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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 139r, page id 00068201:0277
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Sed quoniam prolixum, et difficile lirc determinare  possibilitatem
ejusmodi calculo (quod per methodum de maximis et minimis, alibi facilius fiet:)
nunc quidem rem omnem ab integro ordiri, ac et excimaginaria quantitate supposita
+ Q: et erri
e
Sit aequatio: Y -Y + = 4 - a B. sive y - 3q V, + a r. 1
sinamusPonamus y + c. per:
B
34Y
a
d1 +3 dcc
3dec + 5,
a
- 39d. -34C1.
+ a Y.
sumta jam c. pro arbitrio quaeramus valorem ipsius d, efficiendo, hanc conditionem,
ut sid ut ex qantitate terminorum trium secundi terhi et quarti
c.34 e+ ar
summa extrahi possit radix quadratica, sive ut sit 2d S3c
Mm
F 3dC - 39d, sive 1 3C- 94c + 3arC s (d), () 3E-3. seo
a
C
Jam vider id hoc modo fieu non posse, nam evanescit d. et c nimis alte assurgit Alia
ergo opus arte. Nimirma non tantum neccesse est summam horum terminorum esse
hoc modo quadraticam, sed et hujus summae multiplum antitas cognita
Nimirum efficiendum ut dimidis termini penultimus set media proportionalis
inter tertro secundum et tertium. Nam idem inde sequetur de toto termino
Caeterum ut hoc fieri possit aliter explicabimus, faciemus scilicet: y  d X + ag
fiet +dX +q d ag X . + 3dag X + a g
59d n. - gbd..
+ar...
= 39a9..
13ar b.
et fierr. 3d al a9
c (34 agb2Z
3ar63
3
- 3962d.
-68 bag. -19 agb
+3arb7 + 3arb
- 69 bd (a9) 
392 agb3)
3arb
2 1142
30
4
3
dX +2bd. 4b0.
= 34 ag a g Y
(39’agb2)
+3a rb3)
Od a 9 - (184 2gb = 56) a g 4bd + 18 a  9rb
ft
18
se 
+ (9t b+ d2 + (36)9462 a9 d18. 9b ar d)
18
t
M 1d
-69 q b agr. 9 at r 64)
et ordinata aequatione.
vil
+18079rb.
+ 189462 a9.
VTH
2
= 189 b7 a97
+39 a 9
- 3arb9
ubi commodissimum ut arbitror fuerit reddere huju aequationis terminum secundum
nihilo aequaem et fet: 3 qb + 3a3r 9b - 59 g 10
et b  + ar g
et
b. 1a
292
b
an + abr 297
2
( aer 4 +20 a29
498
+ 98
ag (ar +2046 sed satius tucit torte ipsa l et g.
sumere aequales a.
in aequatione abinitio habereturt 3G. posset fieri
t brevissimo culculo epter de. . sed mobis, hic non licet esse tam felicibus
14
.
rar
+6 a g
-91a gb
+99648
-9a rb9.
1
= ar9 +
e
X 12b X +
X +
FaGX 2bagX agb
+3arb a3gY
C39 a96)
(3a r63
vi
S, loco -9
b 50.