164 
W. SaiElßNEK, 
2. 2Hw Hx H- 3 y H 3 Z = TI-h n t -+■ iT 2 -f- ji 3 , 
2 ¿G X />, X H^jH, Z — /7 + //, — JJ 2 — JI 3 , 
2 X t'/, y Hy Z = II— ll t + II 2 — JT 3 , 
2H 3 wH 3 xHyHz = n-11,-17,4-il 3 , 
[108 
/1 = HmH§H 3 yH 3 £ 
ll l = # 4 £ 
iT 2 = H,mHjHy V Hy£ 
ii 3 = H 3 mH 3 §H v H 
3. 2 H w Hx H 2 y H 2 z 
2 H { W Hy X il 3 y H 3 Z 
2 H^W H^X Hy Hz 
2 H 3 W H 3 X d' i y H y Z 
II 4- //, 4- u 2 4- ll 3 , 
II 4” /7, //. 2 iT 3 J 
n-n i + n i -n 3 , 
= 17 - II. 
n, + n 3 , 
II = HzyH^H^H^ 
n i = & i && i i;& 3 ri H 3 £ 
ü<i — 1< G & 'I\ s y d £ 
J/ 3 = H.mH^Hy^Hyl 
4 2H 3 wH 3 xH i yH^z 
2 H 2 w H^x H 3 y H 3 z 
2 HyW HyX HyHz 
2Hw Hx H i yH l z 
n + n, + n t +n a , 
n+n,-n,-n 3 , 
n-n. + n.-n, , 
n-n t -n,+ n, , 
5- 2 Hy W Hx H^y H 3 z -— 1 / 4- //, + Z/, 4- FI 3 , 
2 «7, x >7 3 ?/ i7 2 z = II -h 17, — Tl 2 — il 3 , 
2 # 2 x H 3 x H t y Hz — ü — lf, 4- U 2 — 77 3 , 
2 dyx H 2 xHy Hy z = II — II t — JfT 2 -+- U 3 , 
II = H 3 m H.J H 2 y H,£ 
n i = 3*] ^ 3 £ 
71 2 = HyOrHy^HrjHC 
il 3 = H&Ht-HyrjHyC 
II = HyüiH^H 2 rjH 3 £ 
IIy = Hm Hy £# 3 *7 .7,£ 
/Z 2 = H.mH^HyTjH 
II3 = 
In diesen fünf Gruppen von Formelquaternionen sind die Argu 
mente der Thetaproducte auf der rechten und linken Seite durch die 
reciproken Gleichungen mit einander verbunden 
a) 
&) 
c ) 
d) 
2 tc = ¡75" 4- £ -f- *7 -»- £ , 
2X = tf4-i;— »J — C, 
2iy = m — ^h- »7 — £ , 
2js = 57 — £ —17 4- £ , 
folglich auch 
X 4- X = rar 4- £ , 
x 4- // = m y , 
w -h z = 04- i , 
2 er = W 4- X 4- y 4- 
2 ij = x 4- c — y — 
2 »7 =iü — x-\- y — 
2 £ = W — X — >/ 4- 
?/ — JZ = 17 — £ 
s — .x = C — £ 
x-y = g — y