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

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        <div xml:id="echoid-div153" type="section" level="1" n="83">
          <p>
            <s xml:id="echoid-s1364" xml:space="preserve">
              <pb o="37" file="049" n="49" rhead=""/>
            li B G A, D G A, B G C, D G C, ex definit. </s>
            <s xml:id="echoid-s1365" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1366" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1367" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1368" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1369" xml:space="preserve">Quare diameter
              <lb/>
            A C, cum per centrum circuli A B C D, tranſeat, ſecetq̃; </s>
            <s xml:id="echoid-s1370" xml:space="preserve">rectam B D, ad
              <lb/>
            angulos rectos, bifariam eam ſecabit. </s>
            <s xml:id="echoid-s1371" xml:space="preserve">Itaque cum latera A G, G B, æqualia
              <lb/>
              <note position="right" xlink:label="note-049-01" xlink:href="note-049-01a" xml:space="preserve">3. tertij.</note>
            ſint lateribus A G, G D, contineantq́; </s>
            <s xml:id="echoid-s1372" xml:space="preserve">angulos æquales, nempe rectos, erunt
              <lb/>
              <note position="right" xlink:label="note-049-02" xlink:href="note-049-02a" xml:space="preserve">4. primi.</note>
            baſes A B, A D, ſubtendentes arcus A B, A D, inter ſe æquales, ac proinde
              <lb/>
              <note position="right" xlink:label="note-049-03" xlink:href="note-049-03a" xml:space="preserve">28. terij.</note>
            & </s>
            <s xml:id="echoid-s1373" xml:space="preserve">arcus A B, A D, æquales erunt. </s>
            <s xml:id="echoid-s1374" xml:space="preserve">Eodem modo oſtendemus arcus C B, C D,
              <lb/>
            æquales eſſe; </s>
            <s xml:id="echoid-s1375" xml:space="preserve">nec non & </s>
            <s xml:id="echoid-s1376" xml:space="preserve">arcus E B, E D; </s>
            <s xml:id="echoid-s1377" xml:space="preserve">& </s>
            <s xml:id="echoid-s1378" xml:space="preserve">F B, F D. </s>
            <s xml:id="echoid-s1379" xml:space="preserve">Circulus igitur A F C E,
              <lb/>
            ſegmenta B A D, B C D, B E D, B F D, bifariam diuidit. </s>
            <s xml:id="echoid-s1380" xml:space="preserve">Quapropter ſi in
              <lb/>
            ſphæra duo circuli ſe mutuo ſecent, &</s>
            <s xml:id="echoid-s1381" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1382" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s1383" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div155" type="section" level="1" n="84">
          <head xml:id="echoid-head96" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1384" xml:space="preserve">_DVO_ alia theoremata in alia verſione hoc loco adduntur, hæc videlicet.</s>
            <s xml:id="echoid-s1385" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div156" type="section" level="1" n="85">
          <head xml:id="echoid-head97" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s1386" xml:space="preserve">SI in ſphæra duo circuli ſe mutuo ſecent, circulus alius eorum
              <lb/>
              <note position="right" xlink:label="note-049-04" xlink:href="note-049-04a" xml:space="preserve">13.</note>
            ſegmenta bifariam ſecans, it per polos eorum, eſtq́; </s>
            <s xml:id="echoid-s1387" xml:space="preserve">circulus ma-
              <lb/>
            ximus.</s>
            <s xml:id="echoid-s1388" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1389" xml:space="preserve">_IN_ eadẽ figura ſecent ſe mutuo duo circuli _A B C D, E D F B,_ in punctis _B, D,_ & </s>
            <s xml:id="echoid-s1390" xml:space="preserve">
              <lb/>
            alius quiſpiã circulus _A F C E,_ ſecet ſegmenta _B A D, B C D, B E D, B F D,_ bifariã. </s>
            <s xml:id="echoid-s1391" xml:space="preserve">_D_i
              <lb/>
            co ciculũ _A F C E,_ ire per polos ipſorũ, eſſeq́; </s>
            <s xml:id="echoid-s1392" xml:space="preserve">circulũ maximũ. </s>
            <s xml:id="echoid-s1393" xml:space="preserve">Quoniã enim arcus _A D,_
              <lb/>
            _A B,_ æquales ſunt, nec nõ _C D, C B,_ erũt toti arcus _A D C, A B C,_ æquales, & </s>
            <s xml:id="echoid-s1394" xml:space="preserve">propte
              <lb/>
            rea ſemicirculi. </s>
            <s xml:id="echoid-s1395" xml:space="preserve">_E_odemq́; </s>
            <s xml:id="echoid-s1396" xml:space="preserve">modo ſemicirculi erũt _E D F, E B F. </s>
            <s xml:id="echoid-s1397" xml:space="preserve">C_irculus igitur _A F C E,_
              <lb/>
            bifariam ſecat circulos _A B C D, E D F B,_ atque adeo communes ſectiones _A C, E F,_
              <lb/>
            ſe interſecantes in _G,_ ipſorum diametri ſunt. </s>
            <s xml:id="echoid-s1398" xml:space="preserve">_Q_uòd ſi connectantur rectæ _B G, D G,_
              <lb/>
            cum tria puncta _
              <emph style="sc">B</emph>
            , G, D,_ in vtroque plano circulorum _A B C D,
              <emph style="sc">EDFb</emph>
            _, ſint, at-
              <lb/>
            que adeo in communi ipſorum ſectione; </s>
            <s xml:id="echoid-s1399" xml:space="preserve">ſit autem communis eorum ſectio linea recta;
              <lb/>
            </s>
            <s xml:id="echoid-s1400" xml:space="preserve">
              <note position="right" xlink:label="note-049-05" xlink:href="note-049-05a" xml:space="preserve">3. vndec.</note>
            recta erit _
              <emph style="sc">B</emph>
            G D. </s>
            <s xml:id="echoid-s1401" xml:space="preserve">Q_uoniam vero ſubtenſæ rectæ _D A, D C,_ ſubtenſis rectis
              <emph style="sc">B</emph>
            _A_,
              <emph style="sc">B</emph>
            _C,_
              <lb/>
              <note position="right" xlink:label="note-049-06" xlink:href="note-049-06a" xml:space="preserve">29. tertij.</note>
            ſingulæ ſingulis æquales ſunt, ob æquales arcus, anguloſq́; </s>
            <s xml:id="echoid-s1402" xml:space="preserve">continent æquales, nem-
              <lb/>
              <note position="right" xlink:label="note-049-07" xlink:href="note-049-07a" xml:space="preserve">31. tertij.</note>
            pe rectos in ſemicirculis exiſtentes; </s>
            <s xml:id="echoid-s1403" xml:space="preserve">æquales erunt anguli _D A C,
              <emph style="sc">B</emph>
            AC. </s>
            <s xml:id="echoid-s1404" xml:space="preserve">Q_uod etiã
              <lb/>
              <note position="right" xlink:label="note-049-08" xlink:href="note-049-08a" xml:space="preserve">4. primi.</note>
            ita probari poterit. </s>
            <s xml:id="echoid-s1405" xml:space="preserve">_Q_uoniam latera _D A, A C,_ lateribus _
              <emph style="sc">B</emph>
            A, A C,_ æqualia ſunt,
              <lb/>
            baſiſq́; </s>
            <s xml:id="echoid-s1406" xml:space="preserve">_D C,_ baſi _
              <emph style="sc">B</emph>
            C,_ æqualis, erunt anguli _D A C,
              <emph style="sc">B</emph>
            AC,_ æquales. </s>
            <s xml:id="echoid-s1407" xml:space="preserve">Rurſus quia
              <lb/>
              <note position="right" xlink:label="note-049-09" xlink:href="note-049-09a" xml:space="preserve">8. primi.</note>
            latera _A D, A G,_ lateribus _
              <emph style="sc">Ab</emph>
            , A G,_ æqualia ſunt, angulosq́; </s>
            <s xml:id="echoid-s1408" xml:space="preserve">continent æqua-
              <lb/>
              <note position="right" xlink:label="note-049-10" xlink:href="note-049-10a" xml:space="preserve">4. primi.</note>
            les, vt demonſtratum eſt; </s>
            <s xml:id="echoid-s1409" xml:space="preserve">æquales erunt anguli _A G D, A G
              <emph style="sc">B</emph>
            ,_ ac propterea recti.
              <lb/>
            </s>
            <s xml:id="echoid-s1410" xml:space="preserve">Perpendicularis igitur eſt _
              <emph style="sc">B</emph>
            GD,_ ad rectam _A C, E_odem modo oſtendemus rectam
              <lb/>
            eandem _
              <emph style="sc">B</emph>
            GD,_ ad _E F,_ perpendicularem eſſe. </s>
            <s xml:id="echoid-s1411" xml:space="preserve">_Q_uare eadem _
              <emph style="sc">B</emph>
            GD,_ perpendicula-
              <lb/>
            ris erit ad planum circuli _A F C E,_ per rectas _A C, E F,_ ductum; </s>
            <s xml:id="echoid-s1412" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s1413" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-049-11" xlink:href="note-049-11a" xml:space="preserve">4. vndec.</note>
            vtrumque planum circulorum _
              <emph style="sc">Ab</emph>
            CD,
              <emph style="sc">EDFb</emph>
            ,_ per rectam _
              <emph style="sc">B</emph>
            GD,_ ductum ad
              <lb/>
            idem planum circuli _A F C E,_ rectum erit: </s>
            <s xml:id="echoid-s1414" xml:space="preserve">& </s>
            <s xml:id="echoid-s1415" xml:space="preserve">vicißim circulus _A F C E,_ ad circu-
              <lb/>
              <note position="right" xlink:label="note-049-12" xlink:href="note-049-12a" xml:space="preserve">18. vndec.</note>
            los _
              <emph style="sc">Ab</emph>
            CD,
              <emph style="sc">EDFb</emph>
            ,_ rectus erit. </s>
            <s xml:id="echoid-s1416" xml:space="preserve">_I_taque circulus _A F C E,_ circulos _A
              <emph style="sc">B</emph>
            C D,_
              <lb/>
              <note position="right" xlink:label="note-049-13" xlink:href="note-049-13a" xml:space="preserve">Schol. 15. 1.
                <lb/>
              huius.</note>
            _E D F
              <emph style="sc">B</emph>
            ,_ & </s>
            <s xml:id="echoid-s1417" xml:space="preserve">bifariam & </s>
            <s xml:id="echoid-s1418" xml:space="preserve">ad angulos rectos ſecat, _Q_uare maximus eſt, tranſitq́; </s>
            <s xml:id="echoid-s1419" xml:space="preserve">per
              <lb/>
            ipſorum polos. </s>
            <s xml:id="echoid-s1420" xml:space="preserve">_Q_uod eſt propoſitum.</s>
            <s xml:id="echoid-s1421" xml:space="preserve"/>
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