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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 141v, page id 00068201:0282
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esumenius est hic calculus:
y p im +n. Ergo y F m +3mnY
sit jam aequatio data intractabilis: Z3 + - pq
1 - 2, ar y
25
3n
a rjo.
+3, ah2 13 E.
1+
a23
90
a9.. (444 a
collatis jam duabus aequationibus
nempe A, et X
ecex
ex 59. 9.
(8
erit m+ n ar
a
=27 mn. (6)
siat aeZ H
aeri aq
27m 3TI
(11)
. et n , aq
27 M.
qu adeoque
VM + Smn + Vmn + 10mn + 5mn + n5
+5 m + 2mn + 2mn + n 3
mns
m +7
mt n
m nn n6
nn
mn + mn I
in + n
unde y e smn. y. - ern Y +vi
= 1 nin - imn sive uun qn
2nc 10
nn
Conferendo eit nn ZCa. et NnL 9Ca3
y3 4 = q7 - ar 0. fiat Z pyea
fier 3 Dy + ca  C
-qu2. 44ca
ar
ex terminia secundis, ut extertiis: mn 3C a-ga
qe
 et fiet equatio  3q) +29a gra
n 390 et m nep 9qa
24
mari C et per aequalio: 5 1 - 2qa = y (135, a y2 (a9 5 1
jam comparando: mnei 39a s4
et mn 5,94’ a (5)
Jam exse 36,6 12 qua sexterminis serundis
et ne 9ga
4,25 m6
 quar
Ergo ne 3ga s 429a
19
 6
25)5 F.
elquao: et n B
2794
4,5,0, 25F1-
et exterminis  ultimis collatis fiet aequatio:
1000MY
9 14
819 al 99a- 2
625m+ 17 4, 25  +I 100
12. 9. 7 11 6
 631 5
n + 27g a + 39a s M  + 3ga s 26 99 a m aqS M
1000
n
sit am aequatio Tubica intractabilis,
5, 1 3Ca - 4a et (7Ca)  () c a Sqta
Unde compatando. es
0
+9 27, quae de terminatio coincidit
ordinariae et nihil inde duci potest
mn i
+ 1nin +1ma
sive y- 5mn V +5 mriv m
et m’ergo eca
J
13
Va a
Unde cu eri mn   a 10 aq un 
494
2
 et 27mn aq
quem valorem inserendo in aequatione 8, fier: n + at gC. 2 B
M - ar M + a8,2
2
Videamus an dividere liceat aequatione y per ye oqu 100
dividi per m +mn +n. I dividanus primum per men. sit: m nn + mn amu nt quam
rursus dividere tentemus per man m  min + mn - mn + n fm-2nn +mn +nnF
in + n
m = in
sn +)
+2nn +2tn
In +ut
3nin - mn
superest ut=mn + n dividi possint
per m+n, sive n n - 4m
quod ut fieri possit, debet esse
n-m r S n + f m., sive
an=fu
 n.
co
si a ma + Am
Aa+
J= M
Ergo ex aequatione
aar