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

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          <p>
            <s xml:id="echoid-s1895" xml:space="preserve">
              <pb o="50" file="062" n="62" rhead=""/>
            ſcribatur G I H K, qui circulum A C E F D B, ſecabit duobus in punctis, vt in
              <lb/>
              <note position="left" xlink:label="note-062-01" xlink:href="note-062-01a" xml:space="preserve">10. 1. huius.</note>
            I, K, ad angulos rectos. </s>
            <s xml:id="echoid-s1896" xml:space="preserve">Quoniam igitur circulus maximus G I H K, per po
              <lb/>
              <note position="left" xlink:label="note-062-02" xlink:href="note-062-02a" xml:space="preserve">15. 1. huius.</note>
            los maximorum circulorum A C E F D B, C D, tranſit, ex conftructione, trã-
              <lb/>
            ſibunt hi viciſsim per illius polos. </s>
            <s xml:id="echoid-s1897" xml:space="preserve">Puncta igitur C, D, vbi ſe duo hi circuli
              <lb/>
              <note position="left" xlink:label="note-062-03" xlink:href="note-062-03a" xml:space="preserve">Schol. 15. 1.
                <lb/>
              huius.</note>
            interſecant, poli erunt circuli GIHK; </s>
            <s xml:id="echoid-s1898" xml:space="preserve">(alias non vterque circulus A C E F D,
              <lb/>
            C D, per polos circuli G I H K, tranſiret) ac proinde ductæ rectę C I, C K, ex
              <lb/>
              <figure xlink:label="fig-062-01" xlink:href="fig-062-01a" number="71">
                <image file="062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/062-01"/>
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            defin. </s>
            <s xml:id="echoid-s1899" xml:space="preserve">poli, æquales erunt, ac propterea & </s>
            <s xml:id="echoid-s1900" xml:space="preserve">ar
              <lb/>
            cus C I, C K, inter ſe erunt æquales. </s>
            <s xml:id="echoid-s1901" xml:space="preserve">Sunt
              <lb/>
              <note position="left" xlink:label="note-062-04" xlink:href="note-062-04a" xml:space="preserve">23. tertij.</note>
            autem & </s>
            <s xml:id="echoid-s1902" xml:space="preserve">arcus A C, C E, per hypotheſim,
              <lb/>
            æquales Reliqui igitur arcus A I, E K, æqua
              <lb/>
            les quoque erunt. </s>
            <s xml:id="echoid-s1903" xml:space="preserve">Rurſus quia ſemicirculus
              <lb/>
            I G K; </s>
            <s xml:id="echoid-s1904" xml:space="preserve">ſemicirculo G K H, æqualis eſt; </s>
            <s xml:id="echoid-s1905" xml:space="preserve">(Diui-
              <lb/>
              <note position="left" xlink:label="note-062-05" xlink:href="note-062-05a" xml:space="preserve">11. 1. huius.</note>
            dunt enim ſe mutuo circuli A C E F D B, & </s>
            <s xml:id="echoid-s1906" xml:space="preserve">
              <lb/>
            G I H K, bifariam; </s>
            <s xml:id="echoid-s1907" xml:space="preserve">ac proinde I G K, ſemicir
              <lb/>
            culus eft; </s>
            <s xml:id="echoid-s1908" xml:space="preserve">Arcus autem G K H, ſemicireulus
              <lb/>
            eſt propter G, H, polos parallelorum.) </s>
            <s xml:id="echoid-s1909" xml:space="preserve">dem
              <lb/>
            pto communi arcu G K, erunt reliqui arcus
              <lb/>
            G I, H K, æquales. </s>
            <s xml:id="echoid-s1910" xml:space="preserve">Quoniam igitur in dia-
              <lb/>
            metro circuli I C K D, ſegmenta circulorũ
              <lb/>
            æqualia I G K, K H I, quæ ſemicirculi ſunt,
              <lb/>
              <note position="left" xlink:label="note-062-06" xlink:href="note-062-06a" xml:space="preserve">@@ 1. huius.</note>
            vt oſtendimus, inſiſtunt ad angulos rectos, ſuntque arcus I G, K H, æquales,
              <lb/>
            & </s>
            <s xml:id="echoid-s1911" xml:space="preserve">non ſunt ſegmentorum ſemiſſes, ſiue quadrantes, cum G, H, non ſint poli
              <lb/>
            circuli I C K D: </s>
            <s xml:id="echoid-s1912" xml:space="preserve">Item æquales ſunt arcus I A, K E, vt demonſtratum eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s1913" xml:space="preserve">erunt rectæ demiſſæ G A, H E, æquales. </s>
            <s xml:id="echoid-s1914" xml:space="preserve">Quarc circuli A B, E F, æquales in-
              <lb/>
              <note position="left" xlink:label="note-062-07" xlink:href="note-062-07a" xml:space="preserve">12. huius.</note>
            ter ſe erunt.</s>
            <s xml:id="echoid-s1915" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Schol. 21. 1
            <lb/>
          huius.</note>
          <p>
            <s xml:id="echoid-s1916" xml:space="preserve">QVOD ſi arcus A C, maiot ponatur arcu C E; </s>
            <s xml:id="echoid-s1917" xml:space="preserve">Dico circulum A B, mi-
              <lb/>
            norom eſſe circulo E F. </s>
            <s xml:id="echoid-s1918" xml:space="preserve">Sumpto enim arcu C L, quiæqualis ſit arcui C E, erit,
              <lb/>
            vt proxime demonſtratum eſt, parallelus per L, deſcriptus æqualis parallelo
              <lb/>
            E F: </s>
            <s xml:id="echoid-s1919" xml:space="preserve">ſed parallclus A B, minor eſt, quàm parallelus per L, deſcriptus, cum ille
              <lb/>
              <note position="left" xlink:label="note-062-09" xlink:href="note-062-09a" xml:space="preserve">6. 1. huius</note>
            longius à maximo parallelorum, atque adeo à centro ſphæræ, abſit. </s>
            <s xml:id="echoid-s1920" xml:space="preserve">Minor igi
              <lb/>
            tur quoque eſt parallelus A B, quam E F. </s>
            <s xml:id="echoid-s1921" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s1922" xml:space="preserve">In ſphæra
              <lb/>
            ergo paralleli circuli, inter quos & </s>
            <s xml:id="echoid-s1923" xml:space="preserve">maximum parallelorum, &</s>
            <s xml:id="echoid-s1924" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1925" xml:space="preserve">Quod erat.
              <lb/>
            </s>
            <s xml:id="echoid-s1926" xml:space="preserve">demonſtrandum.</s>
            <s xml:id="echoid-s1927" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div189" type="section" level="1" n="96">
          <head xml:id="echoid-head108" xml:space="preserve">THEOR 16. PROPOS. 18.</head>
          <note position="left" xml:space="preserve">22.</note>
          <p>
            <s xml:id="echoid-s1928" xml:space="preserve">IN ſphæra circunferentiæ maximorum circu-
              <lb/>
            lorum interceptæ inter maximum parallelorum,
              <lb/>
            & </s>
            <s xml:id="echoid-s1929" xml:space="preserve">duos alios circulos æquales, & </s>
            <s xml:id="echoid-s1930" xml:space="preserve">parallelos, ſunt
              <lb/>
            æquales: </s>
            <s xml:id="echoid-s1931" xml:space="preserve">Illæ vero, quæ intercipiuntur inter maio-
              <lb/>
            rem parallelum, & </s>
            <s xml:id="echoid-s1932" xml:space="preserve">maximum, ſunt minores.</s>
            <s xml:id="echoid-s1933" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1934" xml:space="preserve">IN ſphæra ſint duo paralleli æquales A B, C D, & </s>
            <s xml:id="echoid-s1935" xml:space="preserve">maximus parallelorũ
              <lb/>
            fit E F: </s>
            <s xml:id="echoid-s1936" xml:space="preserve">Hos autem omnes parallelos ſecet maximus alius circulus A C D B.
              <lb/>
            </s>
            <s xml:id="echoid-s1937" xml:space="preserve">Dico arcus A E, E C, nec non B F, F D, æquales eſſe. </s>
            <s xml:id="echoid-s1938" xml:space="preserve">Si enim non ſunt </s>
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