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