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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 159r, page id 00068196:0315
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a22 + 2f = ( prox
fy2) =B. 2Y  10
2 + AE = 0 13 es y2. (apor. 27 3 f. u)
L. VDE auonon v nos
y: 4n22 + V oE mo a2E+ voE
a22+ 212 = 
311+ vo1 =O
pos
st. D2L = LiE H0 ps BA2E = 22
P = 21
ps vol gnos
JL. (aG22.
+
2n +62.  pra f. ( f1+ b f. 2
v 22
 nos f.  1 + E. 2-) =( 102s
= vI
y oses pagna sug ro oceprumero e nnssod sep. n e3e
=
uvisro funs ny ev: 0E. ZE 1 absi vig
y: av22+ yuec nos
y2: ay22. 2 + ∞ 7 f11 = 6 nof a22 + yr: 2 f1 =
a22
Y2+ EfH bxpE. 2)   ns
f: 28n + vb oE. 2  nos
12: f11 = 12
smos
y injnquis
hus orieuis a
 f. bor. 2- = 0, groz. 0- d2 75 fib0c. 2 - f. hpar. 2 = 01
bopZ. fn = 12 quo er f. 6112. 2∞4 gun,. 0 -1C prs f. b12.2 - f. 6112. 2 = 11
ay = V(X + ab XX + ac. fiat X = sam + san Erit
XX = am i 2a smn et x= aamm tbaamn + 4aam Vgrin
an
nn
Ergo x + abxX + aC = aamm tbaamn taabm +aec + Aaamqtmn
+ 2aa b)
nn
videamus an et quomodo hoc possit identificari quadrato ex apm
ubi p variabilis, sed f constans, fiet 12) (ap + fsma) = aapp +2afp rmn  ident
ficando fiet s ob irrationalem partem fp = ram ab superest aequatio ex ratio
in
nali parte aappeffmn = aamm +baa nn + aab im +aec, Haec aequatio multiplicetur
utrinu per ff, fiet aapfpp +ftum = aaff, nm + 6matbm +ac, et pro ffpp substituendo
in
avalorem inventum fiet 4amm +. 4abm + abb + Fm= aa Hum Faassmn t aatsbm +affe
inn -a au B et 4. saut 
4a- aas
vel gaa  s) mn +(F +Ba= 6aass) mn + Aaab (4aa - ff) m + a bb
n = affc
4a . - aaass 12
tmtal + Se. agis (a F  rd)
64F 8a- 2f + 3f -6 ffaa
e
5 - 16, a + 24 a - 6 aaHf, ff. Jaa, S. t aua P. _ Win
Aa
aamm Figasum tantm Hnaeit-a Csf. apa, st - ica
conpendio gun + h hun + al in + _C aa K A = 0. fit M
posito ll = k, h1290
nn
Debet numerator dexteri lateris fieri extrahibilis, aempe un 4 rahl- 4 agl m + aall- aagk
lin- 499
+
49
fiet ∞ mn +2q eY ii erit ats alil- 2agl) - aull- 4 nagk
tih- 19)
Nam
hh- 4d
qul tin- 49g
seu qu  qus ht - 2gl) H 49H, sib - 4gg sen l ha = H apti, h + 29
hagh- 29 = 4a - s (3a- baa H (8a) haas = f  at h + rg = 5 18a buas 19a  8ao H. J. aa ti1
l = a bb (f- ∞aasf + 164) 49t = 16a, au 55, abb - f5C = b a, a bb - s2c - aaffe
ea U-agk = a bof (abb f (+ 16 a bb - 16 a b) E 6ac f + 16 a st C ( 16 a dbs p)
(
Ergo ex aeq. C) fiit a bb ff- 44, s transs = ( a  abibsB 1b actf + 16aC
2444bb
siet  bbss + 2abb= 4 a
(Obb, qu  H 4aa) (H) Hrraa- A s 
auc aal qu
abH
Ergo ex aeg. d fiet
Saat  H Agk
seu l = H -Egk
qu lh+29)
ibbff
tit (Uh) = H129 = Uh) + U29 9Kh - 8ggK seu alg- otih + 2991
seu Al = Bgk + hk seu l = k, h+29
l = bb qu (qua - A K = abb. - ffC - b - 5 + 8 a 6au f g - t a - 4aafs
1ba 1164 -
g = aa fit h+ 29 = 40a - A
h+2g = f + 164 - 14 aa ff
it tit abb = bb- BC, 4aa- ff seu abb = abb - Ac. quod est inconguum fit erim C = 0 cohaspotitu
fiet II = bb K = abbu Hfc h = raa - H
2aa - f
Haa - st
(sg (m +n) t G) = g+ G. B n 
MH
49
n + hmn+ln + K
en
Datur gum tabma + lm +k =0 quaeritur pim + g, mB Y = pmn + 2poma + 9 m + Yq
+ pr
. +Y = um + 2 mn + gip) in Fr9
r
fit h = 29 et K = l1: 4g
un
Datur nn +h mn +lm +k =0 quaeritur P n 49) Dh. fit h- 2 BY = k: 9 et Z + kp =l
n
nn
hini in mistro casu ff- raa = 2aa
seu = aas quid conlicet
seu 99 + Kpp = l p 9 se q9 (p) + t pp = ql p 1
et 9 = =lp + L p SC H - 4K)