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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 124v, page id 00068199:0248
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X = H~ 10D +, , OD. Ducantur invicem XH, X+m, X+n, fint X + lXX + ImX +
X3 = 100 + 3. 100. 112G 10D + 3. 100. 11290D + 112O P LOD
(Lamin) XX Llamtn), 100. 90 + 2. 100. 112 E LOD + 1120D
lmalu tun, X = latlnema, 100  + 112 f0D
XFl, XIm, X F
Et ordinando fiet, X H Xx + luX Flum =
100. 100. 1004
3. 100. 112. 112 907
+
00100. 100p es 4
00. 112. 112p (9
atC
00. 00. 100a pe
un
Compendio sit lam + n = p
Ut shnando fiet
+1C4 GB
3∞00 +10
cntlntum = a
Quaeritur A(XFC, Xtm,
+ 106. 112G0) 12. 114 +12 (d5
d  irE
+ 0), L3100100   200. 100 mpE
1. 112. 12. 1123
quae formula aequoenda quadrato a ad O + aq
coefficienti
197)
a
Forw. oolmn
Et pars rtionalis valoris ipsius X3+ pXX + ap X + amas partis irrationalis aequare oportebit at
parti vero rationali ad + a8D. Quod fieri poterit explicando C et D) per unam
et 21 = + 123. 11. 3(a + ot. 11293: 00 a
0.00. 
Veninmus jam ad partem rationalem. ibi non potest esse Q, nisi in 40D, Ergo ut destruatur
D debet esse 100r1o + 3. H 108. 00 +3. 112. 10. 30. Ergo fit 100 = 100 112 ed 30 +. 5 ( Y. 31030; 
quos duos valores aequando fit 10. 10. 30. 30g = = 3. 10. 30. 00.00 et 10. 30 = 6 - 27,00.00
superssupersunt aequandi termini  in rationalibus ciefficientes ipsorum e, e et G
ope literarum 10. 30, 15, 31, quae ex Itaque ad ad hoc, et ad tollendum terminum e, opus
est aeqq. quatuor, et e arbitrariae sunt etiam quatuor, 10, 30, 11, 31. Nec videntur
haec nimis prolixa. Scribamus ergo omnia distincte; et primum partem irationationalem
300 100. r +3. 00. 00, 100. 112. 112 ~∞ + 2. 00. 00100. 112. 112 p 4 + 1. 00. 04,00. 00. 112a9
+ 1 a 10.3]2112. U2 W2 a8
+ 1. 11. 31. 112. 112. 112 aa
=1. 00 99, 98, 80, 00 a 8 - 1. 00. 21,90. 0087d
F +1. 1V. 30. 112. 112. 112..
11 30.
( aqu0
1. MF 
fit 100 = - 10. 30112: 3.00 et 20 = 2=. 10. 30. 1 p + 10. 317112 a, : 00t a. Et  X 00. 129 + 11311N a.
octa
In parte rationali habebimus, 100. 00 +3. 112. 10. 30, 9=0 fint 100 = 11, + (- 3. 10.30):00 sed prius erat
2
100 = = 10. 30. 112 : 3.00 quos duos valores aequando fit 10. 10. 30.30. 112. 112 = f - 27. 00.00. 10.30. 112. 112
seu 10.30 = -27. 00.00. Ergo (.+ 100 = 9. 112. Hiac ex aeq. l. fit 27 (11100. 00.27. 11282700.00. 112 =8
et ex aqu. 4 fit 81. 112. - 3. 27. 112 =0, ut oporet.
tar pe g
ru quae rui
communem porrit poterit autem  esse secundi gradus, a son a 00 a t= obi PR +000 aroB naa
et ita equatio ivessi inter coefficientes trrationalium, dabit valores ipsarum 20, 21, 22. Superest ergo
debet autem e esse gradus simplices, et poterit esse 204 + na, ita aequando coefficien
tes irrationalium, habetur 20 et 21 sd et ex irrati habobetur  3
2 = 308)+31a fiat 3. 100. 0d = 112. 1030 = 0 seu 100 = - 112. 10. 30 : 3. 00
112ob:6
in se ipso et
11.
i
extractione
Xy = ab
Fd Xx = ab