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

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          <p>
            <s xml:id="echoid-s1134" xml:space="preserve">IN eadem ſphæra A B C D E F, circa eoſdẽ polos A, D, ſint circuli B F,
              <lb/>
            C E. </s>
            <s xml:id="echoid-s1135" xml:space="preserve">Dico eos parallelos eſſe. </s>
            <s xml:id="echoid-s1136" xml:space="preserve">Connexa enim recta A D, erit hæc ad vtrunq;
              <lb/>
            </s>
            <s xml:id="echoid-s1137" xml:space="preserve">
              <note position="right" xlink:label="note-043-01" xlink:href="note-043-01a" xml:space="preserve">10. 1. huius.</note>
            circulum perpendicularis. </s>
            <s xml:id="echoid-s1138" xml:space="preserve">Quare plana circulorum B F, C E, parallela ſunt.
              <lb/>
            </s>
            <s xml:id="echoid-s1139" xml:space="preserve">
              <note position="right" xlink:label="note-043-02" xlink:href="note-043-02a" xml:space="preserve">14. vndec.</note>
            In ſphæra igitur circuli, qui ſunt circa eoſdem polos, ſunt paralleli. </s>
            <s xml:id="echoid-s1140" xml:space="preserve">Quod
              <lb/>
            oſtendendum erat.</s>
            <s xml:id="echoid-s1141" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div131" type="section" level="1" n="73">
          <head xml:id="echoid-head85" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1142" xml:space="preserve">_SED_ & </s>
            <s xml:id="echoid-s1143" xml:space="preserve">hoc theorema ſequens in alia verſione demonſtratur.</s>
            <s xml:id="echoid-s1144" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1145" xml:space="preserve">IN ſphæra non ſunt plures circuli æquales, & </s>
            <s xml:id="echoid-s1146" xml:space="preserve">paralleli, quàm
              <lb/>
              <note position="right" xlink:label="note-043-03" xlink:href="note-043-03a" xml:space="preserve">3.</note>
            duo.</s>
            <s xml:id="echoid-s1147" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1148" xml:space="preserve">_IN_ ſphæra quacunque ſint, ſi fieri poteſt, plu
              <lb/>
              <figure xlink:label="fig-043-01" xlink:href="fig-043-01a" number="46">
                <image file="043-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/043-01"/>
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            res quàm duo circuli æquales, & </s>
            <s xml:id="echoid-s1149" xml:space="preserve">paralleli, nem
              <lb/>
              <note position="right" xlink:label="note-043-04" xlink:href="note-043-04a" xml:space="preserve">1. huius.</note>
            pe tres _A B, C D, E F,_ qui circa eoſdem polos
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s1150" xml:space="preserve">Sint ergo eorum poli G, H, & </s>
            <s xml:id="echoid-s1151" xml:space="preserve">iungatur
              <lb/>
              <note position="right" xlink:label="note-043-05" xlink:href="note-043-05a" xml:space="preserve">10. 1. huius.</note>
            recta _G H,_ quæ tranſibit per I, centrum ſphæ-
              <lb/>
            ræ, & </s>
            <s xml:id="echoid-s1152" xml:space="preserve">per _K, L, M,_ centra circulorum; </s>
            <s xml:id="echoid-s1153" xml:space="preserve">perpen
              <lb/>
            dicularisq́; </s>
            <s xml:id="echoid-s1154" xml:space="preserve">erit ad circulos _A B, C D, E F._ </s>
            <s xml:id="echoid-s1155" xml:space="preserve">Quo
              <lb/>
            niam igitur circuli _A B, C D, E F,_ æquales
              <lb/>
              <note position="right" xlink:label="note-043-06" xlink:href="note-043-06a" xml:space="preserve">6. 1. huius.</note>
            ſunt, ipſi æqualiter diſtabunt à centro ſphæræ _I._
              <lb/>
            </s>
            <s xml:id="echoid-s1156" xml:space="preserve">Per defin. </s>
            <s xml:id="echoid-s1157" xml:space="preserve">ergo 6. </s>
            <s xml:id="echoid-s1158" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1159" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1160" xml:space="preserve">huius, perpendiculares
              <lb/>
            _I K, I L, I M,_ æquales erunt, nempe pars _I L,_
              <lb/>
            & </s>
            <s xml:id="echoid-s1161" xml:space="preserve">totum _I M._ </s>
            <s xml:id="echoid-s1162" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s1163" xml:space="preserve">In ſphæra
              <lb/>
            igitur non ſunt plures circuli æquales, & </s>
            <s xml:id="echoid-s1164" xml:space="preserve">paralleli, quàm duo. </s>
            <s xml:id="echoid-s1165" xml:space="preserve">Quod demonſtran-
              <lb/>
            dum erat.</s>
            <s xml:id="echoid-s1166" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div134" type="section" level="1" n="74">
          <head xml:id="echoid-head86" xml:space="preserve">THEOREMA 3. PROPOS. 3.</head>
          <note position="right" xml:space="preserve">4.</note>
          <p>
            <s xml:id="echoid-s1167" xml:space="preserve">SI in ſphæra duo circuli ſecent in eodem pun
              <lb/>
            cto circunferentiam illius maximi circuli, in quo
              <lb/>
            polos habent, ſe mutuo tangent illi circuli.</s>
            <s xml:id="echoid-s1168" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1169" xml:space="preserve">IN ſphæra duo circuli A B, A C, ſecent
              <lb/>
              <figure xlink:label="fig-043-02" xlink:href="fig-043-02a" number="47">
                <image file="043-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/043-02"/>
              </figure>
            in puncto A, circunferentiam maximi circu-
              <lb/>
            li A B C, qui per illorum polos tranſeat. </s>
            <s xml:id="echoid-s1170" xml:space="preserve">Di
              <lb/>
            co circulos A B, A C, ſe mutuo tangere in
              <lb/>
            A. </s>
            <s xml:id="echoid-s1171" xml:space="preserve">Quoniam enim circulus maximus A B C,
              <lb/>
            ſecat circulos A B, A C, per polos, bifariam
              <lb/>
            ipſos ſecabit, & </s>
            <s xml:id="echoid-s1172" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s1173" xml:space="preserve">Commu-
              <lb/>
              <note position="right" xlink:label="note-043-08" xlink:href="note-043-08a" xml:space="preserve">15. 1. huius.</note>
            nes ergo ſectiones circuli A B C, & </s>
            <s xml:id="echoid-s1174" xml:space="preserve">circulo-
              <lb/>
            rum A B, A C, nempe rectæ A B, A C, dia-
              <lb/>
            metri ſunt circulorum A B, A C. </s>
            <s xml:id="echoid-s1175" xml:space="preserve">Sit quo-
              <lb/>
            que communis ſectio planorum, in quo
              <lb/>
            circuli A B, A C, exiſtunt, recta D E, quæ
              <lb/>
            per punctum A, tranſibit, propterea quod plana circulorum in A, </s>
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