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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 34v, page id 00068022:0068
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+125
1
29, 2
+6,1
46, 15
+6,C
eas
= 25 af
siuve
1di
25 af
+225 ∞V
81
15a+ 18d(a
 C ge
15
41
+90 90 135
51
Valores ergo ipsarum, e, g, l, h. invenimus sane simplicissimos, nempe
e p- 2af
3β
97. f
3a
l
-2 f2
ja
hp1 = 2f
imatiomd emiset aequationes collatitias progre–
(1) diamur, ubi  b  Fea + e BC sive explicata e, fier: +4a5 a - 2af βBC3 sive
(18) b p = 4af - 6aβc
33
es
collatis porro secundis, fiet:
337
(19) = reβdu (’a + eBC9PX B + 2B9t a  + 2β96a( ca + C7 4a f- 3f6aBC- 25 a2 a
+ued
sive explicando e firper i2 fiei
(0) 2409(a +2af Cc3 +. 25 425β426 cas 
adoq
(24)
(22)
(21)
195 a + fda  8 ds =n (ct n(s 18 spe 18 a (, ex entug
divisisque omnibus per fa ( hunc denique habebimus valorem ipsius c
 sive multiplicatis omnibus per 3, et divisis per fBa, fiet:
 +36dBa +18 C∞ (8a+ n5d ( (1) a5) -=185c 7- (8) fa,
ac dividendo per ac destructis destruendis, fiet, C s
22
3
sive c
1 f a + 18 dAa
- 22 f a + 36d βa
collatitiam.
= 15B, +9B
F306 - 18β.
superest ut veniamus ad aequationem ultimam, quam cum
ingrediantur e, b C. ideoque multiplicanda erit tota illa aequatio
per = 135B +81 , itaque fiet:
Cd45(d27 CAs (d a 135C45Bdd81 , + (915(4a5 + (9156a + (39aas g 
(23)
Feganfa B +B9 a18 dea β A + 2f a 15(- 2f a9. Dividum
pro g, et C substituam,e eorum ualorem, et tota aequatio 23 multiplicanda
erit per =15Ba + 9Ba, et siet: sed prius dividemus omnia pe a itaque sufficit
et fiet:
multiplicari omnia per 415+9.
Edrerasrad45e 2fge a-  d.7( af (a =4 32af95
Bd4562a5∞9 P d +5 βhaf = 15Bd27 32af +9(d27 32af 4 15f Cd a 135 B 19 (a15 (
+15fBda 81 (3 +9fBd a81 (3, -5fβB1544f 43f15, 4a-3 (f156(ufa
F3P fB 15,6, 18d3a,, 4. 5(B (379, + a f =3β(5, 9, 2a7, +38789, 6 ufa
+ 355B9, 6, 18dβa  +5fB22 11, 4∞f +3f βP 1,407, +5(18d-3Bf1Sd Ba
N) = 30 f15 32418fa15( 430f a 9 - 18f’ a 9 
Sed ne quis in tam
45 Sed ut error, qui in calculum tam prolixum quam est postremus, irrepere potuit,
itetur; eandem aequationem 23, aliter ita enuntiabimus: 
C45 d, p daf
t
16
+(127
+81
7
2, +45β104)
3, 4 27.....
5,6, + 18,... ..
18....
+16, gC 18 (3 da 9 p421 fa
3f
(=15, 3 Cafg
29,..
F49