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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 126v, page id 00068199:0252
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Hypothesin ferior, relit _ = CD: 88 ad a aX, 4) +U, apt +mn requaenda
sufficit
faciamus 3
quadratis credo non suffecisset. Nam faciendo ax +H =. 9 + IB8= vit
aaa OD = Zaaatit-l 8 = pt + 18. aatue aa t, etaC = apZr + plq et
aD = aa t - aa l8, sit ut aute  = 10X + na D0D =30 X + 31 a, Et
008 = 40 X 1 41 a et t = 60X + 61 a fiet  10 a X + M _ = 60apX + b1 a p
et 30 ax + 31aaba  160aa aX + 61 a
40 plx 41 apl
qoexa qu ae (X - Maaq adeoque ex priore boap, 4o 10aa = 0
itemqe nap + 41p -B aa= 0. Et ex aeq. postertore secu secumatiel 60a -40a - 30 pe 0
ileqe et b1p - 41(- 31p, D0. Ex 3 est 60= 10 aa - 40 pl, :  et ex 4 est b     nBl, : AP
Et ex 5 est 602 30p + 4ol, :a et ex 6. est 61 = 31p + 4il, :a. Et aequando vinos valores
ipsius b0 ejusdem, ex aeqq.7 et confiet 4 10aA 40 qul = 30p + 40 pl, unde 40= 10aa- 30pp: 2pl
Et similiter ex aegq. 8 et 10 aequando binis valores ipsius 62 fiet 41 = 1aa - 31 pp7: 2pl. idem
l Pactenns  aequavimus quadrato ax +H, nunc ut idem fiat cum ax+ um,
eodem modo procedendo, et loco egdem modo procedendo  locot seu 60X + 6ia, ponemus 8
 seu 80X +8Ia et loco p, ponemus 4, et fiet 4d = 10aa - 3099: 29m, et loco _
t loco ponemus m
41= 1paa - 3199: 29m; uad Et ex eq bims valoribus ipsins 40, per aeg9. I et 13, fiet
loaagm -30ppgm = 10aa pl = 30g9pl et Ex quo de 30 : 10 = spaa ( pl. qu)  p9 (9 - p n)
et pari jure ex 12 et 14 fiet 31: 11 = aa (pl - 9m): p9(Gl - p m). Ergo 30 : 1d= 31: 11, Com
pendeo aa(pl - gm): pu (q = pm) r: a = 30: 10 = 31: 1I fiet 30 = 1or: a 31 = 11r: a
 Ergo ex  erit 4V = 1a a = 19r94: a, 29m seu 4D: 1V = ua - ur49. a, 29 m
= (pari jure) 41: 10. Sed ita  in numeratore et e in nominatore se mutuo tollent et
fiit X constans contra intentum
E - 8
E EFC
∞ d C.
D Cp+ 
10 = pd b
nc
DF + X q  E
 en 1I
p
in 
2 p3
E
s re
It
i et 2. 11
f 1d 
 ncE
 3+ F s 0pt +
C  1 
ere A X 
  L C
2t  5  a
 5 +
e
+ 8 3 e
+d C C
∞ + + es
to  5 F F +
1nl 5
1 
il  e
3: 2 = F 2
s
e 
5 + +C
tac tC =LtC F
X ∞
5. ID p K
p .2 7
e
nec
 C+
f. +
~ 1 1C E +
V: s 
e e  X
orus
e
re q
d
e
1 F D D
ei per
5 5. EC
e F eri
it F9 
E. PrC 2
 J. 2
+ ∞.
3 11. Cl
1∞ ∞ +CC
fsi1
+ 1I e
+O Fd + P
euo 10
Ce =5
 + 11 d YC
da= C1
 F E
c ll 10  X
 O... 
: r0
 5 
l. 1CC 
0 f 
a
1E. 2X
 = + 1C∞F
5 F 5 19 5 F F
∞ - 7
f 8
decd ∞ ~
∞ E+ L IC
F +C or
 ∞+ X 1-
1I E ~ H A 
d
N con X . E  
 55 L
 ue 10
 F
id X X =
e Y 11 F + 5 5
P= +
DE Z F 9t  
i F 5 11
D oZ X X  L
0 F A 1I
FEA
F F 5C
d 5
105
+ 72 +
AC FC
n 2 3  =
8ue t
E F FY
∞Z 11 + Y d si +
∞ 10
SF =a
d= = F _=
+ 5
d 5 
++ 
5.
1 11 +
 e+
s
+F
fx-
3+  +
2 ∞ te F1
F +d Z
4 +
2.
ec
F = C. 3.
∞ ∞:
p con
F 1. X=F
A.  W. l2 3
 ex 
LF
d d 
t II =  =
eu e 
E  s 
+ A 
a + E
11 SF)
2 Se
et l
E. 18
c0. L x
s 
= + C
∞E da
. +E=
recle x
a p
 a Ct F
L, 1 F F
 ot
f
ra 
1 D
 C
1 L1 F
i 1 fte ∞
1a
tec of 544 F 2
+ II ∞
 e
= = 32
e. 
C  +
iea