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

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            <s xml:id="echoid-s3300" xml:space="preserve">
              <pb o="85" file="097" n="97" rhead=""/>
            _ergo_ H I, K L, _ponantur æquales, minor erit_ O I, _quàm_ K P. </s>
            <s xml:id="echoid-s3301" xml:space="preserve">_Quod eſt abſurdum._
              <lb/>
            </s>
            <s xml:id="echoid-s3302" xml:space="preserve">_Quia enim arcus_ E M, F N, _dimidij æqualium_ D E, F G, _æquales ſunt, & </s>
            <s xml:id="echoid-s3303" xml:space="preserve">non con=_
              <lb/>
            _tinui, non poterit_ O I, _minor eſſe, quam_ K P, _vt in ſecunda figura demonſtratum_
              <lb/>
            _eſt. </s>
            <s xml:id="echoid-s3304" xml:space="preserve">Nonergo arcus_ H I, _arcui_ K L, _æqualis eſt: </s>
            <s xml:id="echoid-s3305" xml:space="preserve">Sed nequeminor eſt oſtenſus. </s>
            <s xml:id="echoid-s3306" xml:space="preserve">Maior_
              <lb/>
            _igitur eſt. </s>
            <s xml:id="echoid-s3307" xml:space="preserve">Quod eſt propoſitum._</s>
            <s xml:id="echoid-s3308" xml:space="preserve"/>
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        <div xml:id="echoid-div272" type="section" level="1" n="126">
          <head xml:id="echoid-head140" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s3309" xml:space="preserve">SI in ſphæra maximus circulus tangat aliquem ſphæræ circu-
              <lb/>
              <note position="right" xlink:label="note-097-01" xlink:href="note-097-01a" xml:space="preserve">9.</note>
            lum, alius autem maximus circulus ad parallelos obliquus ſit, tan-
              <lb/>
            gatque circulos maiores illis, quos tangit maximus circulus primò
              <lb/>
            poſitus, fuerintque eorum contactus in maximo circulo primo poſi-
              <lb/>
            to; </s>
            <s xml:id="echoid-s3310" xml:space="preserve">& </s>
            <s xml:id="echoid-s3311" xml:space="preserve">ſumantur à circulo obliquo circun ferentiæ æquales, quæ con-
              <lb/>
            tinuæ quidem non ſint, ſed tamen ſintad eaſdem partes maximi pa-
              <lb/>
            rallelorum; </s>
            <s xml:id="echoid-s3312" xml:space="preserve">per puncta autem terminantia æquales circunferentias
              <lb/>
            deſcribantur paralleli circuli: </s>
            <s xml:id="echoid-s3313" xml:space="preserve">HI circunferentias inæ quales interci-
              <lb/>
            pient de maximo circulo primò poſito, quarum ea, quæ propior erit
              <lb/>
            maximo parallelorum, maior erit remotiore.</s>
            <s xml:id="echoid-s3314" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3315" xml:space="preserve">HOC _Theorema demonſtrabitur ex propoſ. </s>
            <s xml:id="echoid-s3316" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3317" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3318" xml:space="preserve">quemadmodum præce=_
              <lb/>
            _dens Theorema ex propoſ. </s>
            <s xml:id="echoid-s3319" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3320" xml:space="preserve">demonſtratũ ſuit: </s>
            <s xml:id="echoid-s3321" xml:space="preserve">dummodo duo circuli maximi_ A B, A C,
              <lb/>
            _præcedentis Theorematis tangant duos parallelos, vt in propoſ. </s>
            <s xml:id="echoid-s3322" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3323" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3324" xml:space="preserve">dictum_
              <lb/>
            _eſt. </s>
            <s xml:id="echoid-s3325" xml:space="preserve">Reliqua conſtructio figuræ à conſtructione præcedentis Theorematis non dif=_
              <lb/>
            _fert, &</s>
            <s xml:id="echoid-s3326" xml:space="preserve">c._</s>
            <s xml:id="echoid-s3327" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div274" type="section" level="1" n="127">
          <head xml:id="echoid-head141" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s3328" xml:space="preserve">SI in ſphæra maximus circulus aliquem ſphæræ circulum tan-
              <lb/>
              <note position="right" xlink:label="note-097-02" xlink:href="note-097-02a" xml:space="preserve">10.</note>
            gat, aliquis autem alius maximus circulus obliquus ad parallelos tan-
              <lb/>
            gat circulos maiores illis, quos tangebat maximus circulus primo
              <lb/>
            poſitus, fuerintque eorum contactus in maximo circulo primo poſi-
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            to; </s>
            <s xml:id="echoid-s3329" xml:space="preserve">ſumantur autem de obliquo circulo æquales circunferentiæ, quæ
              <lb/>
            continuæ quidem non ſint, ſed tamen ſint ad eaſdem partes maximi
              <lb/>
            parallelorum, per que puncta terminantia æquales circunferentias
              <lb/>
            deſcribantur maximi circuli, qui & </s>
            <s xml:id="echoid-s3330" xml:space="preserve">tangant eundem circulum, quem
              <lb/>
            tangebat maximus circulus primo poſitus, & </s>
            <s xml:id="echoid-s3331" xml:space="preserve">ſimiles parallelorum
              <lb/>
            circunferentias intercipiant, habeantque eos ſemicirculos, qui ten-
              <lb/>
            dunt à punctis contactuum ad puncta terminantia æquales obliqui
              <lb/>
            circuli circunferentias, per quæ deſcribuntur, eiuſmodi, vt minimè
              <lb/>
            cõueniant cum illo circuli maximi primò poſiti ſemicirculo, in quo
              <lb/>
            eſt contactus obliqui circuli inter apparentem polum, & </s>
            <s xml:id="echoid-s3332" xml:space="preserve">maximum
              <lb/>
            parallelorum: </s>
            <s xml:id="echoid-s3333" xml:space="preserve">Inæquales intercipient circunferentias de maximo
              <lb/>
            parallelorum, quarum propior circulo maximo primò poſito, ſem-
              <lb/>
            per erit maior remotiore.</s>
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