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

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            <s xml:id="echoid-s2685" xml:space="preserve">
              <pb o="69" file="081" n="81" rhead=""/>
            ſunganturq́ue rectæ A D, C E. </s>
            <s xml:id="echoid-s2686" xml:space="preserve">Dico rectas A D, C E, æquales eſſe. </s>
            <s xml:id="echoid-s2687" xml:space="preserve">Polo enim
              <lb/>
            B, & </s>
            <s xml:id="echoid-s2688" xml:space="preserve">interuallo B A, circulus deſcribatur, qui etiam per C, tranſibit, ob æqua
              <lb/>
            litatem arcuum B A, B C. </s>
            <s xml:id="echoid-s2689" xml:space="preserve">Aut igitur idem circulus tranſit etiam per C, atque
              <lb/>
              <figure xlink:label="fig-081-01" xlink:href="fig-081-01a" number="89">
                <image file="081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/081-01"/>
              </figure>
            adeo & </s>
            <s xml:id="echoid-s2690" xml:space="preserve">per E, ob æquali-
              <lb/>
            tatem arcuum B D, B E,
              <lb/>
            aut non. </s>
            <s xml:id="echoid-s2691" xml:space="preserve">Tranſeat primũ
              <lb/>
            per D, & </s>
            <s xml:id="echoid-s2692" xml:space="preserve">E, vt in priori
              <lb/>
            figura; </s>
            <s xml:id="echoid-s2693" xml:space="preserve">ſintq́ue communes
              <lb/>
            ſectiones circulorum ma-
              <lb/>
            ximorũ, & </s>
            <s xml:id="echoid-s2694" xml:space="preserve">circuli A D C E,
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            rectæ A C, D E. </s>
            <s xml:id="echoid-s2695" xml:space="preserve">Et quo-
              <lb/>
            niã circuli maximi A B C,
              <lb/>
            D B E, per B, polum cir-
              <lb/>
            culi A D C E, tranſeun-
              <lb/>
            tes ſecant ipſum bifariã,
              <lb/>
              <note position="right" xlink:label="note-081-01" xlink:href="note-081-01a" xml:space="preserve">15. 1. huius.</note>
            erunt A C, D E, diametri circuli A D C E, & </s>
            <s xml:id="echoid-s2696" xml:space="preserve">F, centrum; </s>
            <s xml:id="echoid-s2697" xml:space="preserve">ac proinde rectæ
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            F A, F D, rectis F C, F E, æquales. </s>
            <s xml:id="echoid-s2698" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s2699" xml:space="preserve">angulos æquales compre-
              <lb/>
              <note position="right" xlink:label="note-081-02" xlink:href="note-081-02a" xml:space="preserve">15. primi.</note>
            hendant ad verticem F; </s>
            <s xml:id="echoid-s2700" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s2701" xml:space="preserve">rectæ A D, C E, æquales.</s>
            <s xml:id="echoid-s2702" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">4. primi.</note>
          <p>
            <s xml:id="echoid-s2703" xml:space="preserve">SED non tranſeat iam circulus ex B, polo deſcriptus ad interuallum B A,
              <lb/>
            per D, ſed vltra punctum D, atque adeò & </s>
            <s xml:id="echoid-s2704" xml:space="preserve">vltra punctum E, excurrat. </s>
            <s xml:id="echoid-s2705" xml:space="preserve">Produ-
              <lb/>
              <note position="right" xlink:label="note-081-04" xlink:href="note-081-04a" xml:space="preserve">28. tertij.</note>
            cantur arcus B D, B E, ad G, H. </s>
            <s xml:id="echoid-s2706" xml:space="preserve">Quoniam igitur arcus B G, B H, æquales
              <lb/>
            ſunt, quòd ex defin. </s>
            <s xml:id="echoid-s2707" xml:space="preserve">poli, rectæ ſubtenſæ B G, B H, æquales ſint: </s>
            <s xml:id="echoid-s2708" xml:space="preserve">Sunt autem
              <lb/>
            & </s>
            <s xml:id="echoid-s2709" xml:space="preserve">B D, B E, ex hypotheſi, æquales; </s>
            <s xml:id="echoid-s2710" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s2711" xml:space="preserve">reliqui D G, E H, æquales. </s>
            <s xml:id="echoid-s2712" xml:space="preserve">Et
              <lb/>
            quoniam rectæ ductæ A G, C H, æquales ſunt, vt proxime demonſtratum eſt
              <lb/>
            in prima parte huius propoſ. </s>
            <s xml:id="echoid-s2713" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s2714" xml:space="preserve">arcus A G, C H, æquales. </s>
            <s xml:id="echoid-s2715" xml:space="preserve">Quia igitur
              <lb/>
              <note position="right" xlink:label="note-081-05" xlink:href="note-081-05a" xml:space="preserve">28. tertij.</note>
            circulus maximus G B H, per polum B, ductus ſecat circulum A G C H, bifa-
              <lb/>
              <note position="right" xlink:label="note-081-06" xlink:href="note-081-06a" xml:space="preserve">15. 1. huius.</note>
            riam, & </s>
            <s xml:id="echoid-s2716" xml:space="preserve">ad angulos rectos, inſiſtet ſegmentum G H, rectum diametro circuli
              <lb/>
            AGCH. </s>
            <s xml:id="echoid-s2717" xml:space="preserve">Cum ergo arcus D G, E H, æquales ſint, & </s>
            <s xml:id="echoid-s2718" xml:space="preserve">minores dimidio arcu
              <lb/>
            G D H; </s>
            <s xml:id="echoid-s2719" xml:space="preserve">ſintq́ue arcus G A, H C, oſtenſi quoque æquales; </s>
            <s xml:id="echoid-s2720" xml:space="preserve">erunt rectę D A,
              <lb/>
            E C, inter ſe æquales. </s>
            <s xml:id="echoid-s2721" xml:space="preserve">Si igitur in ſphæra duo maximi circuliſe mutuo ſecent,
              <lb/>
              <note position="right" xlink:label="note-081-07" xlink:href="note-081-07a" xml:space="preserve">12. 2. huius.</note>
            &</s>
            <s xml:id="echoid-s2722" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2723" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2724" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div242" type="section" level="1" n="114">
          <head xml:id="echoid-head128" xml:space="preserve">THEOREMA 4. PROPOS. 4.</head>
          <note position="right" xml:space="preserve">2.</note>
          <p>
            <s xml:id="echoid-s2725" xml:space="preserve">SI in ſphæra duo maximi circuli ſe mutuo ſe-
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            cent, ab eorumque altero æquales circunferen-
              <lb/>
            tiæ ſumantur vtrinque à puncto, in quo ſeinterſe-
              <lb/>
            cant, & </s>
            <s xml:id="echoid-s2726" xml:space="preserve">per puncta terminantia æquales circunfe-
              <lb/>
            rentias ducantur duo plana parallela, quorum alte
              <lb/>
            rum conueniat cum communi ſectione ipſorum
              <lb/>
            circulorum extra ſphæram verſus prædictum pun
              <lb/>
            ctum; </s>
            <s xml:id="echoid-s2727" xml:space="preserve">ſit vero vna illarum æqualium circunferen-
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            tiarum maior vtralibet circunferentiarum in </s>
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