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

Page concordance

< >
Scan Original
81 69
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
91 79
92 80
93 81
94 82
95 83
96 84
97 85
98 86
99 87
100 88
101 89
102 90
103 91
104 92
105 93
106 94
107 95
108 96
109
110
< >
page |< < (69) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div239" type="section" level="1" n="113">
          <p>
            <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,
              <lb/>
            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
              <lb/>
            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>
        </div>
        <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-
              <lb/>
            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-
              <lb/>
            tiarum maior vtralibet circunferentiarum in </s>
          </p>
        </div>
      </text>
    </echo>
Impressum