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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 20r, page id 00068197:0039
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(99 +9b dy (yy + by + ac) 
y9) F by + ac = (y + v) =(9y)t 2yv + vr
y = aC - vV, :, 2v - b
y tab gu + ac) = (yy +av). (yst abgy+ ac (9)t 2avyy + aavo
gy = aa vV - aeC,: ab - 2 aV
(∞ + AWB +aC V H aa C).
V +
yy = aavv - ac, aa vv c ab - 2aV
(yy + by + ac)
b + Y (yy + by +ac)
a +by + cyy + dy2. +C7
f+ gy + Ryy + K y
VV = ab, n = WW - ac, m
n vv = abn = m WW = aCm
vn Wu = nvv + ac m = abn,: m
qu (ab = 2av)
Y(y + b) + Yby + C) = Z
(my + ab) = V my + ab = vn
Y = vn - ab,: m
ny + ac) = W nytac = WW
y = WW = ae,: n
n
WH W = S(mnov L ac mm = abmn).
entemus auliceat (yytab, gytac) seu ACy + ab vy + aabe) reducere ad HC. XX+. X+.)
sit y=
x S(L X + am) + (M X + ap). = (per compend) 1aO + 1ad
fiet ys = ad + a D + 2a VOD, ergo si gy + ab, multiplicetur per rytac prodibit:
+ _3D +  (b+0) (O+ D) aa
+  D
+ 4 aa (O+ D  NO3 = y + ab vy + aabc
+ 2 aa (b + C).
quod ut fiat aequale quadrato, ponatur ejus latus esse a  + qYOD, ubi Q est variabilis simplex:. Xt.
164C)D + B bc d
sed q est constans, etsi  adhuc incognita, et fiet
+aa 7
+49 0
 2a98+37
ac
sunt coincidentiandi
inter se
fiet fiet terminum irrationalem irrationali coincidentiando
92 = 2a (C +D) + a (brC), seu  ∞ = 2a (0+D) + a (b+C)
et terminum rationalem coincidentiando rationali pro e substituendo valorem
fiet OO + DD + 6OD + (b+ e)O + D) + bc = EQ + 940D et pro DE substituendo valorem, et ordinando
fiet (1 - +aa) (09 + 3D + 20DB + brc) (0+1) CD + (2 - 12)OD + bc - aa (bb + 2bC + CC) = 0
Hinc si b et c non essent plane data, sed arbitrarii alicuius capacia, res procederet, faciendo enim
2 - 44 = 0 seu q = aa s2 et b6 - aa (bb + 2bc +c9) =0 fieret 2bc - bb - 2b1 - cc = 0, seu
fieret b = ced c = b f-1 et ita exaeq. 5 fie et= (O + D) + (b+C) =0 seu O = b (1+  -1) - D
4qdividendo
Sed talis epsus ubi in datis sit C = bs. 1. meeonunquam offeretur. Itaque videndum an liceat obtinere aliquid
generalius, per compendium sit 2. dt = β et
possit dividi per D1D fiat O= sD + g2 tar
 bc - aa (bb  2bc + cc) = Da videanus an B()D +Zaa
ttee
ensiteri in jate 
G1 +g) aa
et O+D = (5+ 1)D +94 +at, quod mulsiplicetur per YD  
(F,) N  fiat d = ft + gr4 tah et D
A +Ce jh +K 2 + A, es e
et (30 + Jaa = BfikB +gK Z 2 H(HK L7 Ha fAF,  aBX Y tbaahX
+Bgi 12 Ha hi G HatR 2 + a
01 fh1 47 + at in vie e Hende 5 tusot 13 ve
X. + aA l 1et) p   2Z HtunZ F ariset,  
in (at + X4 + a dabib)t
 B astr HaF +at+ (i 2
exagu sint fftik rggi  rfait 
Bor+7aa
quae concidentrando fit i-B etA
h+N a
restant 19 hes aegus, H+   Kt ti si
aa Lthi fiiht+ efi
q) V
 gathit 2) get. X L  gk 20 Fonstrg
Fagtum pro Kponendo K, et prog ponendo h, et fit SA- hc -0
Fst fk - gi -b
Ex altera aequatione prodit idem
 extertia aquatione nt protit idem qued exprdinen tiles ua ia  tiitat bun i te  i