414 
NACHLASS. 
log brigg-|-Q5 = 0.1 176122226 9692.2 
log hyp-|-ffi = 0.2708121550 7159155410 6425 
loghypffi = 0.9639593356 3153686352 36577 
Sinum lemniscaticum ipsius (| G5 — a) cosinum lemniscaticum ipsius a 
dicemus. 
Aequationis 
3. 
d * +77 iL =0 
v/(l — ' y/(l —2/ 4 ) 
integrale completum invenitur hoc 
,1 yy . .1 — XX 
x\J — 4- y\J 
1+ yy \ + xx 
1 — xy\J 
1 XX 1 — yy 
1 + XX l + yy 
= c 
Sed eiusdem aequat, integrale est 
arc sin lemn x -j- arc sin lemny 
unde sequitur C esse functionem ipsius c. Ut appareat qualis, ponamus y = 0. 
tum iit C = x, c = arc sin lemn#, quare erit c = arc sin lemn C, sive 
C = sin lemn c. Hinc si sin lemnjt? = #, sin lemn q = y, erit 
sin lemn (p -j- q) = 
IV /l=Uf + ^i=£f 
i + yy 1 + xx 
iizzl* 
Hinc posito p — ^cs, </ = —a, fit propter 
sin lemn (—a) — —sin lemn a, sin lemn \ a> = 1 
cos lemn a = 
V 
1— sin lemn a 2 
l + sin lemn a 2 
Forma autem praecedens transit in hanc