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

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        <div xml:id="echoid-div263" type="section" level="1" n="123">
          <head xml:id="echoid-head137" xml:space="preserve">THEOREMA 9. PROPOS. 9.</head>
          <note position="left" xml:space="preserve">8.</note>
          <p>
            <s xml:id="echoid-s3153" xml:space="preserve">SI polus parallelorum ſit in circunſerentia ma-
              <lb/>
            ximi circuli, quem duo alij maximi circuli ad an -
              <lb/>
            gulos rectos ſecent, quorum circulorum alter ſit
              <lb/>
            vnus parallelorũ, alter verò ad parallelos obliquus
              <lb/>
            ſit: </s>
            <s xml:id="echoid-s3154" xml:space="preserve">& </s>
            <s xml:id="echoid-s3155" xml:space="preserve">ab hoc obliquo circulo ſumantur æquales
              <lb/>
            circunferentiæ, quæ continuæ quidem non ſint,
              <lb/>
            ſed tamen ſint ad eaſdem partes maximi illius pa-
              <lb/>
            ralleli; </s>
            <s xml:id="echoid-s3156" xml:space="preserve">per polum autem, & </s>
            <s xml:id="echoid-s3157" xml:space="preserve">ſingula puncta æqua-
              <lb/>
            les circunferentias terminantia deſcribantur ma-
              <lb/>
            ximi circuli: </s>
            <s xml:id="echoid-s3158" xml:space="preserve">Inæquales circunferentias de maxi-
              <lb/>
            mo parallelo intercipient, quarum ea, quæ pro-
              <lb/>
            pior erit maximo circulo primo poſito, ſemper
              <lb/>
            erit maior remotiore.</s>
            <s xml:id="echoid-s3159" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3160" xml:space="preserve">IN circunſerentia maximi circuli A B, ſit A, polus parallelorum, eum-
              <lb/>
            que ſecent duo maximi circuli B C, D C, ad angulos rectos, quorum B C,
              <lb/>
            ſit maximus parallelorum, & </s>
            <s xml:id="echoid-s3161" xml:space="preserve">D C, ad parallelos obliquus; </s>
            <s xml:id="echoid-s3162" xml:space="preserve">ex quo ſuman-
              <lb/>
            tur arcus æquales non continui E F, G H: </s>
            <s xml:id="echoid-s3163" xml:space="preserve">& </s>
            <s xml:id="echoid-s3164" xml:space="preserve">per puncta E, F, G, H, & </s>
            <s xml:id="echoid-s3165" xml:space="preserve">polum
              <lb/>
            A, deſcribantur maximi circuli A E I, A F K, A G L, A H M. </s>
            <s xml:id="echoid-s3166" xml:space="preserve">Dico arcum M L,
              <lb/>
              <note position="left" xlink:label="note-094-02" xlink:href="note-094-02a" xml:space="preserve">20. 1. huius</note>
            maiorem eſſe arcu K I. </s>
            <s xml:id="echoid-s3167" xml:space="preserve">Autenim intermedius arcus F G, vtrique æqualium
              <lb/>
              <figure xlink:label="fig-094-01" xlink:href="fig-094-01a" number="100">
                <image file="094-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/094-01"/>
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            E F, G H, commenſurabilis eſt, aut incommen
              <lb/>
            ſurabilis. </s>
            <s xml:id="echoid-s3168" xml:space="preserve">Sit primum commenſurabilis. </s>
            <s xml:id="echoid-s3169" xml:space="preserve">In-
              <lb/>
            uenta autem maxima communi menſura X,
              <lb/>
              <note position="left" xlink:label="note-094-03" xlink:href="note-094-03a" xml:space="preserve">4. decimi.</note>
            diuidantur tres arcus E F, F G, G H, in par-
              <lb/>
            tes ipſi X, æquales, vt in prima figura appa-
              <lb/>
            ret; </s>
            <s xml:id="echoid-s3170" xml:space="preserve">& </s>
            <s xml:id="echoid-s3171" xml:space="preserve">per puncta diuiſionum, & </s>
            <s xml:id="echoid-s3172" xml:space="preserve">polum A,
              <lb/>
            circuli maximi ducantur. </s>
            <s xml:id="echoid-s3173" xml:space="preserve">Quoniam igitur ar-
              <lb/>
              <note position="left" xlink:label="note-094-04" xlink:href="note-094-04a" xml:space="preserve">20. 1. huius.</note>
            cus E Q, Q F, F P, &</s>
            <s xml:id="echoid-s3174" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3175" xml:space="preserve">æquales ſunt, ma-
              <lb/>
            ior erit arcus M R, arcu R L, & </s>
            <s xml:id="echoid-s3176" xml:space="preserve">R L, maior,
              <lb/>
              <note position="left" xlink:label="note-094-05" xlink:href="note-094-05a" xml:space="preserve">6. huius.</note>
            quàm L, S, &</s>
            <s xml:id="echoid-s3177" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3178" xml:space="preserve">Igitur cum M R, maior ſit
              <lb/>
            quàm K V, & </s>
            <s xml:id="echoid-s3179" xml:space="preserve">R L, maior quàm V I, erit & </s>
            <s xml:id="echoid-s3180" xml:space="preserve">
              <lb/>
            totus M L, maior toto K I. </s>
            <s xml:id="echoid-s3181" xml:space="preserve">quod eſt propo-
              <lb/>
            ſitum.</s>
            <s xml:id="echoid-s3182" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3183" xml:space="preserve">SED iam ſit arcus intermedius F G, in
              <lb/>
            commenſurabilis vtrique arcuum æqualium E F, G H. </s>
            <s xml:id="echoid-s3184" xml:space="preserve">Dico Rurſus arcum
              <lb/>
            M L, maiorem eſſe arcu K I. </s>
            <s xml:id="echoid-s3185" xml:space="preserve">Si enim maior non eſt, erit vel minor, vel æqua-
              <lb/>
            lis. </s>
            <s xml:id="echoid-s3186" xml:space="preserve">Sit primum, ſi ſieri poteſt, M L, minor quàm K I, vt in ſecunda figura;</s>
            <s xml:id="echoid-s3187" xml:space="preserve"/>
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