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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 42v, page id 00068198:0084
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Fortua
Formula X tbXX + ac X aequanda est quadrato ayy. sit ax = 22
se
fiet Z2, Z + abZZ + aC = a yy. Ergo Z+ abz3 + aec de bet aequariato qual ad
sit O = Y(10 a 2P + 1a) et D - 1 (20 a 27 21aa) et  = 1 (30 a + 31 a a). Et fiat Z = 0 + D+ 4
ale Fiat etiam av = 120D + 1O∞ + 149  + aY summari debebit 20dx, seu t
VZZZ. Porro ZdZ non Od()  2 90 = pa a V + 21aa et 20dO = 40aadip. Ergo
10 = 10aad : 20 =4 10aa ) dV: -0C.
Ergo habemus
de 1g20aa +  d7 = aa d 10 +
OC
20D = 308
W
00
Ergo Z dZ, non alias habebit  irrationales quam, OD, OE, D8. itque etiam
1200
qusque Z non alias habebit irrationales quam das tres.  sed 2 secus est
vZZ dZ. ibi enim prodibit d, D, e nisi in v7 dZ, destruamus
quod est absolutum praeterea O, D, O (quod quidem nocere non potest
s
in
eetandem; et tandem 09, quad tollere oporteret
13
quod si omisso X,  summare saltem oporieat 
V(Z + abZZ + adC)- avqe erit ODQ multiplicatum.   4- H.. (p +. 1+. 
quod ut evaneseat explicandae 10, 11, 20, 21, 30, 31; Fortasse tamen hunc
et
.. V4.. 1.
sit Rtam in E+ p, fiet  +  P  + sump
tm.
comparand. cum ve + si + ag fiet ptm.f et mp a
divisibilem
sed reperio ut aavo comparetur cum y + abzZ tac, simili aequatione
ous esse; et itafore pro literis aequationibus sex literas 6, quas quae
regulanter non sufficerent; putam tamen hoc loco brevius exiri posse
rem obtineri posse, quoniam ipsae 10, 20, 30, inter se; et ipsae 11, 21, 31, interse
eodem modo se habent. Et fortasse effici potest ut duae aequationes
hiabeant communem divisorem Hoc ergo prosequendum
sed Rasumamus
ut coepimus alia inscheda
du S(2 + abZZ + a). Dividenda est quadratura altior, in simpliciores
d ex= hiy rationaliter quadrabilis, si quidem hoc licet. ideo fiat Z = 0 + D + E, posito esse
O = L(0a PFnaa) D = 1(20 a V + 1 aa)  et E 130 al +Z aa). Ut autem sit 
quaeritur
x Y + ab ZZ + ac extrahibilis aequetur ipsi aavv, posito a = 10D + 1309 + 23D8+ a
t = 0+ 6000) 460b+409,  +88200 +83708+ 86697
aavv = 1200DD + 108 1g 18 1, 13.33990pt 2. 12. 230D98 + 2. 12. 130079
+ 2ar. 12.. + 2ar. 13.. + 2 a r. 23..
sr
ab ZZ = abE.  t: D
x aarr
ut ergo valores ipsius ac + ab7
12. 134
4
2.d
2aY 12 4(O+ D) +94)
is
=4
adeoque fieri debet O7600)D) = (2 00D) 2 3 G 4OODD) unde fit 1+ DX -0
irrationalibus fiet
nctr seu
adeoque fieri debet (.  6005 + ab 00 +400) I 5OD = 2. 12 ar OD. e si 12 = (3 =23
= 2 S2 ar OD
+2ab. d Ergo ar = 12530 += ab 
Sinsa g- 3 fit 1c2. 100D=4OB.
aesi vinir  et videtur topus fit
seu 212 12= 4 seu 13 - 13- 33= f2
E
quae est una aequatio efficienda in qua p ossugit ad I 
sed superest ad dz summanda
quantitas est autem dz =aa d p. 18C + 20P + 30, quad ducto in av, notemus
es
dO
2D
solum quando prodeat ODE, et prodibil . 20 + B. 20 + 10
Lna d4,
DN, 0D8. quod est aequandum
9E
nihilo seu fiet Ed  3090DD + 200095 + 108D2∞ =0 quae conjungenda est priori
ubi erat 9+ + ab 0O +  aa bb 0
aC
habebimus has duas aequationes
3054 + 20EB + 1028
10, 11
d
et si pro 6C, D), Qe ponami
tique 4, 6 habebinus
 0
e
explicentur nae
duae aequa per Y
omuta. 1+ cre, estis acqualis  cedsi care
aC
Hini jam in rationalibus fit (37 6007D) (+ ab DG + ac = (2 00D)  aarr se.)+ (3 1408 33) ab BD + 2aabb) Adeaque parum signis disperunt 11 et 31. Nempe
x
rursus 2. l3=4
 itaque fiet At ar  = CD K, 00+ DD+ ZF
s tauper
boimuta. +d dua gationes d cato es edatu
ata + ol, sucalo aequationes denbi sicatorias pd coostutieus.
2ydg. Ergo
ly = dx12
e