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# Title: LBr. 705 · Overbeck
# Folio 111r, page id DE-611-HS-861255:0221
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Calculus Analyticus pro Aequationibus se mutuo explicantibus
ay=bx tacx + a fx + ahh
Sit O = 2hZ-h D - fz+ hv,: a
a
a 8D2
(2
b0 +c8O+ f820 +h Xo
a E
E= f +v Compendium sit Z-h = X
Facit f+n (f2 + hv) = 8b(X  cff+v 4 2 H Lnx + h (f +v)
a.
aL
seu 2 = X+h
Multiplico totum perc
fit fto (2 schv+lo) = 8bh X (ce 2s +f00) 2hx +k β13k foxhiso  tissi
it AE ffehor f ffiviselioo-solx talicat tghexe tf hxraffonx tehxfo xti olios otiso i
Ex Compendio collantur 2fZhv - 2 fKhv +2fkhv manet ergo
fsezho+ fh + fE +kv= 8blex: a +4kfx +4hx +2f.tx tafolxthf 13lv fo
Tollantur denuo utrinque K2fv + h V3 fiet
2
(232feho +v - 8bl X. a l fx + 4li xv + 2hxfet effvtx + hf3 +3lexf2
fiet
Ex Copendio 2hxf = 2h2f3- 2hhf3
f22 12f7h0 + f2Zv = 8bkX: a + ahe cfx +ahcvx
addo -2hZ F3 +hhf3
Afnhx = 4foh Z - qf vhh
+2hZf + qffohZ- fuhh - f3kh
-2h2f3+h + hhf3
E
fit fZ  2hZf3+ hf3 +2fhv + fZv = 8bh X: a + glcfx ralicox + 4ffvhZ. fnkh
Pono 72 - 2hZ + h = X2
h =X
fit XC+ Effoht + fu  = BbhX: a + gh fx +4hC vx 1afvhF- x vh ffotit
Effoht utrinque tollantur Fiet
Xf, fnt - 8bh X: a +4hc fx + ah cnx + fnht. fuhx fuhh
Aet
 Subtrato
=h = X
Y3f 2- 8bh x: a +gh. fx + 4henx n Eh Essett  ohZ + Hoh
fen
e
rectat
e
= Bbhx: a + 4hec fx +4ACV
L.
c
fnth + fuxti
Totu divido pX2
fit f. = 8bhx: a + ahcf: a + ah.cv:  Muttips per a
fit a f3 = 8bhx + 4ach + 4 a cvti
Ergo V = e a f - 8ba X - qucs
Aach