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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 86r, page id 00068198:0171
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Si aquana hsfe- ageraaac sobb
111I. 11 1, 110. 110 ad
o 4. 1ono
2a)n+ qu (n (+ 1o a) 
4. 10
 2. 111 10al 4. 120. 120I = 4. 190.120 al - 4. 100. 120 a a
a eve
seu n + 111b + 10a =
 2. 120
((1 = 4. n0 20) + 2. 1o( D - 4. 120) al + (110. 110-4. 100. 129 au)
2. 120
1. 2 120 . (16 -4. 100. (20) aa (115- 4 12d
Ergo C.2 qu 1o. 1 10 10a a lu 11. 2 25
qu. 111- 4. 128
118. s qu (at - 2. 120) = (118 - 9. 100. 120) (115- 4. 120)
seu 110. (111- 2. 120) = (110- 4. 10. 129) 111 + 2. 120
(110. 111) -, 110. 120 = (110.111) 5, 118. 120 = 4. 100. 129. 111 = 8. 100. 128. 120
et divisis oumbus per 120 fint (L118 = 4. 100. 1 4. 100. 120 1 seu 110. 10 = 100. 11 4
ae bb - 2 bb (9. 2a) - 4 bb a = 0 se bb - 2bb + 2a bb - 4 a lb = 0 - 1 - 2  - 0
seu 2bb = 2 a bb su g = - 2a = B- qua,:  a firet l = 2aa seu f - a V2
nn + 1M + naa =0 fiet nn + nan +  unaa = Y (11. 1 - 4. 12) aa: 4
et fiet nec n = - na + YC11. 11 - 4. 12) a, : 2
sit c 120l + 11In + 1ca + 100R a fiet nn + (nl + 10a) n + I + Weal 2100 ac
et fiet W na = 111 I + 10 a et 12aa = H1 + 110 al + 100 aa
120
Ergo fet n = = 11L = 10a + Y(nI. m 2.m. 11042 + 110. 10aa) : 2. 120
C4. 20 1oll 4 4. 10. 10 al - 4. 100. 1204a
I + 211 (1 = 2 120) al = 10. 10 = 9. 100. 120 au, debet reddi extrahibilis
2ca
120
1II. 11I - 4, 120. 10.
III. 11I - 4. 120. 120
hoc fet si qu (=. (11 - 2. 120) ) = 110. 110- 4. 100. 120
hoc liet si ubuu1
111. 11I - 4. 120. 120
1II. 11I = 4. 120. 120
ce + aY seu g+ 112 C = 1(. M 4 1o nocC + 3 1 10a p) - (9geC. dage C HaB) e11. 0 C 1M M1 seu seu 11- 242
11L.  = 4. 120. 120 (11+ 2. 120
Ergo fiet 1o. 10 qu C11 - 2. 12o) = 10. 110 = 4. 100. 120, 1, 11 = 4. 120. 120
siu 110. 110  (111 - 2. 120) = 110. 110 - 4, 100. 120, 111 +. 2. 120
aitoque (110. 110. 119 - 2. 10, 10 120 =(110. 10. 11, 4. 100. 120. 111 - L 2. 10 n0. 120 - 8. l0v. 10. 120
destructisque destruendis et divisis omnibus per 2120 fiet
. 100. B. 111 + 2. 100. 120 = 110. 110. aquatio generalis pro solvenda
aequatione 120 l + 1i ln +110dl + 100 aa = 0, ita ut FCeten
ino l’et n habeantur inter se ratione relatione rationali simplice egr
jam in casu praesenti ubi est al + quln + abt + aabl. = 0 fier
un 2a,
 100 = ) Ac- abl - q
120 = a et 111 = q 2a, et 110 = b et 100 = bb : q fiet
150.10
2. 106. 120l
119. 110
bb- 2abb + E abb = bb
quae est aequatio identica, adeoque
itaque calculum exequamur in ipsa aequatione
(h +42a in + b5 + abb =0 firt nn + (2 2a( + b) n + U + bl + abb = 0
ris succedit:
nn + (4 2 al + b) n + 4 (99 - 4 a4+ 4 aa H+ 2b 4 2al + bb) ceq.
(x ef 14 - 4 a q aa)) U + Cab (4 a) 2ab 11 + aa bb
seu
40a
4aab
-44bb :9): 4aa
seu aeq. (94- 4aq H + +2 ab4)) + aabb (1- 4a) reden: qua videatur an
pars dextra aequationis habeat numera torem extrahibilem, fiet dividendo eum
e aab
per 47. 4aq fiet H 4 qui I + 2a 4a 1 + aa bb 
seu
9. 9. 4a
I + rab 1 + aa bb quod est extrabibile. Itaque fient
 + Cg 2a) l taab
seu
2aa
+ ab a1(q 2ai) aq. = f - 4aa et fiet
H- baq
2aa
 tandemque n(-
sud trta malius sint
2aa Hq ai)
∞ seu n
4.49. 2a 
n + s= 40a - 2aad l + aab
raa
(H - 6ac) l + aab + l +
H- 2aa
raass i
2aa  guassu iud 2A Ganssrbu
(ff. 6aa) l + aab l ,eat
s
1auf +164
16a
abiS 1ac  + 324)
8. s.t- 8aaf+ 28a -0
4 aas + 16a = 0 non. i pli s, et  (5 naats + 324) aut = 4, 5f- 2aa
raa
ita enim abjiciendo
2laus
2 -3
s 1
(... )
1oaass uca aa
f. 4aa falia mq
  mculet A. 2aa - 3a
ada 
Vs
seu f f- a1L
iligamus ergo f - Z aa