Full text: Sonderdrucke, Sammelband

(1) 
unde sequitur 
(2) 
г — (z — и) (z a)( z — /5)", 
dx 4- idy (г — «)(2 + a) (z — /5)"+ 1 
~ (0 _ а )2 (г + af ( z _ ¿)«+i ~ ' 
(3) cp (z) = / (0) . (0 — a) 2 , y (0) = / (0) . (0 4- «) 2 , z (0) =/(2) • (* — &)" +1 - 
Ut integrate x-\-iy sit functio rationalis, conditiones sunt 
(4) ?'(«) = 0, y'(-<*) = 0, *C>(6) = 0, 
quarum una, (6) = 0, omitti potest, quod 
cp' (a) + xf/ (— a) 4- ~ x (n) (6) — 0. 
Ex aequationibus (2) et (3) sequitur 
cp' (z) = 1 ^ 1 2_ 
cp (0) 0 — a 
y'(«) 
? (a) 
0 4- a 0 
(3 « — a) 0 4- (3 a ■— a) a 
(0 — a) (0 4- a) (0 4- a) 
a 2 — б a a 4- a 2 
4~ (n 4- 1) 
, 14 — è 
,5—6 
а? — « (/9 4- è) 4- /56 
2 a (a 2 — a 2 ) 
Quare prima conditio haec est 
(5) (a 2 — 6 a a 4- a 2 ) [a 2 — a (/3 4- 6) 4- ¡3 6] = 2 (w 4- 1) a (a 2 — a 2 ) — 6), 
sive conjugata 
(6) (a 2 — 6 a u 4- a 2 ) [a 2 — « (/^4- 4- = 2 («+ 1) « (a 2 — a 2 ) (/5 — 6). 
cp (0) in (z), neque minus in ^4—-j transit, si a et — a commutantur, habe- 
cp{a) ifj (—«) 7 
mus igitur alteram conditionem 
(7) (a 2 — 6 a« 4- « 2 ) [« 2 4- « (fi 4- b) 4- /56] = 2 (w 4- 1) « — a 2 ) (/? — 6). 
Ex aequationibus (6) et (7) collatis elucet 
(8) 
/54-6 = 0, b — — /5, /56 = — 
quo substituto aequationes (5) et (6) transducuntur in 
(a 2 — 6acc 4- « 2 ) (a 2 — /? 2 ) = 4 (я + 1) a (a 2 — a 2 ) /5, 
(a 2 _ Q aa «*) ^ ss 4( n+ i) a (a 2 — ft 2 ) /5, 
(9) 
sive 
(10) 
a 2 — 6a«4-« 2 = 4 (я + 1) (a — u) /5, 
a 2 — 6 a u 4- a 2 
/5 = 
6. 
4(w -}- 1) (a— «) 
Substitutione peracta aequationes (9), factore (a 2 — 6 a u 4- a 1 ) sublato, conditionem, 
qua modulus functionis ellipticae determinatur, significant 
(11) 16 (n 4- l) 2 (« — «) 2 a et 4- (a 2 — 6 au 4- « 2 ) 2 = 0. 
Hoc exemplum sufficiat, ut demonstretur methodum Illustrissimi Serret multo extendi 
posse. Nunc statim aliam rationem ineamus.
	        
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