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

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            <s xml:id="echoid-s2727" xml:space="preserve">
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            ro maximo circulo interceptarum inter prædictũ
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            punctum, & </s>
            <s xml:id="echoid-s2728" xml:space="preserve">vtrumque planorum parallelorum:
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            </s>
            <s xml:id="echoid-s2729" xml:space="preserve">Ea circunferentia, quæ eſt inter illud punctum, & </s>
            <s xml:id="echoid-s2730" xml:space="preserve">
              <lb/>
            planum, quod non conuenit cum communi ſe-
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            ctione ipſorum circulorum, maior eſt, quam ea
              <lb/>
            eiuſdem circuli circunferentia, quæ eſt inter idem
              <lb/>
            punctum, & </s>
            <s xml:id="echoid-s2731" xml:space="preserve">planum, quod conuenit cum com-
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            muni ſectione circulorum.</s>
            <s xml:id="echoid-s2732" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2733" xml:space="preserve">IN ſphæra duo maximi circuli A B C, D B E, ſe mutuo ſecent in B, & </s>
            <s xml:id="echoid-s2734" xml:space="preserve">in
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            A B C, ſumantur arcus B A, B C, æquales, & </s>
            <s xml:id="echoid-s2735" xml:space="preserve">per A, C, puncta duo plana pa-
              <lb/>
            rallela inter ſe ducantur facientia in ſuperficie ſphæræ circunferentias circu
              <lb/>
              <note position="left" xlink:label="note-082-01" xlink:href="note-082-01a" xml:space="preserve">L. 1. huius.</note>
            lorum A F G, C H I, quæ ſecent circunferentiam D B E, in punctis F, H; </s>
            <s xml:id="echoid-s2736" xml:space="preserve">ſit
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            verò arcus B A, vel B C, maior vtralibet circunferentiarum B F, B H, inter
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            punctum B, & </s>
            <s xml:id="echoid-s2737" xml:space="preserve">plana parallela interceptarum. </s>
            <s xml:id="echoid-s2738" xml:space="preserve">Ex polo deinde B, & </s>
            <s xml:id="echoid-s2739" xml:space="preserve">interual-
              <lb/>
            lo B A, vel B C, circulus deſcribatur A D C E, qui puncta F, H, tranſcen-
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            det, propterea quòd arcus B F, B H, minores ponuntur arcubus B A, B C.
              <lb/>
            </s>
            <s xml:id="echoid-s2740" xml:space="preserve">Producantur arcus B F, B H, vſque ad circunferentiam circuli A D C E,
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            ad puncta D, E; </s>
            <s xml:id="echoid-s2741" xml:space="preserve">ſintq́ue communes ſectiones circuli A D C E, & </s>
            <s xml:id="echoid-s2742" xml:space="preserve">circulorum
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            A F G, C H I, rectæ A G, C I; </s>
            <s xml:id="echoid-s2743" xml:space="preserve">communes autem ſectiones circulorum ma-
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              <figure xlink:label="fig-082-01" xlink:href="fig-082-01a" number="90">
                <image file="082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/082-01"/>
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            ximorum, & </s>
            <s xml:id="echoid-s2744" xml:space="preserve">circuli A D C E, rectæ A C,
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            D E; </s>
            <s xml:id="echoid-s2745" xml:space="preserve">quæ ipſius diametri erunt, atque adeo
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            eiuſdem centrum K, cum circuli maximi ip-
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            ſum per B, polum bifariam ſecent: </s>
            <s xml:id="echoid-s2746" xml:space="preserve">Secet au-
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              <note position="left" xlink:label="note-082-02" xlink:href="note-082-02a" xml:space="preserve">15. 1. huius.</note>
            tem recta D E, rectas A G, C I, in M, N.
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            </s>
            <s xml:id="echoid-s2747" xml:space="preserve">Sit quoque maximorum circulorum commu
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            nis ſectio K B, recta, cum qua producta ad par
              <lb/>
            tes B, conueniat planum A F G, productum
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            extra ſphæram in puncto L. </s>
            <s xml:id="echoid-s2748" xml:space="preserve">Quo poſito, non
              <lb/>
            conueniet alterum planum C H I, cum re-
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            cta K B, ad partes B, necum ſibi parallelo
              <lb/>
            plano A F G, conueniat. </s>
            <s xml:id="echoid-s2749" xml:space="preserve">Dico arcum B H,
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            maiorem eſſe arcu B F. </s>
            <s xml:id="echoid-s2750" xml:space="preserve">Sint enim rectæ F M,
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            H N, communes ſectiones circuli D B E, & </s>
            <s xml:id="echoid-s2751" xml:space="preserve">
              <lb/>
            circulorum A F G, C H I. </s>
            <s xml:id="echoid-s2752" xml:space="preserve">Et quoniam pla-
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            num A F C, conuenit productum cum recta
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            K B, producta in L, erit L, punctum tam in
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            plano D B E, quàm in plano A F G; </s>
            <s xml:id="echoid-s2753" xml:space="preserve">atque
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            adeo in cõmuni eorum ſectione, nempe in recta M F. </s>
            <s xml:id="echoid-s2754" xml:space="preserve">Producta ergo M F, coi-
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            bit cum K B, producta in L. </s>
            <s xml:id="echoid-s2755" xml:space="preserve">Quoniam verò planum D B E, ſecat plana pa-
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            rallela A F G, C H I, erunt ſectiones factæ M F, N H, parallelæ. </s>
            <s xml:id="echoid-s2756" xml:space="preserve">Rurſus quia
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              <note position="left" xlink:label="note-082-03" xlink:href="note-082-03a" xml:space="preserve">16. vndee.</note>
            planum A D C E, eadem plana parallela ſecat, erunt quoque ſectiones factæ
              <lb/>
              <note position="left" xlink:label="note-082-04" xlink:href="note-082-04a" xml:space="preserve">16. vndec.</note>
            A G, C I, parallelæ. </s>
            <s xml:id="echoid-s2757" xml:space="preserve">Anguli ergo alterni K A M, K C N, æquales ſunt:
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            </s>
            <s xml:id="echoid-s2758" xml:space="preserve">
              <note position="left" xlink:label="note-082-05" xlink:href="note-082-05a" xml:space="preserve">29. primi.</note>
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