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

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            <s xml:id="echoid-s3518" xml:space="preserve">
              <pb o="91" file="103" n="103" rhead=""/>
            ad ſectorem GEB; </s>
            <s xml:id="echoid-s3519" xml:space="preserve">quòd triangulum GEI, minus ſit ſectore GEB. </s>
            <s xml:id="echoid-s3520" xml:space="preserve">Mul-
              <lb/>
            to igitur maior erit proportio trianguli GAE, ad triangulum GEI,
              <lb/>
            quàm ſectoris GCE, ad ſectorem GEB: </s>
            <s xml:id="echoid-s3521" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s3522" xml:space="preserve">componendo
              <lb/>
            maior erit proportio trianguli GAI, ad triangulum GEI, quàm ſe-
              <lb/>
            ctoris GCB, ad ſectorem GEB: </s>
            <s xml:id="echoid-s3523" xml:space="preserve">Eſt autem vt triangulum GAI, ad
              <lb/>
              <note position="right" xlink:label="note-103-01" xlink:href="note-103-01a" xml:space="preserve">28. quinti.</note>
            triangulum GEI, itarecta AI, ad rectam IE; </s>
            <s xml:id="echoid-s3524" xml:space="preserve">& </s>
            <s xml:id="echoid-s3525" xml:space="preserve">vt ſector GCB,
              <lb/>
              <note position="right" xlink:label="note-103-02" xlink:href="note-103-02a" xml:space="preserve">1.ſexti.</note>
            ad ſectorem GEB, ita angulus BGC, ad angulum BGE. </s>
            <s xml:id="echoid-s3526" xml:space="preserve">Maior igitur
              <lb/>
              <note position="right" xlink:label="note-103-03" xlink:href="note-103-03a" xml:space="preserve">Corol. 1. 33
                <lb/>
              ſexti.</note>
            erit quoque proportio AI, ad IE, quàm anguli BGA, hoc eſt, quàm an-
              <lb/>
            guli ſibi æqualis IKE, ad angulum IGE: </s>
            <s xml:id="echoid-s3527" xml:space="preserve">Vt autem AI, ad IE, ita eſt
              <lb/>
              <note position="right" xlink:label="note-103-04" xlink:href="note-103-04a" xml:space="preserve">29. primi.</note>
            GI, ad IK. </s>
            <s xml:id="echoid-s3528" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3529" xml:space="preserve">maior erit proportio rectæ GI, adrectam IK,
              <lb/>
              <note position="right" xlink:label="note-103-05" xlink:href="note-103-05a" xml:space="preserve">2. vel 4. ſex
                <lb/>
              ti.</note>
            quàm anguli IKE, ad angulum IGE. </s>
            <s xml:id="echoid-s3530" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s3531" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div286" type="section" level="1" n="132">
          <head xml:id="echoid-head146" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3532" xml:space="preserve">_ADDITVR_ in alia verſione hoc loco ſequens Theorema.</s>
            <s xml:id="echoid-s3533" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3534" xml:space="preserve">IISDEM poſitis, Diameter ſphæræ ad diametrum paralleli per
              <lb/>
              <note position="right" xlink:label="note-103-06" xlink:href="note-103-06a" xml:space="preserve">13.</note>
            punctum obliqui circuli, per quod maximus circulus è polo tranſit,
              <lb/>
            deſcripti, minorem rationem habet quàm circunferentia maximi pa
              <lb/>
            rallelorum intercepta inter maximum circulum primo poſitum, & </s>
            <s xml:id="echoid-s3535" xml:space="preserve">
              <lb/>
            maxmum circulum per polos parallelorum tranſeuntem, ad circun-
              <lb/>
            ferentiam obliqui circuli inter eoſdem circulos interceptam.</s>
            <s xml:id="echoid-s3536" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3537" xml:space="preserve">_SINT_ deſcripti circuli, vt in præcedenti propoſ. </s>
            <s xml:id="echoid-s3538" xml:space="preserve">Dico minorem eſſe proportionem
              <lb/>
            diametri ſphæræ ad diametrum paralleli _GE,_ quàm circunferentiæ _BC,_ ad circun-
              <lb/>
            ferentiam _DE._ </s>
            <s xml:id="echoid-s3539" xml:space="preserve">Sint _GH, BI,_ communes ſectiones circulorum _GE, BC,_ cum circule
              <lb/>
            _
              <emph style="sc">Ab</emph>
            ,_ quæ diametri illorum
              <lb/>
            erunt, cum _AB,_ per eorum po-
              <lb/>
              <figure xlink:label="fig-103-01" xlink:href="fig-103-01a" number="107">
                <image file="103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/103-01"/>
              </figure>
            los ductus ipſos ſecet bifariã,
              <lb/>
              <note position="right" xlink:label="note-103-07" xlink:href="note-103-07a" xml:space="preserve">15. 1. huius.</note>
            & </s>
            <s xml:id="echoid-s3540" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s3541" xml:space="preserve">Erit er
              <lb/>
            go _BI,_ diameter etiã ſphæræ.
              <lb/>
            </s>
            <s xml:id="echoid-s3542" xml:space="preserve">Et quoniã circulus _DE,_ po-
              <lb/>
            nitur rectus ad _AB,_ tranſi-
              <lb/>
            bit _DE,_ per polos ipſius _AB._ </s>
            <s xml:id="echoid-s3543" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-103-08" xlink:href="note-103-08a" xml:space="preserve">13. 1. huius.</note>
            Eodem modo _
              <emph style="sc">B</emph>
            C,_ per polos
              <lb/>
            eiuſdem _AB,_ tanſibit, cum re-
              <lb/>
            ctus ad ipſum ponatur. </s>
            <s xml:id="echoid-s3544" xml:space="preserve">Qua-
              <lb/>
            re M, punctum, vbi ſe mutuo
              <lb/>
            ſecant, polus erit circuli _AB;_
              <lb/>
            </s>
            <s xml:id="echoid-s3545" xml:space="preserve">ac propterea ſegmẽtum _DEL,_
              <lb/>
            quod rectum eſt ad circulum
              <lb/>
            _AB,_ inæqualiter diuidetur in
              <lb/>
            E, puncto, vbi circuli _DE, GE,_
              <lb/>
            ſe interſecant, minorq́ pars
              <lb/>
            erit _ED:_ </s>
            <s xml:id="echoid-s3546" xml:space="preserve">quandoquidem ar-
              <lb/>
            cus _MD, ML,_ æquales ſunt, quod rectæ illis ſubtenſæ, ex defin. </s>
            <s xml:id="echoid-s3547" xml:space="preserve">poli, æquales ſint. </s>
            <s xml:id="echoid-s3548" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-103-09" xlink:href="note-103-09a" xml:space="preserve">28. tertij.</note>
            </s>
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