Zur Reduction elliptischer Integrale. 
während die Integration der übrigen Quotienten die Formeln liefert 
, r<P dcp 
= ~ßr p = arclg ( x 't8<p) = 'P-'P 
^ n q n sin 2 nu 
u $u , , f(p dcp _ Jcp 4- x'sincp _ tg 2 ^ [\7t 4- x) 
- y I ■- - J 8 cos - p - *8—“ 
i) n q 1 n ~ 1 sin (2 n — i) u 
, ,, f u xtU . _ . , ( ,( P _ 
V 0 0-^u C U A J 0 cos cp /1 cp ' D COS cp tg -\(\rt-hcp) 
= •g l gi ii™ ■+■ u ) 4 ^ 
= i g t 8^(i- 7r + u ) + x ) n lg 
„ „ P u &‘,« , PV cos cp dcp i + )t sin cp 
tu dU = \h = = 
— 4 
i — q“' 1 ‘ 2ii—i i—29" 2 simi + g 
, „ r u &i u , rw dcp , ' . . 1 . 1 4-sinrß 
Vo ^2 W Jo COSi jP ' n - v - 2 I — sn\cp 
= lg lg l [\7t 4- u) 4- 4 N