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# Title: LBr. 705 · Overbeck
# Folio 105r, page id DE-611-HS-861255:0209
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=209
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a4D
Calculus Analyticus pro Aequationibus se mutuo explicantibus
C
b63 +C8 + f8O +h
3
2 2 (2)
ay= =bX tacx + a fx +ah
Sit O = 2hx sit vero x = Z - h.  Sit D - f2+ hB, :a
a
Sit 4-f +v
Ergo f1~ (f2thu) = 8kx b  +c (f1V) 4 lX, 2 (f1 hx + Li (f +D) Maltipl. totupsa
ana
a
a
fit (f+ v f2 + hofzatio = 8h.bx: a + (Cf 1 CvakiX + 2fhx (f +V) + h f2+3 f oh + 3 fvk + V E2
Et explicite
a
ut habeatur v expliate scribo
(382 2hyffZ+ flv +fEv + EhfEV +kV -8Rbx: a + 4cfh x + 4cvh XJ: a 12xh F 14 Xhf fv + 2xhfD +h2(3
Tollo utrinque hfr +tv3 fiet
+3 fvh +3fr h + B3h
P hvf+fv 12hfZV- 8tbx: a +4 cfhX: a + gentix: a, 12hxf3 ahxoff 2hyfot h f. 3foh 12tif
2hfZB perdi  2hfxn 12hhfr quibus utrinque ablatis fiet
(352
+2hv2f + vff = Bh bx: a 14 cfh X: a + a cvhX: a +Ehxfo ah vf tls +h f 2, 3f vti
Transferendo totum f3 ad sinijoram fit
2
f22- 2hX f3 +kf3 + 2hoZf + ZEnf = 8k3b∞3
24cfhx: a + gentex: a + 4hxnff. + 3 frti
PX est - 2hx f3 = -2h2f + 2hhf3 Haec utriaa atendo scribetur
(392
2hEf+ hf. 12h0E f2 + 72yf2
per d est 3 2 h + hi = X Fiet Xf.
eno
8kbx: a + 4cfk X: a + a cvh X: a + gh X Vf +3f3h2
+2h∞Z f+ 2v f - 8 AhEbX: a + 4c fhx: a + 4cuhX. a tghavs
2hv2 e
fiet X f+ 20f = 8Lbx: a +4c fhX: a +4coh x: a +2hxvH + fevhh
fo f
n n pera. artivie 
2lXVf- EAfEhhvH
fiet X f3+2vf = 8kbx: a +4cfhX: a +4cvkx: a + 2hZvf - hhvf
Transferendo fadsinistram fiet
2, 2 nf- 2hEnf + hhvff = 8h bx: a +4cfhX: a + 4 cptex: a
22 - 2hZ + hh = XX per _
tix
fiet 2f2 + x vf = 8hbx3: a +4c fh X: a + + cnhx: a Dividototum perqur
fit Hf3 + vf = Bh bx: a + 4c fh: a + 4cvh: a
Id est BkbX: a + 4c FhE: a, - f3 Propertionando p a
f2 = Ach: a.
Ergo C = 2h Z. h
fit v = 8h3bX + 4c fka - f292
D = f7 + 8h bX + 4c fha - hf222
a3 f2 - 4a c hE
Z = f + 8hebx +4ctha - f32
Resum antur initialia
a f2 - 4 ac h
elle
Facit
E
a f-4 a ach
2h-
F+ 8Ab . Id nacftia  fa
h bx + 4cfha - hf
a3 f2 - 4 a c h
a
e
Multipl per
f+ 8 h bx +4 cfh a - f3 a a372-4d ch
a fr - 4 ach
il9- s2a f- 4)2 a ch +6h2bX +4cfla -hf’a
1273- 4 ach f +8h 6x + 4cfh a- f.
a f2- 4ach