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

Table of figures

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          <p>
            <s xml:id="echoid-s1622" xml:space="preserve">
              <pb o="43" file="055" n="55" rhead=""/>
              <figure xlink:label="fig-055-01" xlink:href="fig-055-01a" number="61">
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            cus K O, arcui N A, & </s>
            <s xml:id="echoid-s1623" xml:space="preserve">
              <lb/>
            arcus K P, arcui N B, æ-
              <lb/>
            qualis, vt ſint quoque ſe
              <lb/>
            micirculi A M O, O F A;
              <lb/>
            </s>
            <s xml:id="echoid-s1624" xml:space="preserve">B G P, P H B. </s>
            <s xml:id="echoid-s1625" xml:space="preserve">Eruntigi-
              <lb/>
            tur ſemicirculi A M O,
              <lb/>
            B H P, non coeuntes, cũ
              <lb/>
            ſe mutuo non ſecent. </s>
            <s xml:id="echoid-s1626" xml:space="preserve">Eo
              <lb/>
            dem modo nõ coeuntes
              <lb/>
            erunt ſemicirculi B G P,
              <lb/>
            A F O. </s>
            <s xml:id="echoid-s1627" xml:space="preserve">Dico arcus paral
              <lb/>
            lelorum A B, L E, M H,
              <lb/>
            interceptos inter ſemi-
              <lb/>
            circulos A M O, B H P,
              <lb/>
            non coeuntes ſimiles eſ-
              <lb/>
            ſe, necnon & </s>
            <s xml:id="echoid-s1628" xml:space="preserve">arcus A B,
              <lb/>
            C D, F G, interceptos in
              <lb/>
            ter ſemicirculos B G P,
              <lb/>
            A F O, non concurren-
              <lb/>
            tes ſimiles eſſe: </s>
            <s xml:id="echoid-s1629" xml:space="preserve">Arcus vero maximorum circulorum A C, A L, B D, B E, æ-
              <lb/>
            quales eſſe; </s>
            <s xml:id="echoid-s1630" xml:space="preserve">necnon & </s>
            <s xml:id="echoid-s1631" xml:space="preserve">arcus C F, L M, D G, E H: </s>
            <s xml:id="echoid-s1632" xml:space="preserve">quorum illi inter paralle-
              <lb/>
            los A B, C D E, hi vero inter parallelos C D E, F G H, interijciuntur: </s>
            <s xml:id="echoid-s1633" xml:space="preserve">Eo-
              <lb/>
            demq́; </s>
            <s xml:id="echoid-s1634" xml:space="preserve">pacto æquales eſſe arcus A F, A M, B G, B H, inter parallelos A B,
              <lb/>
              <note position="right" xlink:label="note-055-01" xlink:href="note-055-01a" xml:space="preserve">20 1. huius.</note>
            F G H, interiectos. </s>
            <s xml:id="echoid-s1635" xml:space="preserve">Per polum enim I, & </s>
            <s xml:id="echoid-s1636" xml:space="preserve">puncta contactuum A, B, circuli
              <lb/>
            maximi deſcribantur Q A I R, S B I T, ſecantes parallelos in Q, S, V, X.
              <lb/>
            </s>
            <s xml:id="echoid-s1637" xml:space="preserve">Tranſibunt hi circuli maximi per polos quoque circulorum A F K, B H K; </s>
            <s xml:id="echoid-s1638" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-055-02" xlink:href="note-055-02a" xml:space="preserve">5. huius.</note>
            ac proinde bifariam ſecabunt ſegmenta C A L, D B E, C V L, D X E: </s>
            <s xml:id="echoid-s1639" xml:space="preserve">necnõ
              <lb/>
              <note position="right" xlink:label="note-055-03" xlink:href="note-055-03a" xml:space="preserve">9. huius.</note>
            ſegmenta F A M, G B H, F Q M, G S H. </s>
            <s xml:id="echoid-s1640" xml:space="preserve">Præterea ijdem circuli ad angulos
              <lb/>
            rectos ſecabunt parallelos A B, C D E, F G H, & </s>
            <s xml:id="echoid-s1641" xml:space="preserve">maximos circulos A F K,
              <lb/>
              <note position="right" xlink:label="note-055-04" xlink:href="note-055-04a" xml:space="preserve">15. 1. huius.</note>
            B H K. </s>
            <s xml:id="echoid-s1642" xml:space="preserve">Quoniam igitur diametris circulorum æqualium A F K, B H K, inſi
              <lb/>
            ſtunt ad angulos rectos ſegmenta circulorum æqualia, nempe ſemicirculi in-
              <lb/>
            choati à punctis A, B, & </s>
            <s xml:id="echoid-s1643" xml:space="preserve">per I, tranſeũtes, donec iterũ ſecent circulos A F K,
              <lb/>
            B H K; </s>
            <s xml:id="echoid-s1644" xml:space="preserve">ſuntq́; </s>
            <s xml:id="echoid-s1645" xml:space="preserve">arcus æquales A I, B I, quòd ex defin. </s>
            <s xml:id="echoid-s1646" xml:space="preserve">poli recta I A, IB æqua
              <lb/>
              <note position="right" xlink:label="note-055-05" xlink:href="note-055-05a" xml:space="preserve">28. tertij.</note>
            les ſint; </s>
            <s xml:id="echoid-s1647" xml:space="preserve">qui quidem minores ſunt dimidijs ſemicirculorum partibus: </s>
            <s xml:id="echoid-s1648" xml:space="preserve">(cum
              <lb/>
            enim dimidij ſint arcuum A I R, B I T, quòd, ex defin. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">poli, rectæ ex I, ad
              <lb/>
              <note position="right" xlink:label="note-055-06" xlink:href="note-055-06a" xml:space="preserve">28. tertij.</note>
            puncta A, B, R, T, atque adeo arcus quoque ſint æquales: </s>
            <s xml:id="echoid-s1650" xml:space="preserve">ſint autem arcus
              <lb/>
            A I R, B I T, ſemicirculo minores, quòd ſemicirculi tendant ex A, & </s>
            <s xml:id="echoid-s1651" xml:space="preserve">B, per
              <lb/>
            I, vſque ad circulos A F K, B H K; </s>
            <s xml:id="echoid-s1652" xml:space="preserve">erunt arcus A I, B I, minores dimidijs par
              <lb/>
            tibus illorum ſemicirculorum.) </s>
            <s xml:id="echoid-s1653" xml:space="preserve">ſunt quoque æquales rectæ I C, I E, ex po-
              <lb/>
            li defin. </s>
            <s xml:id="echoid-s1654" xml:space="preserve">erunt arcus A C, B E, æquales: </s>
            <s xml:id="echoid-s1655" xml:space="preserve">Eſt autem A C, ipſi A L, & </s>
            <s xml:id="echoid-s1656" xml:space="preserve">B E, ipſi
              <lb/>
              <note position="right" xlink:label="note-055-07" xlink:href="note-055-07a" xml:space="preserve">11. huius.</note>
            B D, æqualis, propterea quòd arcus C A L, D B E, bifariam ſecantur, vt de-
              <lb/>
              <note position="right" xlink:label="note-055-08" xlink:href="note-055-08a" xml:space="preserve">9. huius.</note>
            monſtratum eſt. </s>
            <s xml:id="echoid-s1657" xml:space="preserve">Quatuor ergo arcus A C, A L, B E, B D, æquales ſunt. </s>
            <s xml:id="echoid-s1658" xml:space="preserve">Eo-
              <lb/>
            dem modo oſtendemus, æquales eſſe quatuor arcus A F, A M, B H, B G; </s>
            <s xml:id="echoid-s1659" xml:space="preserve">ac
              <lb/>
            propterea & </s>
            <s xml:id="echoid-s1660" xml:space="preserve">reliquos C F, L M, E H, D G, qui quidem ſinguli inter binos
              <lb/>
            parallelos intercipiuntur. </s>
            <s xml:id="echoid-s1661" xml:space="preserve">Quodſecundo loco proponebatur demonſtrandũ.</s>
            <s xml:id="echoid-s1662" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1663" xml:space="preserve">QVIA vero arcus toti C A L, D B E, æquales ſunt, quòd ipſorum dimi
              <lb/>
            dia æqualia ſint, vt demonſtratum eſt; </s>
            <s xml:id="echoid-s1664" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s1665" xml:space="preserve">rectæ ſubtenſæ C L, D E, æ-
              <lb/>
              <note position="right" xlink:label="note-055-09" xlink:href="note-055-09a" xml:space="preserve">29. tertij.</note>
            quales, quæ quidem arcubus quoque C V L, D X E, ſubtenduntur; </s>
            <s xml:id="echoid-s1666" xml:space="preserve">ac </s>
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