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

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        <div xml:id="echoid-div50" type="section" level="1" n="33">
          <head xml:id="echoid-head44" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s393" xml:space="preserve">SI ſit in ſphæra circulus, & </s>
            <s xml:id="echoid-s394" xml:space="preserve">ab altero polorum eius recta duca-
              <lb/>
              <note position="right" xlink:label="note-025-01" xlink:href="note-025-01a" xml:space="preserve">11.</note>
            tur per centrum illius, erit hęc ad planum circuli perpendicularis,
              <lb/>
            & </s>
            <s xml:id="echoid-s395" xml:space="preserve">producta cadet in reliquum polum.</s>
            <s xml:id="echoid-s396" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s397" xml:space="preserve">_IN_ eadem adbuc figura ex _A,_ polo circuli _B G D H,_ per centrum eius _F,_ demit
              <lb/>
            tatur linea recta _A F,_ occurrens ſuperficiei ſphæræ in _C._ </s>
            <s xml:id="echoid-s398" xml:space="preserve">Dico rectam _A F,_ perpen
              <lb/>
            dicularem eſſe ad planum circuli _B G D H,_ & </s>
            <s xml:id="echoid-s399" xml:space="preserve">_C,_ eſſe reliquum polum eiuſdem cir-
              <lb/>
            culi. </s>
            <s xml:id="echoid-s400" xml:space="preserve">Quoniam enim duo triangula _A F B, A F D,_ duo latera _A F, F B,_ duobus la-
              <lb/>
            teribus _A F, F D,_ & </s>
            <s xml:id="echoid-s401" xml:space="preserve">baſim _A B,_ baſi _A D,_ æqualem habent, ex defin. </s>
            <s xml:id="echoid-s402" xml:space="preserve">poli; </s>
            <s xml:id="echoid-s403" xml:space="preserve">habebunt
              <lb/>
            quoque duos angulos _A F B, A F D,_ æquales, atque adeo rectos. </s>
            <s xml:id="echoid-s404" xml:space="preserve">Igitur _A F,_ re-
              <lb/>
              <note position="right" xlink:label="note-025-02" xlink:href="note-025-02a" xml:space="preserve">8 primi.</note>
            ctæ _B D,_ inſiſtit ad angulos rectos. </s>
            <s xml:id="echoid-s405" xml:space="preserve">Similiter oſtendemus, eandẽ _A F,_ ad angulos rectos
              <lb/>
            inſiſtere rectæ _G H._ </s>
            <s xml:id="echoid-s406" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s407" xml:space="preserve">plano circuli _B G D H,_ per rectas _B D, G H,_ ducto eadẽ
              <lb/>
              <note position="right" xlink:label="note-025-03" xlink:href="note-025-03a" xml:space="preserve">4. vndec.</note>
            recta _A F,_ ad rectos inſiſtet angulos. </s>
            <s xml:id="echoid-s408" xml:space="preserve">Quod eſt primò propoſitum. </s>
            <s xml:id="echoid-s409" xml:space="preserve">Quoniamigitur _A F,_
              <lb/>
            ad rectos eſt angulos plano circuli _B G D H,_ ducta erit _F A,_ ex centro circuli _F,_ ad pla
              <lb/>
            num circuli perpendicularis. </s>
            <s xml:id="echoid-s410" xml:space="preserve">Quare, vt in hoc ſcholio proxime demonſtratum eſt, in
              <lb/>
            vtramque partem protracta in vtrumque polum circuli cadet, ac proinde _C,_ reli-
              <lb/>
            quus polus erit circuli _B G D H,_ quod eſt ſecundo loco propoſitum.</s>
            <s xml:id="echoid-s411" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div53" type="section" level="1" n="34">
          <head xml:id="echoid-head45" xml:space="preserve">THEOR. 8. PROPOS. 9.</head>
          <note position="right" xml:space="preserve">12.</note>
          <p>
            <s xml:id="echoid-s412" xml:space="preserve">SI ſit in ſphæra circulus, & </s>
            <s xml:id="echoid-s413" xml:space="preserve">ab altero polorum
              <lb/>
            eius in ipſum ducatur perpẽdicularis recta linea,
              <lb/>
            cadet hæc in circuli centrum, & </s>
            <s xml:id="echoid-s414" xml:space="preserve">inde producta ca
              <lb/>
            det in reliquum polum ipſius circuli.</s>
            <s xml:id="echoid-s415" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s416" xml:space="preserve">IN Sphæra A B C D, ſit circulus B F D G, à cuius polo A, ad eius pla-
              <lb/>
            num perpendicularis ducatur A E, occurrens ſuperficiei ſphæræ in C. </s>
            <s xml:id="echoid-s417" xml:space="preserve">Dico
              <lb/>
              <figure xlink:label="fig-025-01" xlink:href="fig-025-01a" number="18">
                <image file="025-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/025-01"/>
              </figure>
              <note position="right" xlink:label="note-025-05" xlink:href="note-025-05a" xml:space="preserve">11. vndce.</note>
            E, centrum eſſe circuli B F D G, & </s>
            <s xml:id="echoid-s418" xml:space="preserve">C, reliquũ
              <lb/>
            polum. </s>
            <s xml:id="echoid-s419" xml:space="preserve">Ductis enim per E, duabus rectis vtcun
              <lb/>
            que B D, F G, connectantur earum extrema
              <lb/>
            cum polo A, rectis A B, A D, A F, A G, quæ
              <lb/>
            omnes inter ſe æquales erũt, ex definitione po
              <lb/>
            li. </s>
            <s xml:id="echoid-s420" xml:space="preserve">Omnes item anguli, quos recta A E, facit ad
              <lb/>
            E, recti, ex defin. </s>
            <s xml:id="echoid-s421" xml:space="preserve">3. </s>
            <s xml:id="echoid-s422" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s423" xml:space="preserve">11. </s>
            <s xml:id="echoid-s424" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s425" xml:space="preserve">Erit igitur tam
              <lb/>
            quadratũ ex A B, quadratis ex A E, E B, quàm
              <lb/>
              <note position="right" xlink:label="note-025-06" xlink:href="note-025-06a" xml:space="preserve">47. primi.</note>
            quadratum ex A G, quadratis ex A E, E G, æ-
              <lb/>
            quale; </s>
            <s xml:id="echoid-s426" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s427" xml:space="preserve">adeò cum quadrata rectarum A B,
              <lb/>
            A G, æqualium æqualia ſint, erunt quadrata
              <lb/>
            ex A E, E B, ſimul quadratis ex A E, G E, ſi-
              <lb/>
            mul æqualia. </s>
            <s xml:id="echoid-s428" xml:space="preserve">Dempto ergo communi quadrato rectæ A E, reliqua quadrata
              <lb/>
            rectarum E B, E G, æqualia erunt, ac proinde & </s>
            <s xml:id="echoid-s429" xml:space="preserve">rectæ E B, E G, æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s430" xml:space="preserve">Eodem modo oſtendemus, rectas E G, E D, æquales eſſe. </s>
            <s xml:id="echoid-s431" xml:space="preserve">Quare E, centrum
              <lb/>
            eſt circuli BFDG; </s>
            <s xml:id="echoid-s432" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s433" xml:space="preserve">Quoniam igitur ex E, centro cir
              <lb/>
              <note position="right" xlink:label="note-025-07" xlink:href="note-025-07a" xml:space="preserve">9. tertij.</note>
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