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

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          <p>
            <s xml:id="echoid-s1973" xml:space="preserve">
              <pb o="52" file="064" n="64" rhead=""/>
            ta L F M, O I P, ęqualia eſſe. </s>
            <s xml:id="echoid-s1974" xml:space="preserve">Per polum
              <lb/>
            enim Q, & </s>
            <s xml:id="echoid-s1975" xml:space="preserve">punctum B, circulus maximus
              <lb/>
              <note position="left" xlink:label="note-064-01" xlink:href="note-064-01a" xml:space="preserve">20. 1. huius.</note>
              <figure xlink:label="fig-064-01" xlink:href="fig-064-01a" number="74">
                <image file="064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/064-01"/>
              </figure>
            deſcribatur QBRD; </s>
            <s xml:id="echoid-s1976" xml:space="preserve">qui per reliquum po-
              <lb/>
            lum R, tranſibit ex coroll. </s>
            <s xml:id="echoid-s1977" xml:space="preserve">ſcholij pro-
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            poſ. </s>
            <s xml:id="echoid-s1978" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1979" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1980" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1981" xml:space="preserve">huius; </s>
            <s xml:id="echoid-s1982" xml:space="preserve">nec non per pun-
              <lb/>
            ctum D, cum vtrumque circulum G B H D,
              <lb/>
              <note position="left" xlink:label="note-064-02" xlink:href="note-064-02a" xml:space="preserve">11. 1. huius.</note>
            A B C D, bifariam diuidat; </s>
            <s xml:id="echoid-s1983" xml:space="preserve">circuli au-
              <lb/>
            tem hi ſecentur bifariam in B, D. </s>
            <s xml:id="echoid-s1984" xml:space="preserve">Ex
              <lb/>
            quo fit, circulum Q B R D, paralle-
              <lb/>
            lum E F, ſecare ſupra circulum A B C D,
              <lb/>
            at parallelum I K, infra eundem; </s>
            <s xml:id="echoid-s1985" xml:space="preserve">vt in pun-
              <lb/>
            ctis S, T; </s>
            <s xml:id="echoid-s1986" xml:space="preserve">& </s>
            <s xml:id="echoid-s1987" xml:space="preserve">V, X. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">Quoniam vero circulus
              <lb/>
            Q B R D, parallelos E F, I K, bifariam ſe-
              <lb/>
              <note position="left" xlink:label="note-064-03" xlink:href="note-064-03a" xml:space="preserve">15. 1. huius.</note>
            cat, erunt S F T, V K X, ſemicirculi; </s>
            <s xml:id="echoid-s1989" xml:space="preserve">ac
              <lb/>
            propterea arcus L F M, ſemicirculo maior, & </s>
            <s xml:id="echoid-s1990" xml:space="preserve">O K P, ſemicirculo minor erit.
              <lb/>
            </s>
            <s xml:id="echoid-s1991" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s1992" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1993" xml:space="preserve">SINT iam paralleli E F, I K, ęquales. </s>
            <s xml:id="echoid-s1994" xml:space="preserve">Dico alterna ſegmenta L F M, O I P,
              <lb/>
            ęqualia inter ſe eſſe; </s>
            <s xml:id="echoid-s1995" xml:space="preserve">nec non ſegmenta alterna L E M, O K P. </s>
            <s xml:id="echoid-s1996" xml:space="preserve">Nam per polos
              <lb/>
            parallelorũ, & </s>
            <s xml:id="echoid-s1997" xml:space="preserve">polos circuli A B C D, deſcribatur circulus maximus A G C H,
              <lb/>
              <note position="left" xlink:label="note-064-04" xlink:href="note-064-04a" xml:space="preserve">20. 1. huius.</note>
            qui diuidet ſegmenta L A M, O C P, bifariam. </s>
            <s xml:id="echoid-s1998" xml:space="preserve">Aequales ergo ſunt arcus A L,
              <lb/>
              <note position="left" xlink:label="note-064-05" xlink:href="note-064-05a" xml:space="preserve">9. huius.</note>
            A M, inter ſe, & </s>
            <s xml:id="echoid-s1999" xml:space="preserve">C O, C P, inter ſe. </s>
            <s xml:id="echoid-s2000" xml:space="preserve">Et quoniam circulus maximus A G C H,
              <lb/>
            tranſit per polos maximorum circulorum G H, A C; </s>
            <s xml:id="echoid-s2001" xml:space="preserve">tranſibunt viciſsim hi
              <lb/>
              <note position="left" xlink:label="note-064-06" xlink:href="note-064-06a" xml:space="preserve">Schol. 15. 1.
                <lb/>
              huius.</note>
            per illius polos. </s>
            <s xml:id="echoid-s2002" xml:space="preserve">Puncta igitur B, D, poli ſunt circuli AGCH; </s>
            <s xml:id="echoid-s2003" xml:space="preserve">ac propte-
              <lb/>
            rea rectę B A, B C, æquales erunt, ex defin. </s>
            <s xml:id="echoid-s2004" xml:space="preserve">poli; </s>
            <s xml:id="echoid-s2005" xml:space="preserve">atque idcirco & </s>
            <s xml:id="echoid-s2006" xml:space="preserve">arcus ipſi B A
              <lb/>
              <note position="left" xlink:label="note-064-07" xlink:href="note-064-07a" xml:space="preserve">28. tertij.</note>
            B C, æquales erunt: </s>
            <s xml:id="echoid-s2007" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s2008" xml:space="preserve">arcus B L, B O, ęquales; </s>
            <s xml:id="echoid-s2009" xml:space="preserve">propterea quod
              <lb/>
              <note position="left" xlink:label="note-064-08" xlink:href="note-064-08a" xml:space="preserve">18. huius.</note>
            æquales ponuntur paralleli E F, I K. </s>
            <s xml:id="echoid-s2010" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s2011" xml:space="preserve">reliqui arcus A L, C O, ęqua-
              <lb/>
            les erunt: </s>
            <s xml:id="echoid-s2012" xml:space="preserve">Sunt autem arcus A L, C O, dimidij arcuum E A M, O C P; </s>
            <s xml:id="echoid-s2013" xml:space="preserve">pro-
              <lb/>
            pterea quòd A L, ipſi A M, & </s>
            <s xml:id="echoid-s2014" xml:space="preserve">C O, ipſi C P, oſtenſus eſt ęqualis. </s>
            <s xml:id="echoid-s2015" xml:space="preserve">Aequales ergo
              <lb/>
            ſunt quoque arcus L A M, O C P, ae proinde & </s>
            <s xml:id="echoid-s2016" xml:space="preserve">rectę ſubtenſę L M, O P,
              <lb/>
              <note position="left" xlink:label="note-064-09" xlink:href="note-064-09a" xml:space="preserve">29. tetij.</note>
            æquales erunt. </s>
            <s xml:id="echoid-s2017" xml:space="preserve">Quare ex circulis ęqualibus E F, I K, auferent æquales arcus,
              <lb/>
              <note position="left" xlink:label="note-064-10" xlink:href="note-064-10a" xml:space="preserve">28. tertij.</note>
            maiorem quidem L F M, maiori O I P, & </s>
            <s xml:id="echoid-s2018" xml:space="preserve">minorem L E M, minori O K P,
              <lb/>
            (hoc eſt alternum ſegmentum alterno ſegmento) ęqualem. </s>
            <s xml:id="echoid-s2019" xml:space="preserve">Quod eſt pro po-
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            ſitum. </s>
            <s xml:id="echoid-s2020" xml:space="preserve">Itaque ſi in ſphęra maximus circulus parallelos aliquot circulos in
              <lb/>
            ſphęrica ſuperficie deſcriptos ſecet quidem, &</s>
            <s xml:id="echoid-s2021" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2022" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2023" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div195" type="section" level="1" n="98">
          <head xml:id="echoid-head110" xml:space="preserve">THEOREMA 18. PROPOS. 20.</head>
          <note position="left" xml:space="preserve">24.</note>
          <p>
            <s xml:id="echoid-s2024" xml:space="preserve">SI in ſphæra maximus circulus parallelos ali-
              <lb/>
            quot circulos ſecet, non tamen per polos; </s>
            <s xml:id="echoid-s2025" xml:space="preserve">de paral
              <lb/>
            lelorum aſſumptis cirtumferentijs in vno hemi-
              <lb/>
            ſphærio, illæ quæ propius accedunt ad polũ con-
              <lb/>
            ſpicuum, erunt maiores, quàm vt ſimiles eſſe poſ-
              <lb/>
            ſint illis, quæ ab eodem conſpicuo polo longius
              <lb/>
            abſunt.</s>
            <s xml:id="echoid-s2026" xml:space="preserve"/>
          </p>
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