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

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        <div xml:id="echoid-div79" type="section" level="1" n="49">
          <pb o="20" file="032" n="32" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s707" xml:space="preserve">_IN_ ſphæra tranſeat maximus circulus
              <lb/>
              <figure xlink:label="fig-032-01" xlink:href="fig-032-01a" number="27">
                <image file="032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/032-01"/>
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            _A B C D,_ per _A, C,_ polos circuli maximi _B D._
              <lb/>
            </s>
            <s xml:id="echoid-s708" xml:space="preserve">_Dico_ & </s>
            <s xml:id="echoid-s709" xml:space="preserve">maximum circulum _B D,_ per polos ma-
              <lb/>
            ximi circuli _A B C D,_ tranſire. </s>
            <s xml:id="echoid-s710" xml:space="preserve">Quoniam enim
              <lb/>
            circulus maximus _A B C D,_ circulum _B D,_ ſe-
              <lb/>
              <note position="left" xlink:label="note-032-01" xlink:href="note-032-01a" xml:space="preserve">15. huius.</note>
            cat per polos, ſecabit ipſum ad angulos rectos.
              <lb/>
            </s>
            <s xml:id="echoid-s711" xml:space="preserve">Quare vicißim maximus circulus _B D,_ circu-
              <lb/>
            lum _A B C D,_ ad angulos rectos ſccabit; </s>
            <s xml:id="echoid-s712" xml:space="preserve">at-
              <lb/>
            que adeo per ipſius polos eum ſecabit. </s>
            <s xml:id="echoid-s713" xml:space="preserve">Quod eſt
              <lb/>
              <note position="left" xlink:label="note-032-02" xlink:href="note-032-02a" xml:space="preserve">13. huius.</note>
            pr opoſitum.</s>
            <s xml:id="echoid-s714" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div82" type="section" level="1" n="50">
          <head xml:id="echoid-head61" xml:space="preserve">II.</head>
          <note position="left" xml:space="preserve">22.</note>
          <p>
            <s xml:id="echoid-s715" xml:space="preserve">SI in ſphæra circulus circulum per polos ſecet, circulus maxi-
              <lb/>
            mus eſt, & </s>
            <s xml:id="echoid-s716" xml:space="preserve">bifariam eum ſecat, & </s>
            <s xml:id="echoid-s717" xml:space="preserve">ad angulos rectos.</s>
            <s xml:id="echoid-s718" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s719" xml:space="preserve">_IN_ ſphæra circulus _A B C D,_ ſecet circu-
              <lb/>
              <figure xlink:label="fig-032-02" xlink:href="fig-032-02a" number="28">
                <image file="032-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/032-02"/>
              </figure>
            lum _B D,_ per polos _A, C._ </s>
            <s xml:id="echoid-s720" xml:space="preserve">Dico ipſum eſſe circu-
              <lb/>
            culum maximum, ſecareq́; </s>
            <s xml:id="echoid-s721" xml:space="preserve">circulum _B D,_ bifa-
              <lb/>
            riam, & </s>
            <s xml:id="echoid-s722" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s723" xml:space="preserve">Coniungat enim re-
              <lb/>
            cta _A C,_ polos _A, C,_ quæ neceſſario in plano
              <lb/>
            circuli _A B C D,_ erit, quod circunferentia eius
              <lb/>
            per eoſdem polos _A, C,_ ponatur tranſire. </s>
            <s xml:id="echoid-s724" xml:space="preserve">Quo-
              <lb/>
            niam vero recta _A C,_ per _A, C,_ polos circuli
              <lb/>
              <note position="left" xlink:label="note-032-04" xlink:href="note-032-04a" xml:space="preserve">10. huius.</note>
            _B D,_ ducta tranſit per centrum ſphæræ, tranſi-
              <lb/>
            bit quoque cir culus _A B C D,_ (cum per rectã
              <lb/>
            _A C,_ ducatur) per centrũ ſphæræ; </s>
            <s xml:id="echoid-s725" xml:space="preserve">atque adeo
              <lb/>
              <note position="left" xlink:label="note-032-05" xlink:href="note-032-05a" xml:space="preserve">6. huius.</note>
            maximus erit. </s>
            <s xml:id="echoid-s726" xml:space="preserve">Quare cum per _A, C,_ polos cir
              <lb/>
              <note position="left" xlink:label="note-032-06" xlink:href="note-032-06a" xml:space="preserve">15. huius.</note>
            culi _B D,_ ponatur tranſire, ſecabit eum bifariam, & </s>
            <s xml:id="echoid-s727" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s728" xml:space="preserve">Quod eſt
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s729" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div84" type="section" level="1" n="51">
          <head xml:id="echoid-head62" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s730" xml:space="preserve">SI in ſphæra circulus circulum bifariam, & </s>
            <s xml:id="echoid-s731" xml:space="preserve">ad angulos rectos
              <lb/>
              <note position="left" xlink:label="note-032-07" xlink:href="note-032-07a" xml:space="preserve">23.</note>
            ſecet, circulus maximus eſt, & </s>
            <s xml:id="echoid-s732" xml:space="preserve">per polos eum ſecat.</s>
            <s xml:id="echoid-s733" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s734" xml:space="preserve">_IN_ſphæra circulus _A B C D,_ ſecet circulum
              <lb/>
              <figure xlink:label="fig-032-03" xlink:href="fig-032-03a" number="29">
                <image file="032-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/032-03"/>
              </figure>
            _B D,_ bifariam, & </s>
            <s xml:id="echoid-s735" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s736" xml:space="preserve">_Dico_ ipſum
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            eſſe circulum maximum, tranſireq́; </s>
            <s xml:id="echoid-s737" xml:space="preserve">per polos cir-
              <lb/>
            culi _B D._ </s>
            <s xml:id="echoid-s738" xml:space="preserve">Sit recta _BD;_ </s>
            <s xml:id="echoid-s739" xml:space="preserve">communis circu lorum ſe-
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            etio. </s>
            <s xml:id="echoid-s740" xml:space="preserve">Quo niam igitur circulus _A B C D,_ circu-
              <lb/>
            lum _B D,_ ſecat bifariam, erit recta _B D,_ nempe
              <lb/>
            communis ſectio circulorũ, diameter circuli B D,
              <lb/>
            atque adeo diuiſa recta _B D,_ bifari am in E: </s>
            <s xml:id="echoid-s741" xml:space="preserve">erit
              <lb/>
            E, eiuſdem circuli centrum. </s>
            <s xml:id="echoid-s742" xml:space="preserve">Ducatur in plano cir
              <lb/>
            culi _A B C D,_ recta E A, perpendicularis ad re
              <lb/>
            etam _B D._ </s>
            <s xml:id="echoid-s743" xml:space="preserve">Et quoniam circulus _A B C D,_ </s>
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