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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 30v, page id 00068198:0060
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aequanda oto
X= atbc x- a+ 4ab +6ab n abe
1X +12 in 20X +2L, aequenda quadrato a Chogus L31913I + Seogy + 4ry + 42
quadrato a Lao y + 41, 509+ 5i 1 Lbo3 +61, 509+51
sit X = b Saoy+ 41, 5oy+ 5I + c f60y +61, 509+5Y
10X + 12 = 10 b. 40. G0. yy + 10. bb. 40. 5 y + 10. bb. 41. 51
10. bb. 50. 41
10 cc60.50 10EC. 60. 5,. + 10. Cc. 61.51
12, X=n, alm + rabunn
emn 2bcnulm
X aIm 1 eabemn t4 abl
cemu 2betmn
10. CC. 50. 61
mstu
racmiln
apu racima
Z= d situt esin +f sun
yy = dd lm + 2del smn
Ee te in
+abIm smn
aab en
X=Ba ln +6ab  n + Aa mttun
In
ac lmn
enin belmu
e 12
4aebm snn +4aclnun +ab ClnHn
be mn.
c p aenn..
aBe B
1abelmnsmn 12 abclun sn 12 a bchun m
item d, ef
ut ergo 10X + 12X + 1 F + 14 aequetur ipsi Z., ponendo l, m, n esse quantitates in quibus y
est gradus simplicis, et a, b c sunt constantes arbitrariae, et d, c, f, sunt in quibus
affurgitum ad yu, habebimus arbitrareas  itidem ad y et a, b, c esse
stantes
habemus arbitrarias novem sed minime ad tollendum sufficientes, sin faliamus esse
a = 0. et d =0
debent V esse 2ef- B 4bC + abemn
et  10b Pn +1OCn +6)10b Clum bl +nem + e, 4 ∞ el + fm
et (4) 10. bc In + (4) 10. bemn +) 2bC ∞ rCf
pro priore 3paratione requiruntur arbitrariae 4, pro 2da tres. nob summa soptem
oi
cer
X = b sim + c Snn X= VIm + (2bcm Vin em +(4) bcl sIn
mn
oniu
ebClmn
repex ans.
Ze sim + f smn
Ui ema
Si ergo 10X + 1X + 14 debeat aequari quadrato ZZ, fiet
ben.
(8
10bV m 110bE lnm + 1 bIm bi  C Im et (1) 10bclm + 2HC ∞ref
m
eum
1obeam
pro priore cotucide sunt autem b, c, constantes, 1= 40y+ 41 m  60y+ 61 m= 5oy+ 51
nn
et  et C= 70y+71, et f= 80y+ 81
ex  Ex caeq. 7. fet : 10b 40. 50 +16) 10be 40. b0 5 lle = 10. 40 = 80. 6050
10b 40250. 51, + 10b (2). 40. 41. 50 +6) 10b5, 40. 61. 50 = 70. 40. 51 +6), 70.71.4050
70. 41. 50 6) 90.8160.50
80. 60. 51
10C60.50
30- 61. 50
10C 602)50. 51 c (2)- 60. 61. 50 (6) 10. bc. 60. 41. 58
10c4 65. 51 10c3.61. 50 (6) 10bC. 40. 61 (2). 50.51 + 12b. 40. 50 = 70. 41. 51 + (2). 70. 71. 40. 51 +71. 40.50
11. 50
3. 61. 51 + (2). 90. 81 60. 51 + 81. 6050
61. 5
10b 10b7 40. 51 + 10b 41. 50 +(6) 10b5 40. 60. 50
(6) 10bc 60. 41 42)5051 12 F2. 60. 50
(6) 10. b5. 41.61. 50
+ 2bc. (50y151 140.9141, 60y161
labecmmec
abc lmn sin
10gosoyeomsoy i
30. 50. 51
50y+51
tartto 175.
∞. st (0.51
F L. X. p. 91.50
102
6o. 51.
1. 41. 50
2.90. 861. 50 g= 61.50
70.71. 4
s1
70. 41.51
A0. (. 51 2. 8881 61. 51 81. b1.5
et nn 2 n s (Z = 70y 171 frograi + g0y +81 160ytb1
Im Sim. Mn
Im sIn