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# Title: LBr. 705 · Overbeck
# Folio 110r, page id DE-611-HS-861255:0219
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=219
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Calculus Analyticq pro Nequationibus se mutuo explicantibus
aubx +acx + afx + ahh
ftr
a
16
3
Sit O = 2h
a
a
e
h
fit fv (Shv= 8bh2 (2 -h) 31 (C f +C V) 4 h s
fit H2+f
a
aZ D2
D = fZ + hv,: a
a
qu
E. h) +2h7 2l7
2
b0 +c8O +fG
Q- f+v siet
sar
a
F
C + h2 ∞3
a P
  +effo + fo) +h2f3+ 3hfo +3lfo +tv
fit f. fnefchoftrfeho 7 flv +tiv3- oble 2. e + Th c f + gta (2. h) + l Xf  2hf Ah efsu - 4lt +2h) L tfi
C
a
a
Tollo utrinque h2v + fh v +2f2hv = h v +3sfv- 2lfo 2 fn
fit par (f1V) +2fChv = 8bL (2 h3 + 4Ecf + 4h ev (2 -h + 2h2f.
2
fit (1) 
3
a2
aLl
a a a
a
+REf3 + 3h f2x +3h fv + k2∞3
Tollo utrinque 2f2ho d a dextris -h f+ hX3
12
+3h f2p -2
h) +2h2F3 ∞f hfV + 2(f∞) 1  FEs
34f72- ebh (24h) +4 h Ef (2. h 14hcr- 5 k c1Zh + explicite capiendo fit.
2
a2
2(292 2 (292
afE+avf
2(92
as
Maltiplicando per a fiet a
hhcot
f3
th
q
AheffoH 12 fht
2(23
0
=5bh 2 + aacfh (F- h) (gakcvF dahc BZ tqah v + rahf ahf= a vh f +2(7
d
Et sumendo D. seorsim fiet
-8bh, (2h)  4acfh (2- h)- 2a h2f3 + a
s
4a chZ - a2 f27 - 8 ah 7 + 4 ahc - an f + 2afhF
seu 8bh, (2- h)3 + 4ac fh (2 - h +2 a 22 f3 a
2
t
e
(3
29253
= a
a fF = 4ah 2 + 8 al c a4 a hc + a h f - 2a h2
= V
Ergo capiatur C = 2h Z - h  4ah Z + 8a h Z + 4h ac = X a ch
a
D = fZ: a + D  fZ. a + 8bl 2. ld +4 cfh (2- h +2 a hF f- auf- anf3
2
12
a f22 - 4at cZ + 8 ah32- 4a h + ahff-2ahH
= 4 ahCF2
2  +(2 hZ- h2- 22)
(a. f 4 atrc) Z + 8 ah cZ - 4 ahtc + (h2- 2hZ) af
Tribatur pro Compendio Z - h = X. 2 - 2ht + h = X2
erit  - 8bhx +stacfh - a f2)X
Na fr- quch2 X2
= (2 - h) 
seu 5ebh X + + acfse - a (3
2
= 5bh (E. h) + ac fh - a f3) Fh
(af- ac k1 (2- 1
213
f3
seu 6 = 8bh(F -h) + 4 ac fh2 - a f3
2f jach
S2