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

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            <s xml:id="echoid-s433" xml:space="preserve">
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            culi B F D G, ad ipſius planum educta eſt perpendicularis E A, tranſibit hęc
              <lb/>
              <note position="left" xlink:label="note-026-01" xlink:href="note-026-01a" xml:space="preserve">Coroll. 2.
                <lb/>
              huius.</note>
            per H, centrum ſphæræ, atq; </s>
            <s xml:id="echoid-s434" xml:space="preserve">adeo ex H, centro ſphæræ eadem H E, ducta
              <lb/>
            erit perpendicularis ad planum circuli B F D G. </s>
            <s xml:id="echoid-s435" xml:space="preserve">Quocirca H E, vtrinq; </s>
            <s xml:id="echoid-s436" xml:space="preserve">edu-
              <lb/>
              <note position="left" xlink:label="note-026-02" xlink:href="note-026-02a" xml:space="preserve">8. huius.</note>
            cta cadetin polos eiuſdem circuli; </s>
            <s xml:id="echoid-s437" xml:space="preserve">ac proinde C, reliquus polus erit circuli
              <lb/>
            BFDG. </s>
            <s xml:id="echoid-s438" xml:space="preserve">Si igitur ſit in ſphæra circulus, & </s>
            <s xml:id="echoid-s439" xml:space="preserve">ab altero polorum eius, &</s>
            <s xml:id="echoid-s440" xml:space="preserve">c. </s>
            <s xml:id="echoid-s441" xml:space="preserve">Quod
              <lb/>
            oſtendendum erat.</s>
            <s xml:id="echoid-s442" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div55" type="section" level="1" n="35">
          <head xml:id="echoid-head46" xml:space="preserve">THEOR. 9. PROPOS. 10.</head>
          <note position="left" xml:space="preserve">13.</note>
          <p>
            <s xml:id="echoid-s443" xml:space="preserve">SI ſit in ſphæra circulus, linea recta per eius po
              <lb/>
            los ducta, ad circulum recta eſt, tranſitq́ per cen-
              <lb/>
            trum circuli, & </s>
            <s xml:id="echoid-s444" xml:space="preserve">ſphæræ.</s>
            <s xml:id="echoid-s445" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s446" xml:space="preserve">IN ſphæra A B C D, ſit circulus B F D G, per cuius polos A, C, recta du
              <lb/>
            catur A C, occurrens plano circuli in E. </s>
            <s xml:id="echoid-s447" xml:space="preserve">Dico rectam A C, ad planum circu
              <lb/>
            li rectam eſſe, tranſireq́; </s>
            <s xml:id="echoid-s448" xml:space="preserve">per eius centrum, (hoc eſt, E, eſſe ipſius centrum)
              <lb/>
            nec non per centrũ ſphæræ. </s>
            <s xml:id="echoid-s449" xml:space="preserve">Ductis namq; </s>
            <s xml:id="echoid-s450" xml:space="preserve">per E, duabus rectis vtcunq; </s>
            <s xml:id="echoid-s451" xml:space="preserve">B D,
              <lb/>
            F G, quarum extrema cum polis A, C, iungantur rectis, vt in figura; </s>
            <s xml:id="echoid-s452" xml:space="preserve">erunt
              <lb/>
              <figure xlink:label="fig-026-01" xlink:href="fig-026-01a" number="19">
                <image file="026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/026-01"/>
              </figure>
            tam A B, A G, A F, A D, inter ſe, quàm C B,
              <lb/>
            C G, C F, C D, inter ſe æquales, ex defin. </s>
            <s xml:id="echoid-s453" xml:space="preserve">poli.
              <lb/>
            </s>
            <s xml:id="echoid-s454" xml:space="preserve">Igitur duo triangula A B C, A D C, duo late-
              <lb/>
            ra A B, A C, duobus lateribus A D, A C, & </s>
            <s xml:id="echoid-s455" xml:space="preserve">ba
              <lb/>
            ſim B C, baſi D C, æqualem habent. </s>
            <s xml:id="echoid-s456" xml:space="preserve">Quapro-
              <lb/>
            pter & </s>
            <s xml:id="echoid-s457" xml:space="preserve">angulos B A C, D A C, æquales habe-
              <lb/>
              <note position="left" xlink:label="note-026-04" xlink:href="note-026-04a" xml:space="preserve">8. primi.</note>
            bunt. </s>
            <s xml:id="echoid-s458" xml:space="preserve">Quoniam igitur duo triangula A B E,
              <lb/>
            A D E, duo latera A B, A E, duobus lateribus
              <lb/>
            A D, A E; </s>
            <s xml:id="echoid-s459" xml:space="preserve">æqualia habent, anguloſq́; </s>
            <s xml:id="echoid-s460" xml:space="preserve">ſub ip-
              <lb/>
            ſis contentos B A E, D A E, æquales, vt pro-
              <lb/>
            xime demonſtratum eſt, erunt & </s>
            <s xml:id="echoid-s461" xml:space="preserve">anguli A E B,
              <lb/>
              <note position="left" xlink:label="note-026-05" xlink:href="note-026-05a" xml:space="preserve">4. primi.</note>
            A E D, æquales, & </s>
            <s xml:id="echoid-s462" xml:space="preserve">ob id recti. </s>
            <s xml:id="echoid-s463" xml:space="preserve">Non aliter de-
              <lb/>
            monſtrabimus, rectos eſſe angu los A E G, A E F. </s>
            <s xml:id="echoid-s464" xml:space="preserve">Recta igitur A E, duabus re-
              <lb/>
            ctis B D, F G, ad rectos inſiſtit angulos. </s>
            <s xml:id="echoid-s465" xml:space="preserve">Quare perpendicularis erit ad planũ
              <lb/>
            circuli B F D G, per rectas B D, F G, ductum. </s>
            <s xml:id="echoid-s466" xml:space="preserve">Quod eſt primo loco propoſi-
              <lb/>
              <note position="left" xlink:label="note-026-06" xlink:href="note-026-06a" xml:space="preserve">4. vndec.</note>
            tum. </s>
            <s xml:id="echoid-s467" xml:space="preserve">Quoniam igitur ex A, polo circuli B F D G, ad eius planum perpendi-
              <lb/>
            cularis eſt ducta A E, cadet A E, in centrum ipſius. </s>
            <s xml:id="echoid-s468" xml:space="preserve">Eſt ergo E, centrum cir-
              <lb/>
              <note position="left" xlink:label="note-026-07" xlink:href="note-026-07a" xml:space="preserve">9. huius.</note>
            culi B F D G. </s>
            <s xml:id="echoid-s469" xml:space="preserve">Rurſus quia ex E, centro circuli B F D G, educta eſt ad eius pla
              <lb/>
            num perpendicularis E A, tranſibit hæc per centrum quoq; </s>
            <s xml:id="echoid-s470" xml:space="preserve">ſphæræ. </s>
            <s xml:id="echoid-s471" xml:space="preserve">Quare
              <lb/>
              <note position="left" xlink:label="note-026-08" xlink:href="note-026-08a" xml:space="preserve">Coroll. 2.
                <lb/>
              huius.</note>
            recta A C, perpendicularis eſt ad planum circuli B F D G, tranſitq́ per eius
              <lb/>
            centrum, & </s>
            <s xml:id="echoid-s472" xml:space="preserve">ſphæræ. </s>
            <s xml:id="echoid-s473" xml:space="preserve">quod eſt propoſitum. </s>
            <s xml:id="echoid-s474" xml:space="preserve">Si ſit igitur in ſphæra circulus,
              <lb/>
            linea recta per eius polos ducta, &</s>
            <s xml:id="echoid-s475" xml:space="preserve">c. </s>
            <s xml:id="echoid-s476" xml:space="preserve">Quod erat demonftrandum.</s>
            <s xml:id="echoid-s477" xml:space="preserve"/>
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        <div xml:id="echoid-div57" type="section" level="1" n="36">
          <head xml:id="echoid-head47" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s478" xml:space="preserve">_ADDVNTVR_ hoc loco alia duo theoremata huiuſmodi.</s>
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