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

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        <div xml:id="echoid-div246" type="section" level="1" n="116">
          <p>
            <s xml:id="echoid-s2836" xml:space="preserve">
              <pb o="73" file="085" n="85" rhead=""/>
            erit & </s>
            <s xml:id="echoid-s2837" xml:space="preserve">arcus G Q, omnium ex G, cadentium minimus, hoc eſt, minor, quàm
              <lb/>
              <note position="right" xlink:label="note-085-01" xlink:href="note-085-01a" xml:space="preserve">Schol. 21. 2
                <lb/>
              huius.</note>
            G H: </s>
            <s xml:id="echoid-s2838" xml:space="preserve">quod arcus G Q, G H, minores ſint ſemicirculo, cum ſe non inter-
              <lb/>
            ſecent, antequàm parallelo N O, occurrant. </s>
            <s xml:id="echoid-s2839" xml:space="preserve">Vterque igitur arcus F G,
              <lb/>
            G H, vtroque G P, G Q, maior eſt. </s>
            <s xml:id="echoid-s2840" xml:space="preserve">Et quoniam recta per G, & </s>
            <s xml:id="echoid-s2841" xml:space="preserve">centrum
              <lb/>
            ſphæræ ducta, id eſt, communis ſectio circulorum maximorum A P, E C, ſe-
              <lb/>
            cant paralleli I K, planum intra ſphæram; </s>
            <s xml:id="echoid-s2842" xml:space="preserve">(non enim recta illa ad centrum
              <lb/>
            ſphæræ perueniet, hoc eſt, ad centrum maximi circuli B D, niſi prius planum
              <lb/>
            circuli I K, ſecet; </s>
            <s xml:id="echoid-s2843" xml:space="preserve">quòd parallelus I K, poſitus ſit inter maximum parallelo-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s2844" xml:space="preserve">punctum G.) </s>
            <s xml:id="echoid-s2845" xml:space="preserve">ſecabit eadem recta planum paralleli N O, extra ſphæ-
              <lb/>
            ram, ſirecta illa, & </s>
            <s xml:id="echoid-s2846" xml:space="preserve">planum circuli ad partes G, producantur: </s>
            <s xml:id="echoid-s2847" xml:space="preserve">propterea
              <lb/>
            quòd punctum G, poſitum eſt inter maximum parallelorum, & </s>
            <s xml:id="echoid-s2848" xml:space="preserve">parallelum
              <lb/>
            N O. </s>
            <s xml:id="echoid-s2849" xml:space="preserve">Quoniam igitur duo circuli maximi A P, E C, ſe mutuo ſecant in G,
              <lb/>
            puncto, & </s>
            <s xml:id="echoid-s2850" xml:space="preserve">à circulo E C, vtrinque à puncto G, duo arcus æquales ſumpti
              <lb/>
            ſunt G F, G H, & </s>
            <s xml:id="echoid-s2851" xml:space="preserve">per F, H, plana parallela circulorum I K, N O, ducta,
              <lb/>
            quorum N O, occurrit commnni ſectioni circulorum maximorum A P,
              <lb/>
            E C, extra ſphæram, vt oſtenſum eſt, eſtq́ue vterque arcuum G F, G H, ma-
              <lb/>
            ior vtroque arcuum G P, G Q, erit arcus G P, maior arcu G Q. </s>
            <s xml:id="echoid-s2852" xml:space="preserve">Eſt au-
              <lb/>
              <note position="right" xlink:label="note-085-02" xlink:href="note-085-02a" xml:space="preserve">4. huius.</note>
            tem arcus G P, arcui I L, & </s>
            <s xml:id="echoid-s2853" xml:space="preserve">arcus G Q, arcui L N, æqualis. </s>
            <s xml:id="echoid-s2854" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s2855" xml:space="preserve">arcus
              <lb/>
              <note position="right" xlink:label="note-085-03" xlink:href="note-085-03a" xml:space="preserve">10. 2. huius.</note>
            I L, arcu L N, maior erit. </s>
            <s xml:id="echoid-s2856" xml:space="preserve">Quare ſi in circunferentia maximi circuli ſit po-
              <lb/>
            lus, &</s>
            <s xml:id="echoid-s2857" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2858" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s2859" xml:space="preserve"/>
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        <div xml:id="echoid-div248" type="section" level="1" n="117">
          <head xml:id="echoid-head131" xml:space="preserve">THEOREMA 6. PROPOS. 6.</head>
          <p>
            <s xml:id="echoid-s2860" xml:space="preserve">SI in circunferentia maximi circuli ſit polus
              <lb/>
            parallelorum, huncq́; </s>
            <s xml:id="echoid-s2861" xml:space="preserve">maximum circulum ad an-
              <lb/>
            gulos rectos ſecentduo alij circuli maximi, quo-
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            rum alter ſit vnus parallelorũ, alter verò obliquus
              <lb/>
            ſit ad parallelos; </s>
            <s xml:id="echoid-s2862" xml:space="preserve">ſumantur autem ab obliquo circu
              <lb/>
            lo æquales circunferentiæ deinceps ad eaſdem par
              <lb/>
            tes maximi illius paralleli, & </s>
            <s xml:id="echoid-s2863" xml:space="preserve">per puncta terminan-
              <lb/>
            tia æquales circũferentias, perq́; </s>
            <s xml:id="echoid-s2864" xml:space="preserve">polum, deſcriban-
              <lb/>
            tur maximi circuli: </s>
            <s xml:id="echoid-s2865" xml:space="preserve">Hi circunferentias inæquales
              <lb/>
            intercipient de maximo parallelorum, quarum
              <lb/>
            propior maximo circulo primo poſito ſemper erit
              <lb/>
            remotiore maior.</s>
            <s xml:id="echoid-s2866" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2867" xml:space="preserve">IN circunferentia maximi circuli A B C D, ſit A, polus parallelorum,
              <lb/>
            eumq́ue ſecent duo maximi circuli B D, E C, adangulos rectos, quorum B D,
              <lb/>
            ſit parallelorum maximus, at E C, ad parallelos obliquus, ex quo </s>
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