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

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        <div xml:id="echoid-div134" type="section" level="1" n="74">
          <p>
            <s xml:id="echoid-s1175" xml:space="preserve">
              <pb o="32" file="044" n="44" rhead=""/>
              <figure xlink:label="fig-044-01" xlink:href="fig-044-01a" number="48">
                <image file="044-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/044-01"/>
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            tur ſecare circulum A B C. </s>
            <s xml:id="echoid-s1176" xml:space="preserve">Et quoniam pla
              <lb/>
            num circuli A B C, ad plana circulorũ A B,
              <lb/>
            A C, rectum eſt oſtenſum, erunt vicisſim pla
              <lb/>
            na circulorum A B, A C, ad planum circuli
              <lb/>
            A B C, recta; </s>
            <s xml:id="echoid-s1177" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s1178" xml:space="preserve">D E, communis
              <lb/>
              <note position="left" xlink:label="note-044-01" xlink:href="note-044-01a" xml:space="preserve">19. vndec.</note>
            ipſorum ſectio ad idem planũ circuli A B C,
              <lb/>
            perpendicularis erit. </s>
            <s xml:id="echoid-s1179" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s1180" xml:space="preserve">ad diametros
              <lb/>
            A B, A C, in eodem plano exiſtentes perpen
              <lb/>
            dicularis erit, ex defin. </s>
            <s xml:id="echoid-s1181" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1182" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1183" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1184" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1185" xml:space="preserve">Quare
              <lb/>
            D E, vtrumque circulum A B, A C, tanget
              <lb/>
              <note position="left" xlink:label="note-044-02" xlink:href="note-044-02a" xml:space="preserve">Coroll. 16.
                <lb/>
              tertij.</note>
            in A; </s>
            <s xml:id="echoid-s1186" xml:space="preserve">ac proinde per deſin. </s>
            <s xml:id="echoid-s1187" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s1188" xml:space="preserve">circuli
              <lb/>
            A B, A C, ſe mutuo tangent in A, puncto.
              <lb/>
            </s>
            <s xml:id="echoid-s1189" xml:space="preserve">Si igitur in ſphæra duo circuli ſecent, &</s>
            <s xml:id="echoid-s1190" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s1192" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div136" type="section" level="1" n="75">
          <head xml:id="echoid-head87" xml:space="preserve">THEOREMA 4. PROPOS. 4.</head>
          <note position="left" xml:space="preserve">5.</note>
          <p>
            <s xml:id="echoid-s1193" xml:space="preserve">SI in ſphæra duo circuli ſe mutuo tangant, ma-
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            ximus circulus per eorum polos deſcriptus, per
              <lb/>
            eorum contactum tranſibit.</s>
            <s xml:id="echoid-s1194" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1195" xml:space="preserve">IN ſphæra tangant ſe mutuo circuli A B, C B, in B; </s>
            <s xml:id="echoid-s1196" xml:space="preserve">& </s>
            <s xml:id="echoid-s1197" xml:space="preserve">per D, polum cir-
              <lb/>
              <note position="left" xlink:label="note-044-04" xlink:href="note-044-04a" xml:space="preserve">20. 1. huius.</note>
            culi A B, & </s>
            <s xml:id="echoid-s1198" xml:space="preserve">E, polum circuli C B, deſcribatur circulus maximus D E. </s>
            <s xml:id="echoid-s1199" xml:space="preserve">Dico
              <lb/>
            circulum D E, per contactum B, tranſire. </s>
            <s xml:id="echoid-s1200" xml:space="preserve">Non tranſeat enim, ſi fieri poteſt,
              <lb/>
            per tactum B, ſed ſecet circunferentiam v. </s>
            <s xml:id="echoid-s1201" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1202" xml:space="preserve">circuli C B, in F. </s>
            <s xml:id="echoid-s1203" xml:space="preserve">Polo igitur
              <lb/>
            D, & </s>
            <s xml:id="echoid-s1204" xml:space="preserve">interuallo D F, circulus deſcribatur F G, qui, cum ad maius interual-
              <lb/>
              <figure xlink:label="fig-044-02" xlink:href="fig-044-02a" number="49">
                <image file="044-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/044-02"/>
              </figure>
            lum deſcriptus ſit, quàm circu
              <lb/>
            lus A B, ſecabit circulũ C B,
              <lb/>
            in F; </s>
            <s xml:id="echoid-s1205" xml:space="preserve">quandoquidem circulus
              <lb/>
            A B, eundem tangit in B, pun
              <lb/>
            cto, vltra quod circulus G F,
              <lb/>
            ex polo D, deſcriptus eſt. </s>
            <s xml:id="echoid-s1206" xml:space="preserve">Quo
              <lb/>
            niam vero in ſphæra duo cir-
              <lb/>
            culi G F, C F, ſecant in eodẽ
              <lb/>
            puncto F, maximum circulum
              <lb/>
            D F E, per eorum polos de-
              <lb/>
            ſcriptum, tangent ſe mutuo in
              <lb/>
            F, duo circuli G F, C F: </s>
            <s xml:id="echoid-s1207" xml:space="preserve">Sed
              <lb/>
              <note position="left" xlink:label="note-044-05" xlink:href="note-044-05a" xml:space="preserve">3. huius.</note>
            & </s>
            <s xml:id="echoid-s1208" xml:space="preserve">mutuo ſeſe ſecant in F, vt
              <lb/>
            dictum eſt. </s>
            <s xml:id="echoid-s1209" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s1210" xml:space="preserve">Non ergo circulus maximus D E, ſecat ali-
              <lb/>
            bi circulos A B, C B, quàm in B, contactu, atque adeo per eorum tactũ tran
              <lb/>
            ſibit. </s>
            <s xml:id="echoid-s1211" xml:space="preserve">Itaque ſi in ſphæra duo circuli ſe mutuo tangant, &</s>
            <s xml:id="echoid-s1212" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1213" xml:space="preserve">Quod oſtenden-
              <lb/>
            dum erat.</s>
            <s xml:id="echoid-s1214" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">6.</note>
        </div>
        <div xml:id="echoid-div138" type="section" level="1" n="76">
          <head xml:id="echoid-head88" xml:space="preserve">THEOR. 5. PROPOS. 5.</head>
          <p>
            <s xml:id="echoid-s1215" xml:space="preserve">SI in ſphęra duo circuli ſe mutuo tangant, </s>
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