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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 337r, page id 00068196:0669
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Ex aeq. 66 exhahendo radicem, fit 60 +40 = 40 60. 10 ni 1So : Y. 1 
Rursus ex aeq. 35 , ubi valorem ipsius bd hactenus dilatum inveniramus erut 602-40  4. ab tad: 10. 31 - 11.3C
adderdo aeq. 6B ad ag. 67 fiit 260 40. s Y 4. F H. 31 abu ad: sF  1 91  Qsu
a s inicem detrahendo aegu aeq. 68 ab aeg. 67. fiet 2. A 60 2: 40 40. 60. 513 - 4 f- 11. 31. ab ade si. 1.
et fit 2. 40. 51. f- 11. 31 F a ab -ad. 4 f - 11. 31, : 40. 51= 60  (per 68) 4 ab - ad + 40. 51,: 31
jam et tractanda aequatio est
compendii causa 10. 31+ 11.36271 fiet 15n B 40 51. 71 + 40. 5I. 4. 10, 11. 30. 3) + 4. ab - ad. 9. 10130. 31
= ab. 4. 10. 38. 51 + ac. 4. 10. 36. 5 0
pourmnu autem 31 -0 hoc enim in pe ct
pte est, fiet et ex cq. 73. fieet 40 = 2fab ad 2 et fiet _st  H. 30 et 71 = + I1. 3
et ex aeq.  73 fiit 40  ad ab: s1 A og.74 fiet qu . Gato a
40= 2 Yab -ac . H1 Ergo ab   per 75 et 76 fiit ad ab  ab ac sex
+d, ubi b et d non tactatur eodem modo, quia
sic facunus 606 videamus anam hoc possibile sint tria Z+L, Etm
cel ex 4g. 71
videamus am an aeq. 79 sit i pte: sit Zl, Zum, Ze et fiat Z- xt Y
prodibit S+t YEmet Htner IEr = b, mA =C nt Y
Ergo ob
a set lr= mn Erg ut lacramur nec habernus sotutionem
B
X+B, X+B, A+d = X + b X + bC X + bcd et proses ponendo e+9: E
fiet X + ZeB X + erdi 4acd X + Cd c quo egunti poteri eslat pdra
gitandum euu nobis est dej evolatione aequationum 7 3.  sed puto eriorem
qualis fi cuis radio proinde poterit, summari.
an
C
Porro ex aer. 74 fit 40. 51 ab - ac. 415. 30. 55 = gub ad 16. 1. 1. X. 31 . ab - ad; 1 210
sit AOas ( porro F
(4 . 10
Ergo ex aeq.73 fiet Pab. Pac B. 18. 4B. sI (C 32. 10. 11. 30. 21 ab - ad f - 11 3 D + 4a b - ad. L. 1 3 1. 11 (F) a ubm ad L. 1 31
(~I1. 3I
40. 7C +4, p. 11. 30. 31 V, 4 ab - ad. 71 (+ 4 ab- ad. 4. 10. 3130. 3)) + 4. ab. ac. 18. 30 31 ( 16, 10. 1 30 31. ab.
seu 40 =, a n. s  4. ab- ad (7, - 4. 1. p1. 202, . 3est) e si
L71 + 4.10. 113031 (4ab 4 ab ad 71 + 4 avaac.
(78
sed per 25 est 40 =
2 V ab -ac, 10. 38. 51 = 16. 10. 1. 30. 31 ab ad
 V712 +4. 10. 11.30. 31
su Ergo Eh
Ergo fit
2st autem 10.30 = 1.
(-n.si. Si a 12 ab = ad - dac = 2 t ab - ac si = (16) 1. pab - ad, Sgab. autdiraune
iuplicat, quod sublato quantilate 40, b, et a, se non habent eodem modo
(- 410. 30. a
 per 31 41 = 40, 70: 2.10.30  et per 1713 02 - (10 ∞ 468. 1L21 - ab 340. 11 46s. 10. 130. 5
10.3C
 aba
10.3+ 4. 30=21
poo EX 22 et 3I est 6 60. 71:, 2 10.30. Ergo  per 16, 02 = b. 1 + 4. 10. 11. 31. fon 02= 60. 31. + 4. 90. 14 130 2 ( . 1. 
 18. 8 . 11. 30.  - 1p. 31  150 pergpand 51: 1. 1131
1 10. . 1. 30
suprestae quatre orta ex essumta 64 quia posumus 02 + ac =0 fiet sit
tandem est aqu60 et agitur de invemenda 40
2ab = ac ad seu Z1
nisi casu specialis
C
nandum
E
Ergo ex71, 72. fil 2. 48. 51 f. 11. 31 + ab- ad 4 f- 11. 31 = 40 V 4 ab- ad + 48. si ubi sublata
3
P. 3
4. 10. 30
sit sit.  31 130C St
Ergo 60 - 40 = ad- ab, 4. 18. 30, :, 7 1 + 4 10. 11. 30.3)
idem autam
+ 8 ab - ac si