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

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        <div xml:id="echoid-div222" type="section" level="1" n="106">
          <p style="it">
            <s xml:id="echoid-s2408" xml:space="preserve">
              <pb o="61" file="073" n="73" rhead=""/>
            _
              <emph style="sc">G</emph>
            B,_ verò maior quàm _
              <emph style="sc">G</emph>
            C;_ </s>
            <s xml:id="echoid-s2409" xml:space="preserve">& </s>
            <s xml:id="echoid-s2410" xml:space="preserve">_
              <emph style="sc">G</emph>
            B,
              <emph style="sc">G</emph>
            E,_ æquales Item _
              <emph style="sc">G</emph>
            H,_ minor quàm _
              <emph style="sc">G</emph>
            I;_ </s>
            <s xml:id="echoid-s2411" xml:space="preserve">& </s>
            <s xml:id="echoid-s2412" xml:space="preserve">_
              <emph style="sc">G</emph>
            H_
              <lb/>
            _
              <emph style="sc">G</emph>
            K,_ æquales. </s>
            <s xml:id="echoid-s2413" xml:space="preserve">Quapropter cum arcubus ſemicirculo minoribus ſubtendantur, ex by-
              <lb/>
              <note position="right" xlink:label="note-073-01" xlink:href="note-073-01a" xml:space="preserve">Schol. 28.
                <lb/>
              tertij.</note>
            pothcſi, erit quoque arcus _
              <emph style="sc">G</emph>
            A,_ omnium maximus, & </s>
            <s xml:id="echoid-s2414" xml:space="preserve">_
              <emph style="sc">G</emph>
            D,_ minimus: </s>
            <s xml:id="echoid-s2415" xml:space="preserve">at _
              <emph style="sc">G</emph>
            B,_ mater,
              <lb/>
            quàm _
              <emph style="sc">G</emph>
            C;_ </s>
            <s xml:id="echoid-s2416" xml:space="preserve">& </s>
            <s xml:id="echoid-s2417" xml:space="preserve">_
              <emph style="sc">G</emph>
            H,_ minor quàm _
              <emph style="sc">G</emph>
            I:_ </s>
            <s xml:id="echoid-s2418" xml:space="preserve">Denique _
              <emph style="sc">G</emph>
            B,
              <emph style="sc">G</emph>
            E,_ nec non _
              <emph style="sc">G</emph>
            H,
              <emph style="sc">G</emph>
            K,_ æqua-
              <lb/>
              <note position="right" xlink:label="note-073-02" xlink:href="note-073-02a" xml:space="preserve">28. tertij.</note>
            les inter ſe. </s>
            <s xml:id="echoid-s2419" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s2420" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2421" xml:space="preserve">_PERSPICVVM_ autem eſt in proximis duobus theorematibus arcus ſingulorũ
              <lb/>
            ex
              <emph style="sc">G</emph>
            , ductos non debere eſſe maiores ſemicirculo: </s>
            <s xml:id="echoid-s2422" xml:space="preserve">alias non auferrent maiores lineæ
              <lb/>
            maiores arcus, & </s>
            <s xml:id="echoid-s2423" xml:space="preserve">contra, vt conſtat exſcholio propoſ. </s>
            <s xml:id="echoid-s2424" xml:space="preserve">28. </s>
            <s xml:id="echoid-s2425" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2426" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2427" xml:space="preserve">Eucl.</s>
            <s xml:id="echoid-s2428" xml:space="preserve"/>
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        <div xml:id="echoid-div225" type="section" level="1" n="107">
          <head xml:id="echoid-head119" xml:space="preserve">THEOREMA 20. PROPOS. 22.</head>
          <note position="right" xml:space="preserve">33.</note>
          <p>
            <s xml:id="echoid-s2429" xml:space="preserve">SI in ſphæra maximus circulus vnum quidem
              <lb/>
            circulum tangat, alium vero ei parallelum ſecet,
              <lb/>
            poſitum inter ſphæræ centrum, & </s>
            <s xml:id="echoid-s2430" xml:space="preserve">eum circulum,
              <lb/>
            quem tangit maximus circulus, polus autem maxi
              <lb/>
            mi circuli fuerit inter vtrumque parallelorum, de-
              <lb/>
            ſcribanturque maximi circuli tangentes duorum
              <lb/>
            parallelorum maiorem: </s>
            <s xml:id="echoid-s2431" xml:space="preserve">hi omnes erunt inclinati
              <lb/>
            ad maximum circulum, & </s>
            <s xml:id="echoid-s2432" xml:space="preserve">eorum rectiſſimus qui-
              <lb/>
            dem eritille, cuius contactus erit in eo puncto, in
              <lb/>
            quo maius ſegmentum paralleli maioris bifariam
              <lb/>
            diuiditur; </s>
            <s xml:id="echoid-s2433" xml:space="preserve">humillimus vero & </s>
            <s xml:id="echoid-s2434" xml:space="preserve">maxime inclina-
              <lb/>
            tus, cuius contactus eritin eo puncto, in quo mi-
              <lb/>
            nus ſegmentum bifariã diuiditur; </s>
            <s xml:id="echoid-s2435" xml:space="preserve">Reliquorum au-
              <lb/>
            tem illi quidem, quiæqualiter diſtant ab alterutro
              <lb/>
            eorum punctorum, in quibus fegmenta bifariam
              <lb/>
            ſecantur, ſunt ſimiliter inclinati: </s>
            <s xml:id="echoid-s2436" xml:space="preserve">qui vero conta-
              <lb/>
            ctum remotiorem habet à puncto, in quo maius
              <lb/>
            ſegmentum bifariam ſecatur, inclinatior perpetuo
              <lb/>
            eſt, quam qui contactum eidem puncto propio-
              <lb/>
            rem habet. </s>
            <s xml:id="echoid-s2437" xml:space="preserve">Poli denique maximorum circulorum
              <lb/>
            erunt in vno circulo, qui & </s>
            <s xml:id="echoid-s2438" xml:space="preserve">minor erit eo </s>
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