml:id="echoid-s2038" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2039" xml:space="preserve">Quod
              <lb/>
            demonſtrandum erat.</s>
            <s xml:id="echoid-s2040" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div197" type="section" level="1" n="99">
          <head xml:id="echoid-head111" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s2041" xml:space="preserve">HINC fit, ſimpliciter arcum O B H, maiorem eſſe partem ſui paralleli A B, quàm ar-
              <lb/>
            cum N D I, ſui paralleli, &</s>
            <s xml:id="echoid-s2042" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2043" xml:space="preserve">quandoquidem arcus R B S, tanta pars eſt ſui paralleli, quanta
              <lb/>
            eſt arcus I D N, ſui paralleli, cum hi arcus demonſtrati ſint eſſe ſimiles, &</s>
            <s xml:id="echoid-s2044" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2045" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div198" type="section" level="1" n="100">
          <head xml:id="echoid-head112" xml:space="preserve">THEOREMA 19. PROPOS. 21.</head>
          <note position="right" xml:space="preserve">25.</note>
          <p>
            <s xml:id="echoid-s2046" xml:space="preserve">SI in ſphæris æqualibus maximi circuli ad ma-
              <lb/>
            ximos circulos inclinentur, ille cuius polus ſubli-
              <lb/>
            mior ſupra planum ſubiectum eſt, inclinatior erit:
              <lb/>
            </s>
            <s xml:id="echoid-s2047" xml:space="preserve">illi vero circuli, quorum poli æqualiter diſtant à ſu
              <lb/>
            biectis planis, æqualiter inclinantur.</s>
            <s xml:id="echoid-s2048" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2049" xml:space="preserve">IN ſphæris æqua-
              <lb/>
            libus A B C D, E F G H,
              <lb/>
              <figure xlink:label="fig-065-02" xlink:href="fig-065-02a" number="76">
                <image file="065-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/065-02"/>
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            quarum centra I, K,
              <lb/>
            ad circulos maximos
              <lb/>
            A B C D, E F G H, quo
              <lb/>
            rum poli L, M, incli-
              <lb/>
            nẽtur duo circuli ma-
              <lb/>
            ximi B N D, F O H, quo-
              <lb/>
            rum poli, P, Q; </s>
            <s xml:id="echoid-s2050" xml:space="preserve">ſitque
              <lb/>
            primum polus P, ſubli-
              <lb/>
            mior ſupra planum cir
              <lb/>
            culi A B C D, quàm po
              <lb/>
            lus Q, ſupra planũ cir-
              <lb/>
            culi E F G H. </s>
            <s xml:id="echoid-s2051" xml:space="preserve">Dico </s>
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