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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 53v, page id 00068198:0106
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s
proponatur res hoc modo, pro de ponendo V dissimulando scopo
19aa + 1I1 av + 121 ay + 112VBF 122yy = 1 = 0
catis (200aa + 211 av + 271 ay + 212VV + 222 9y = 2 =0
quoesitae 910 aa + 91 av 2 +912 avV
gzoaa
+ 921 ay
2320
=922 9y = 4=0
1.. significat primam
2.
0j.
69
sicuadam
120 coefficienter
t significat s simplicem
.2 gradum
quadratum
Multiplicentur aequ. 1 per stoi aequ. 2 per 802, atque inde subtrahatur aeq. 3 multiplicata
coincidentietur
per B+ 900 residuum aequetur aequationi 4 multiplicatae
Aequ. el per l, aequ 2. per m aqu. 3 per a, aeq. 4 per n,
et
sublaaatur summa duarum priorum subtiacta ontia residuum aquaeturtlae
fiet F. Fioolaa + nlav +12. lay + 12 l vv + 12 l yy l
Xv.
+300maa + 21mav F23) may + 212 m vV F 222 m Gy
910g aa - 9114a
=912ar
492onaa   grinay
ut l + 2um = gua 12l+ 212m = 912a
Bgrenyys V
1 00c III. 112l =  112. 9H a - 112. 2Um = 11I. 912a - 111, 21277
compendio
+11. 2
M = 1p. 1, 1II. 912a = 112 qua, :, 11I. 212 - 112. 211 = 111912a - 112. qua, :soe
pendio
211. 912 a - 212.911a, :, 211. 112 = 212. 111=212. 911a -211.912a, : 10
Et pari jure l =
92On = 100 p)ron B, 00 10 =, 100. 212. gu a = 100. 211. 912a + 200 - 111. 912a - 200. 112. 911a (910a. N 12
C1
11. 12
+921n. 1 10 =, 1121.  . . . . - 131 . . . . . +221 . . . . . - 221......
4922n. 000 = 122 . . . . . - 122 . . . . .. + 222 ... .  - 322... . .
1
ed parijure poluissomus praecedere  prmulsiplicando ogib 1. per p, aeq. 2. per
a9. 3 per Y, et 59. 4. per a, et illas a summa priorum subtrahendo factum)
ex uniducta utsimae, reliquum aequando penutimae ita 
possunt omitti p et g, tantumque prodibunt novissimae aequationes
tres, ut novi nuper, pro a ponendo Y, et pornutando . 1. cum. 2.
et fiet (P, 91OY. 50W0 = 100. 222. 921a - 100. 221. 922a t 200. 121. 922a - 200122 92144920, .. 2
2. 22 (4)
FOHY 00 20 = 11I . . . . . . - 11I .. . . .. + 211 . . . . . - 211.. . . .
2. 22 (5
2. 22  112 . . . . . - 112.. . . . + 212.. . . .- 212....
4 912Y 10 20
Mer a99. 2. 3, et 4, 5, o inveniantur 911, 912, 921, 922
quanquam revera
tantum rationes inter has duas inveniantur, remanearque relati inter ret n
postremi ex aegque. 1 et 4, habebuntur 910, 920
caeterum contrahentur prius coefficentes ipsam g11, 92) esc. in his baeque
ic compendioque exprimaatur. Et ita stabit
H2ieuu 11. 12. non est mutiplicatio 
sebsiguo (M. 12 = 11P. 212-
- 11. 12, 920n 4 00. 12. 91 a  00. 11. G12a  - 11. 12910. a
0
cleo
13. EHC
21. 22 = 121. 222 -121. 221
- 11. 12. 921n + 21. 12. gua ( - 21. 11. 912a
(00, 12 = 100, 21 = 112. 200
00. 27 - 10. 212 - 122. 20c
(() (21.
= 11. 12. 922n 4 22. 12. 911 a 522. 11. 912a=0
= 21. 22. 910Y + 00. 22.921 a (400. 21. 922 a  - 21. 22. 920a =0, n. 13 - 122. 22 - 112. 212
= 21. 22 911N + 11: 21 92a 11. 21 922 a 1=0
=21. 22 912N + 12, 22 92ia 12. 21 922a 20
11. 22= 11I. 222=12221
12. 22 =112. 212- 122. 212
100. 11= 100, 213-112.200
00. 21 = 100. 221- 121.200
3l. 11 = 12). E= III. LC
(II. 21 = II. 221 = 181.211
22.II =122.211-11.212
12. 21 = 112. 2C] - 121. 210