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

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          <p>
            <s xml:id="echoid-s673" xml:space="preserve">
              <pb o="19" file="031" n="31" rhead=""/>
            circulus maximus A B C D, circulum B E D, non maximum ad angulos re-
              <lb/>
            ctos. </s>
            <s xml:id="echoid-s674" xml:space="preserve">Quod eſt primo loco propoſitum. </s>
            <s xml:id="echoid-s675" xml:space="preserve">Et quoniam oſtenſum eſt, rectã F G,
              <lb/>
            ex G, centro ſphæræ ductam ad planum circuli B E D, eſſe perpendicularẽ,
              <lb/>
            cadet F G, vtrinque producta in polos circuli B E D. </s>
            <s xml:id="echoid-s676" xml:space="preserve">Quare cum G F, in
              <lb/>
              <note position="right" xlink:label="note-031-01" xlink:href="note-031-01a" xml:space="preserve">8. huius.</note>
            plano circuli A B C D, exiſtens, producta cadat in circunferentiam eius ad
              <lb/>
            puncta A, C, quæ etiam in ſuperficie ſphæræ funt, erunt A, C, poli circuli
              <lb/>
            B E D, atque adeo circulus maximus A B C D, circulũ non maximũ B E D,
              <lb/>
            per polos A, C, ſecabit. </s>
            <s xml:id="echoid-s677" xml:space="preserve">quod ſecundo loco propoſitũ fuit. </s>
            <s xml:id="echoid-s678" xml:space="preserve">Si igitur in ſphæ
              <lb/>
            ra maximus circulus circulum non maximum, &</s>
            <s xml:id="echoid-s679" xml:space="preserve">c. </s>
            <s xml:id="echoid-s680" xml:space="preserve">Quod erat oftendendum.</s>
            <s xml:id="echoid-s681" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div76" type="section" level="1" n="47">
          <head xml:id="echoid-head58" xml:space="preserve">THEOREMA 14. PROPOS. 15.</head>
          <note position="right" xml:space="preserve">20.</note>
          <p>
            <s xml:id="echoid-s682" xml:space="preserve">Si in ſphæra maximus circulus, eorum, qui in
              <lb/>
            ſphæra ſunt, circulorum aliquem per polos ſecet;
              <lb/>
            </s>
            <s xml:id="echoid-s683" xml:space="preserve">bifariam, & </s>
            <s xml:id="echoid-s684" xml:space="preserve">ad angulos rectos eum ſecat.</s>
            <s xml:id="echoid-s685" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s686" xml:space="preserve">IN Sphæra maximus circulus A B C D, ſecet circulum B E D, per polos
              <lb/>
            A, C. </s>
            <s xml:id="echoid-s687" xml:space="preserve">Dico circulum A B C D, ſecare circulum B E D, fifariam, & </s>
            <s xml:id="echoid-s688" xml:space="preserve">ad angu
              <lb/>
              <figure xlink:label="fig-031-01" xlink:href="fig-031-01a" number="26">
                <image file="031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/031-01"/>
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            los rectos. </s>
            <s xml:id="echoid-s689" xml:space="preserve">Connectat enim recta A C, polos
              <lb/>
            A, C, occurrens plano circuli B E D, in F,
              <lb/>
            puhcto. </s>
            <s xml:id="echoid-s690" xml:space="preserve">Et quoniam recta A C, ad planũ cir
              <lb/>
            culi B E D, per pendicularis eſt, tranſitq́; </s>
            <s xml:id="echoid-s691" xml:space="preserve">per
              <lb/>
              <note position="right" xlink:label="note-031-03" xlink:href="note-031-03a" xml:space="preserve">10. huius.</note>
            centrum ſphæræ, & </s>
            <s xml:id="echoid-s692" xml:space="preserve">circuli B E D; </s>
            <s xml:id="echoid-s693" xml:space="preserve">erit F, cen
              <lb/>
            trum circuli B E D. </s>
            <s xml:id="echoid-s694" xml:space="preserve">Cum ergo circulus ma
              <lb/>
            ximus A B C D, circulum B E D, ſecans tran
              <lb/>
            ſeat per rectam A C, ac proinde per centrũ
              <lb/>
            F, erit communis ſectio B F D, diameter cir
              <lb/>
            culi B E D. </s>
            <s xml:id="echoid-s695" xml:space="preserve">Bifariam ergo ſecatur circulus
              <lb/>
            B E D. </s>
            <s xml:id="echoid-s696" xml:space="preserve">Dico quod & </s>
            <s xml:id="echoid-s697" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s698" xml:space="preserve">Cum
              <lb/>
            enim recta A C, oſtenſa ſit perpendicularis
              <lb/>
            ad planum circuli B E D, erit quoque planũ
              <lb/>
            circuli maximi A B C D, per rectam A C, ductum ad idem planum circuli
              <lb/>
              <note position="right" xlink:label="note-031-04" xlink:href="note-031-04a" xml:space="preserve">18. vndes.</note>
            B E D, rectum. </s>
            <s xml:id="echoid-s699" xml:space="preserve">Igitur ſi in ſphęra maximus circulus, &</s>
            <s xml:id="echoid-s700" xml:space="preserve">c. </s>
            <s xml:id="echoid-s701" xml:space="preserve">Quod demonſtran
              <lb/>
            dum erat.</s>
            <s xml:id="echoid-s702" xml:space="preserve"/>
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        <div xml:id="echoid-div78" type="section" level="1" n="48">
          <head xml:id="echoid-head59" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s703" xml:space="preserve">_QVATVOR_alia theoremata hoc loco addútur in alia verſione, hoc ordine.</s>
            <s xml:id="echoid-s704" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div79" type="section" level="1" n="49">
          <head xml:id="echoid-head60" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s705" xml:space="preserve">SI in ſphæra maximus circulus per polos alterius cuiuſpiam ma
              <lb/>
              <note position="right" xlink:label="note-031-05" xlink:href="note-031-05a" xml:space="preserve">21.</note>
            ximi circuli tranſeat, tranſibit viciſſim hic per polos illius.</s>
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