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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 126v, page id 00068201:0252
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Data sit aequatio:
q  side 1ode
+  ge . ..
pXe + ulf ode.
agX p) aGs
tar e
X + X ∞ + aqX + ar 5. Sonamus X⊓ F 14C +1de
e se de + 6s ide
+92de 00.
+3fgedl. ..
ragg.
psde
P31d
ubi tres habemus aequationes subsidiarias, exquibus
duae priores una dividi possunt, prima perf, per f.
secunda per g, et si post divisionem una ab
altera ab altera subtradatur, habebimus:
(3)fd + 39 e 0 quae aequatio promitit
aliquid ob simplicitatem suam. itaque si ipsius g’e
valor repertus. inseratur in aequatione 2.
et ponatur de v. fiet:
55v d + 3 afgpV + aq fo
Habemus ergo eti fd. et dF - a g - 3afg p V
sic et - aq. 2at9 pr
553p2
ope igitur horum valorum repertorum vel assumtorum, tollamus de, et d. in aequatione ultima,
fiet: 2p 2pa 2. 3a59pV + 6v f92
= a 4
ar pEd0 Quae aequatio est semper
posribilis, et si aersit quantitas negativa.
Nseusaem rujus requa lionid ope nees Sed una ad huc aequatio construenda est, nimirum:
er Y e9 sd. et v ) a 52 (+)- aq
et fiet: d agpd 1 a 9g. l0
unde necesse est f et
5fd+ 3a59P
oblisa est liam
quae aequatio semper est tractabilis, si p. et g. sunt ejusdem signi, aut si 
pura foret si abesset  P plana si abesset g.
debet esse t
ergo pe
25 (19) 24
sines
4 44 H
Caeterum pro d ponamus cot
Egae
100
 o fier.
Q et debet esse vel p. et 9. ejusdem signi, vel
2s, A p sive  q f 100 p3, quod atique semper freri potest
fEo gu adeoque 22 (1)6
 53
in aequatione 10. fet: 29a c0t3
:Quem vatorem inserendo 27
I corsu
t9Pa
orfus L
82
(23)
...
et s
asq...
sive aspacop paq + 30a59 + a Yco f9) 0. quae aequatio cum sit puva
simplex erit utique semper possibilis fiei: - 3 pa ap atq ab -  pa a 9 +61395 a6
sive + a Y C04- p a c02
-2 paq ....
= 6a 770.
XN = 10 d’e +  d 110 de
H S
qxri
fa .
+ aer
+itd
 10 de + 1 10 de
XH 219...
PX,
 ascribatur qX fiet:
+35919...
+(510
restat ultima aequatio:
cor
c04
Unde jam patet non esse nobis satis incognitatum
en aesde  dre faghed ( de  2ohe de
a 1 de... 113225d... 
1 d ersge  . . .
a chie. . Atgd arghie e
+g. d 19...
Fd’e cut d
de2
2de
+ ar
+H. 7g de- tp9a
es pta. et de 7 s’a
 sed in ea omnes incognitae ded -p3
evarescunt
35gde + pg’ ea + 45 a B si esset dpe. vel sulter si esset DY  e
39 f de + pf da + gg a3
Unde novissima aequatio:
fiet f9 y =P qa unde  
ge2f + g’e +2p9 e a 9 tatrf
sive - ge 94 + ge (2p aq 4+ ar gat
jam faciendo erit aet
+yh de
Adee
gide
2753
a fier. a 9a4 9a V - 2 p a6q 4 ar 28
Sed supest adhic una equatio  8gas- d 2
= N dre
pons jam emines terminios aequationis, cubiae
datae esse affirmativos quod semper fieri potest
habebimus desideratum
e oe aieits
A
alter.
fl.v. Hrce p)
nneren