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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 157v, page id 00068124:0318
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solutio problemalis pendentis ab his fubus gq. _ 3Ins+bhik L. mo) has+ 2K e rb
tacetbhh en(2) 3, a C+bgh2 ∞ 2dcC+ 6919, 2acs + ZGgK N a0e +bph
Midonst bust dan calclinu ausegulosan a
Et denm 3li∞) ae 5+ bhk, auC +bhDS, a +bkk, de 4 b99
fscon, sit aef+ bhA =C
afs +bKK = 6 aCC + bg9 = ∞:
1
V
adsolstio
aec Fbhu = D, 2CF + aee = e
21
Eyaequu fiet 30=28
2b9K bkh 
6 30+28
1)
odq
n par e e  prmone
in R ada
a n enulu 
x valores ex 1 et2
substituendo in aeq. 3 tit (25. 3) 18Q = 46 seu 6 oe quo valore substituto in
Naq 1 et 2. fiet 90= 4. 36C
3. seu 14=16839 et 54 = 1650. quibus valo-
pa
Eribus substitutis in aeq. 3 fint 16. 16. dC
=9. 8+ et quae est identica signum calculi
Fertenus veri ac inventis ergo ipsis D, D, 8 per 6 et 8, seu per f, K, C, 9
quaeramus e et h per O et D. fit e = C - bhR: af = D - bhg: ac. Ergo fit
FOc - bhcK = Df = bhfg. unde h = Oc - Df,: b- bf9 et pari
e
jure, e pro. b, k, 9, f, C ponenderespective, a f, C, K, d fiet similiter
10)
e Og -DK, :, at9 - ack. unde e: H = _, O9- DK: A, DC+ Df
videamus utrum ob arbitrarias supernumerarias assumere liciat GM
e
ita AF in aequ 7 et 8, quia ck- 5920 evanescerent het e, fieretque pery
Oc- D5=0 et per 8, O9-DK=0 ita enim ex 1 et 12 fieret dC = DF et
2
Og=DK, et poinde Dividendo has duas aequationes per se invicem fieret
Ci g = f: K, seu Ck= sicecundum aequ. 10 quod hactenus feliciter sucedie
A
forro ex 11, S, 6 fit f: et = 0
3)A +F:0. seu
est seu Et: et
ind debet + esse +, a spalet si i daloribusd, et
Sier explicationem 55: CC = af + bkK, :, acc + b99
4)
aliti
seu ura
= a +b(KK: 5F) :, a + b (9g: CC) seu ob 10) + = a + b(99: cc): atblggc
seu +a  b (ogr + a +bgg: ce = a + b (99: cc) quod si vi
5+
(15
quod si + sit +, tunc haec aequatio est identica et per se succedit, nego
adeo quicquam determinat, sin  = sit =, fieret 99: CC = - a 2b 3
graeteres ob aequ. 9. junctis H1. 12
sit e:h = b0: a0 seu aeo = bh0. Unde quidem non sequitur
ocu g: C = V. a: b =K: 
necessario e: h = b: a potest tamen locum habere. Quod una cumvalore
ipsius Z eventui totius calculi est committendum, a quo proinde  pernt
e  qq1
p e lodeina Aequandi jam etiam sunt duo
adhuc pendent agg. 16. et 17, imo ipsa coq. 10 assumta
vabrelatius   6r0eseu e
1
u
+ QQfficC. ergo per 4 est 
Z = (25: C) +I seu (6c: 5) Y+1  
jam per 13 et 6
am
igsis & valor ab initio est 2ac f + 2bgK  a eC + bhh. Etos duos valores
es
hact 4 aee quia antm
(20)
(19
bhk
omnibus licet paribus aliqua tandem velut sorte Eucenda est litera,  quam prius tollumus, ideo
aequando fit ( f+1, esic seu (+1, OL: f = LbEK
oponamus sortum cadere super H, ergo etiam evit abimus S, et  pro Z per 10 panendo
acs +b
(=fg: C, fiet 1+1. 95: c= 2ac5 +2b59C + a ee +bhh = 1
seu raccf + 2b599 + ace + bhh = s+1, accf +b5d9. seu
(20
t
acetbhh = (1+ 1) -2, accs +bf99 seu f= aee + bhs
acc + b99
Rotandam etsi videri possit necessario  signiticare +, quia ( +1) - 23
Va oidetur absurdum vil impossibile ego tamen nonstatim resicio et aut