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

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          <p>
            <s xml:id="echoid-s2971" xml:space="preserve">
              <pb o="77" file="089" n="89" rhead=""/>
            cunferentiæ æquales, & </s>
            <s xml:id="echoid-s2972" xml:space="preserve">continuæ ad eaſdem par-
              <lb/>
            tes maximi parallelorum; </s>
            <s xml:id="echoid-s2973" xml:space="preserve">per puncta autem termi-
              <lb/>
            nantia æquales circunferentias deſcribantur paral
              <lb/>
            leli circuli: </s>
            <s xml:id="echoid-s2974" xml:space="preserve">Hi circumferentias inæquales interci-
              <lb/>
            pient de maximo circulo primo poſito, quorum
              <lb/>
            ea, quæ propior erit maximo parallelorum, erit
              <lb/>
            maior remotiore.</s>
            <s xml:id="echoid-s2975" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2976" xml:space="preserve">IN ſphæra maximus circulus A B C D, tangat circulum A E, in puncto
              <lb/>
            A; </s>
            <s xml:id="echoid-s2977" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s2978" xml:space="preserve">alium C F, illi æqualem: </s>
            <s xml:id="echoid-s2979" xml:space="preserve">Alius autem circulus maximus G H,
              <lb/>
              <note position="right" xlink:label="note-089-01" xlink:href="note-089-01a" xml:space="preserve">6. 3. huius.</note>
            ad parallelos obliquus tangat alios duos circulos maiores illis, quos A B C D,
              <lb/>
            tangit, ſintq́ue puncta contactuum G, H, in maximo circulo ABCD; </s>
            <s xml:id="echoid-s2980" xml:space="preserve">ſitq́;
              <lb/>
            </s>
            <s xml:id="echoid-s2981" xml:space="preserve">B D, maximus parallelorum: </s>
            <s xml:id="echoid-s2982" xml:space="preserve">Ex obliquo denique circulo G H, ſumantur
              <lb/>
            arcus æquales Ik, K L, & </s>
            <s xml:id="echoid-s2983" xml:space="preserve">per puncta I, k, L, paralleli deſcribantur M N, O P,
              <lb/>
            Q R. </s>
            <s xml:id="echoid-s2984" xml:space="preserve">Dico arcum M O, maiorem eſſe arcu O Q. </s>
            <s xml:id="echoid-s2985" xml:space="preserve">Nam per k, & </s>
            <s xml:id="echoid-s2986" xml:space="preserve">S, polum pa-
              <lb/>
            rallelorum circulus maximus dcfcribatur Sk, ſecans parallelos in punctis T,
              <lb/>
              <note position="right" xlink:label="note-089-02" xlink:href="note-089-02a" xml:space="preserve">20. 1. huius</note>
              <figure xlink:label="fig-089-01" xlink:href="fig-089-01a" number="96">
                <image file="089-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/089-01"/>
              </figure>
            V. </s>
            <s xml:id="echoid-s2987" xml:space="preserve">Item per k, deſcribatur ma-
              <lb/>
            ximus circulus kE, tangens
              <lb/>
            parallelum A E, in E, ſecansq́;
              <lb/>
            </s>
            <s xml:id="echoid-s2988" xml:space="preserve">
              <note position="right" xlink:label="note-089-03" xlink:href="note-089-03a" xml:space="preserve">15. 1. huius</note>
            parallelos alios in X, Y; </s>
            <s xml:id="echoid-s2989" xml:space="preserve">ita ta-
              <lb/>
            men, vt hæc puncta X, Y, ſint
              <lb/>
            inter puncta L, T, & </s>
            <s xml:id="echoid-s2990" xml:space="preserve">V, I. </s>
            <s xml:id="echoid-s2991" xml:space="preserve">quod
              <lb/>
            ita fiet. </s>
            <s xml:id="echoid-s2992" xml:space="preserve">Quoniam per k, duo
              <lb/>
              <note position="right" xlink:label="note-089-04" xlink:href="note-089-04a" xml:space="preserve">ſchol 15. 2.
                <lb/>
              huius.</note>
            circuli deſcribi poſſunt tágen-
              <lb/>
            ntes circulum A E, quorum
              <lb/>
            vnus inter arcus kG, kS, ca-
              <lb/>
            dit, alter vero extra ipſos; </s>
            <s xml:id="echoid-s2993" xml:space="preserve">(Nã
              <lb/>
            ſi ambo ex eadem parte circu-
              <lb/>
            lum A E, tangerent, ſecarent
              <lb/>
            ſeſe mutuo prope puncta con-
              <lb/>
            tactuum, quòd alter alteri oc-
              <lb/>
            curreret. </s>
            <s xml:id="echoid-s2994" xml:space="preserve">quod eſt abſurdum;
              <lb/>
            </s>
            <s xml:id="echoid-s2995" xml:space="preserve">cum ſe interſecent in puncto,
              <lb/>
            quod ipſi K, opponitur inter
              <lb/>
            alterum polum, & </s>
            <s xml:id="echoid-s2996" xml:space="preserve">maximum
              <lb/>
            parallelorũ.) </s>
            <s xml:id="echoid-s2997" xml:space="preserve">ſi prior ſumatur,
              <lb/>
            cadẽt puncta X, Y, inter puncta L, T, & </s>
            <s xml:id="echoid-s2998" xml:space="preserve">V, I, vt patet. </s>
            <s xml:id="echoid-s2999" xml:space="preserve">Igitur quoniã in ſpheræ
              <lb/>
            ſuperficie intra peripheriam circuli M N, punctum k, ſignatum eſt præter po-
              <lb/>
            lum S, & </s>
            <s xml:id="echoid-s3000" xml:space="preserve">ex k, tres arcus cadunt in eius circunferentiam kV, kY, kI; </s>
            <s xml:id="echoid-s3001" xml:space="preserve">erit
              <lb/>
            kV, omnium minimus, & </s>
            <s xml:id="echoid-s3002" xml:space="preserve">K Y, minor, quàm kI. </s>
            <s xml:id="echoid-s3003" xml:space="preserve">Rurſus quia in ſuperficie
              <lb/>
              <note position="right" xlink:label="note-089-05" xlink:href="note-089-05a" xml:space="preserve">Schol. 21. 2
                <lb/>
              huius.</note>
            ſphæræ extra peripheriam circuli Q R, ſignatum eſt punctum K, præter eius
              <lb/>
            polum, & </s>
            <s xml:id="echoid-s3004" xml:space="preserve">ex K, in eius circunferentiam cadunt tres arcus K T, K X, K L,
              <lb/>
              <note position="right" xlink:label="note-089-06" xlink:href="note-089-06a" xml:space="preserve">Schol. 21. 2
                <lb/>
              huius.</note>
            erit K T, omnium minimus, & </s>
            <s xml:id="echoid-s3005" xml:space="preserve">kL, minor quam K L. </s>
            <s xml:id="echoid-s3006" xml:space="preserve">Vterque igitur </s>
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