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

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              <pb o="78" file="090" n="90" rhead=""/>
            K I, K L, vtroque K Y, K X, maior eſt. </s>
            <s xml:id="echoid-s3007" xml:space="preserve">Et quoniam recta per K, & </s>
            <s xml:id="echoid-s3008" xml:space="preserve">ſphęræ centrũ
              <lb/>
            ducta, id eſt, communis ſectio maximorum circulorum G H, E Y, ſecat pla-
              <lb/>
            num paralleli Q R, extra ſphæram, ſi recta illa, & </s>
            <s xml:id="echoid-s3009" xml:space="preserve">planum circuli Q R,
              <lb/>
            producantur ad partes K, vt in demonſtratione propoſ. </s>
            <s xml:id="echoid-s3010" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3011" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3012" xml:space="preserve">dictum
              <lb/>
            eſt; </s>
            <s xml:id="echoid-s3013" xml:space="preserve">erit arcus K Y, maior arcu K X: </s>
            <s xml:id="echoid-s3014" xml:space="preserve">Sed arcui K Y, arcus M O, & </s>
            <s xml:id="echoid-s3015" xml:space="preserve">arcui K X,
              <lb/>
              <note position="left" xlink:label="note-090-01" xlink:href="note-090-01a" xml:space="preserve">4. huius.</note>
            arcus O Q, æqualis eſt; </s>
            <s xml:id="echoid-s3016" xml:space="preserve">Sunt enim ſemicirculi, quorum vnus ex A, per B, al-
              <lb/>
              <note position="left" xlink:label="note-090-02" xlink:href="note-090-02a" xml:space="preserve">13. 2. huius</note>
            ter vero ex E, per K, ducitur, non conuenientes, vt ex ijs, quæ in demonſtra-
              <lb/>
            tione propoſ. </s>
            <s xml:id="echoid-s3017" xml:space="preserve">13. </s>
            <s xml:id="echoid-s3018" xml:space="preserve">ſecundi lib. </s>
            <s xml:id="echoid-s3019" xml:space="preserve">diximus, perſpicuum eſt. </s>
            <s xml:id="echoid-s3020" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3021" xml:space="preserve">arcus M O, ma-
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            ior erit arcu O Q. </s>
            <s xml:id="echoid-s3022" xml:space="preserve">Siergo in ſphæra maximus circulus tangat, &</s>
            <s xml:id="echoid-s3023" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3024" xml:space="preserve">Quod
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            demonſtrandum erat.</s>
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        <div xml:id="echoid-div256" type="section" level="1" n="120">
          <head xml:id="echoid-head134" xml:space="preserve">THEOREMA 8. PROPOS. 8.</head>
          <note position="left" xml:space="preserve">6.</note>
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            <s xml:id="echoid-s3026" xml:space="preserve">SI in ſphæra maximus circulus aliquem ſphæ-
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            ræ circulum tangat, aliquis autem alius maximus
              <lb/>
            circulus obliquus ad parallelos tangat circulos ma
              <lb/>
            iores illis, quos tangebat maximus circulus primo
              <lb/>
            poſitus, fuerintque eorum contactus in maximo
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            circulo primo poſito; </s>
            <s xml:id="echoid-s3027" xml:space="preserve">ſumantur autem de obliquo
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            circulo æquales circunferentiæ continuæ ad eaſ-
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            dem partes maximi parallelorum, perque puncta
              <lb/>
            terminantia æquales circunferentias deſcribantur
              <lb/>
            maximi circuli, qui & </s>
            <s xml:id="echoid-s3028" xml:space="preserve">tangant eundem circulum,
              <lb/>
            quem tangebat maximus circulus primo poſitus,
              <lb/>
            & </s>
            <s xml:id="echoid-s3029" xml:space="preserve">ſimiles parallelorú circunferentias intercipiant,
              <lb/>
            habeantque eos ſemicirculos, qui tendunt à pun-
              <lb/>
            ctis contactuum ad puncta terminantia æquales
              <lb/>
            obliqui circuli circunferentias, per quæ deſcribun-
              <lb/>
            tur, eiuſmodi, vt minime conueniant cum illo cir
              <lb/>
            culi maximi primo poſiti ſemicirculo, in quo eſt
              <lb/>
            contactus obliqui circuli inter apparentem po-
              <lb/>
            lum, & </s>
            <s xml:id="echoid-s3030" xml:space="preserve">maximum parallelorum: </s>
            <s xml:id="echoid-s3031" xml:space="preserve">Inæquales </s>
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