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

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        <div xml:id="echoid-div292" type="section" level="1" n="134">
          <head xml:id="echoid-head148" xml:space="preserve">THEOREMA 12. PROPOS 12.</head>
          <note position="right" xml:space="preserve">14.</note>
          <p>
            <s xml:id="echoid-s3584" xml:space="preserve">Slin ſphæra maximi circuli tangant vnum, eun
              <lb/>
            demq́; </s>
            <s xml:id="echoid-s3585" xml:space="preserve">parallelorum, intercipiantq́; </s>
            <s xml:id="echoid-s3586" xml:space="preserve">ſimiles paralle-
              <lb/>
            lorum circunferentias inter vtrũque maximorum
              <lb/>
            circulorum interiectas; </s>
            <s xml:id="echoid-s3587" xml:space="preserve">alius autem maximus cir-
              <lb/>
            culus ad parallelos obliquus circulos tangat ma-
              <lb/>
            iores illis, quos tangunt maximi circuli primò po-
              <lb/>
            ſiti, ſecetq́; </s>
            <s xml:id="echoid-s3588" xml:space="preserve">obliquus idem circulus eoſdem maxi-
              <lb/>
            mos circulos primò poſitos in punctis poſitis in-
              <lb/>
            ter maximum parallelorum, & </s>
            <s xml:id="echoid-s3589" xml:space="preserve">circulum, quem tan
              <lb/>
            gunt circuli maximi primo poſiti: </s>
            <s xml:id="echoid-s3590" xml:space="preserve">Diameter ſphæ
              <lb/>
            ræ ad diametrum circuli, quem tangit obliquus
              <lb/>
            circulus, maiorem rationem habet, quàm circun-
              <lb/>
            ferentia maximi paralleli intercepta inter circulos
              <lb/>
            primo poſitos, eundemq́; </s>
            <s xml:id="echoid-s3591" xml:space="preserve">circulum tangentes ad
              <lb/>
            circunferentiam obliqui circuli inter eoſdem cir-
              <lb/>
            culos interceptam.</s>
            <s xml:id="echoid-s3592" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3593" xml:space="preserve">IN ſphæra duo maximi circuli AB, CD, tangant eundem parallelum
              <lb/>
            AC, intercipiantq́; </s>
            <s xml:id="echoid-s3594" xml:space="preserve">ſimiles paralle-
              <lb/>
              <figure xlink:label="fig-105-01" xlink:href="fig-105-01a" number="109">
                <image file="105-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/105-01"/>
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            lorum circunferentias inter ipſos in-
              <lb/>
            teriectas; </s>
            <s xml:id="echoid-s3595" xml:space="preserve">alius autem circulus maxi-
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            mus EF, tangat parallelum EG, ma-
              <lb/>
            iorem parallelo AC, in E, ſitque o-
              <lb/>
            bliquus ad parallelos, & </s>
            <s xml:id="echoid-s3596" xml:space="preserve">ſecet duos
              <lb/>
            priores AB, CD, inter maximum pa
              <lb/>
            rallelorum HF, & </s>
            <s xml:id="echoid-s3597" xml:space="preserve">parallelum AC,
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            in punctis I, K. </s>
            <s xml:id="echoid-s3598" xml:space="preserve">Dico maiorem eſſe
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            rationem diametri ſphæræ ad diame-
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            trum paralleli EG, quàm circunfe-
              <lb/>
            rentiæ BD, ad circunferentiam IK.
              <lb/>
            </s>
            <s xml:id="echoid-s3599" xml:space="preserve">Per L, enim polum parallelorum, & </s>
            <s xml:id="echoid-s3600" xml:space="preserve">
              <lb/>
            puncta E, I, K, maximi circuli deſcri-
              <lb/>
              <note position="right" xlink:label="note-105-02" xlink:href="note-105-02a" xml:space="preserve">20.1.huius.</note>
            bantur LH, LM, LN; </s>
            <s xml:id="echoid-s3601" xml:space="preserve">ac per K, pa-
              <lb/>
            rallelus KO, ſecanscirculum AB, in P. </s>
            <s xml:id="echoid-s3602" xml:space="preserve">Quoniam igitur maior eſt ratio dia-
              <lb/>
            metri ſphæræ ad diametrum circuli EG, quàm arcus HM, ad arcum EI; </s>
            <s xml:id="echoid-s3603" xml:space="preserve">ra-
              <lb/>
              <note position="right" xlink:label="note-105-03" xlink:href="note-105-03a" xml:space="preserve">11.huius.</note>
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