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

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        <div xml:id="echoid-div189" type="section" level="1" n="96">
          <p>
            <s xml:id="echoid-s1938" xml:space="preserve">
              <pb o="51" file="063" n="63" rhead=""/>
            les, ſit A E, maior. </s>
            <s xml:id="echoid-s1939" xml:space="preserve">Erit igitur circulus A B, minor circulo C D. </s>
            <s xml:id="echoid-s1940" xml:space="preserve">quod eſt con-
              <lb/>
              <figure xlink:label="fig-063-01" xlink:href="fig-063-01a" number="72">
                <image file="063-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/063-01"/>
              </figure>
              <note position="right" xlink:label="note-063-01" xlink:href="note-063-01a" xml:space="preserve">17. huius.</note>
            tra hypotheſim. </s>
            <s xml:id="echoid-s1941" xml:space="preserve">Sunt ergo ęquales arcus A E,
              <lb/>
            E C, nec non B F, F D.</s>
            <s xml:id="echoid-s1942" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1943" xml:space="preserve">QVOD ſi circulus A B, maior po-
              <lb/>
            natur circulo C D; </s>
            <s xml:id="echoid-s1944" xml:space="preserve">Dico arcum A E, mino-
              <lb/>
            rem eſſe arcu E C. </s>
            <s xml:id="echoid-s1945" xml:space="preserve">Si enim non eſt minor,
              <lb/>
            erit vel æqualis, vel maior. </s>
            <s xml:id="echoid-s1946" xml:space="preserve">Si æqualis, erunt
              <lb/>
            circuli A B, C D, æquales: </s>
            <s xml:id="echoid-s1947" xml:space="preserve">ſi maior, erit cir-
              <lb/>
              <note position="right" xlink:label="note-063-02" xlink:href="note-063-02a" xml:space="preserve">17. huius.</note>
            culus A B, minor circulo C D, quorum vtrũ-
              <lb/>
              <note position="right" xlink:label="note-063-03" xlink:href="note-063-03a" xml:space="preserve">17. huius.</note>
            que eſt cõtra hypotheſim. </s>
            <s xml:id="echoid-s1948" xml:space="preserve">Minor ergo eſt ar-
              <lb/>
            cus A E, quam E C. </s>
            <s xml:id="echoid-s1949" xml:space="preserve">Quamobrem In ſphæra
              <lb/>
            circunferenriæ maximorum circulorum in-
              <lb/>
            terceptæ, &</s>
            <s xml:id="echoid-s1950" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1951" xml:space="preserve">Quod oſtendendũ erat.</s>
            <s xml:id="echoid-s1952" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div192" type="section" level="1" n="97">
          <head xml:id="echoid-head109" xml:space="preserve">THEOR. 17. PROPOS. 19.</head>
          <note position="right" xml:space="preserve">23.</note>
          <p>
            <s xml:id="echoid-s1953" xml:space="preserve">SI in ſphæra maximus circulus parallelos ali-
              <lb/>
            quot circulos in ſphærica ſuperficie deſcriptos ſe-
              <lb/>
            cet quidẽ, non tamen per polos, in partes inæqua-
              <lb/>
            les eos ſecabit, excepto maximo parallelorum: </s>
            <s xml:id="echoid-s1954" xml:space="preserve">De
              <lb/>
            parallelorum autem ſegmentis in vno hemiſphæ-
              <lb/>
            riorum interceptis, ea quæ ſunt inter maximum
              <lb/>
            parallelorum, & </s>
            <s xml:id="echoid-s1955" xml:space="preserve">polum conſpicuum, ſunt maiora
              <lb/>
            ſemicirculo; </s>
            <s xml:id="echoid-s1956" xml:space="preserve">reliqua vero, quæ ſunt inter maximũ
              <lb/>
            parallelorum, & </s>
            <s xml:id="echoid-s1957" xml:space="preserve">polum occultum, ſunt ſemicircu
              <lb/>
            lo minora: </s>
            <s xml:id="echoid-s1958" xml:space="preserve">Æqualium denique ac parallelorum cir
              <lb/>
            culorum alterna ſegmenta ſunt inter ſe æqualia,</s>
          </p>
          <p>
            <s xml:id="echoid-s1959" xml:space="preserve">IN ſphęra maximus circulus A B C D,
              <lb/>
            parallelos E F, G H, I K, ſecet in L, M; </s>
            <s xml:id="echoid-s1960" xml:space="preserve">B,
              <lb/>
              <figure xlink:label="fig-063-02" xlink:href="fig-063-02a" number="73">
                <image file="063-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/063-02"/>
              </figure>
            D; </s>
            <s xml:id="echoid-s1961" xml:space="preserve">& </s>
            <s xml:id="echoid-s1962" xml:space="preserve">O, P, non per polos, qui ſint Q, R; </s>
            <s xml:id="echoid-s1963" xml:space="preserve">& </s>
            <s xml:id="echoid-s1964" xml:space="preserve">
              <lb/>
            fit G H, parallelorum maximus, & </s>
            <s xml:id="echoid-s1965" xml:space="preserve">Q, polus
              <lb/>
            conſpicuus, & </s>
            <s xml:id="echoid-s1966" xml:space="preserve">R, occultus in hemiſphęrio,
              <lb/>
            quod ſupra circulum maximum A B C D, ex
              <lb/>
            tat, & </s>
            <s xml:id="echoid-s1967" xml:space="preserve">ad partes F, vergit. </s>
            <s xml:id="echoid-s1968" xml:space="preserve">Dico circulum
              <lb/>
            A B C D, parallelos non bifariam ſecare, ex
              <lb/>
            cepto maximo G H; </s>
            <s xml:id="echoid-s1969" xml:space="preserve">hunc enim bifariam ſe-
              <lb/>
              <note position="right" xlink:label="note-063-05" xlink:href="note-063-05a" xml:space="preserve">11. 1. huius</note>
            cat: </s>
            <s xml:id="echoid-s1970" xml:space="preserve">ſegmentum autem L F M, inter maximũ
              <lb/>
            parallelum, & </s>
            <s xml:id="echoid-s1971" xml:space="preserve">polum Q, conſpicuum ſemicir
              <lb/>
            culo eſſe maius, & </s>
            <s xml:id="echoid-s1972" xml:space="preserve">O K P, minus. </s>
            <s xml:id="echoid-s1973" xml:space="preserve">Si denique
              <lb/>
            paralleli E F, I K, ęquales ſint, alterna </s>
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