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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 107v, page id 00068201:0214
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si ponamus XB SB +Y + s  Y + 4 +  1B ex - l2  + 4
fier x Y 4 4 X, et X + q X H r. et X + 29 X  + qX - r
sit data aequalio X y  -12Y - 12 7. fac y e 7 4- 10. fier: Z 43oZ +200Z +- 1000
25 sed tunc aequatio data ad eam formam revocanda est
ut ocune, termini proter altimum
sit, an equatio data qualibet. sint affinuatibi, quod generaliter
y
difficile est.
= 12 Z +120
73 - 30Z 100Z. ogr
Crbicom
Melior ergo est ratio prior. Si sumamus tantum aequationem quadraticam
NA- bq X + = Y + 9 o. cujus utique habemus constractionem,
sit data N X - qu X
+ a h r.
reditur ad eande determi nationem nec alio opus ealenlo
Rectius: sumta aequatione X Y. 24 X +4 X - _ r
tollatur trminus secundus, ponendo X e Z. + 24 fiet:
(+319
22) 130297 et q
14 27
- 243 39
+q..
-39, 491
12q
1012
P92
 B. eit debet esse a h p 46P13 et quod si
verum est, mutata determinatio est, hoc enim semper fieri potest
en  6m a 15 m nt  15 m n 16
n + b mn + 15  n + 20 m3n2 + 15 n n
m 6 men + 15  n +2omn + 15 m nt +bmu + n6
e
+15 mn + Cit
erit
in
57 9. 1t 90
H
M+n., Z P
ns
6mt  9 mt + 15m n + 20
110
eur scipsi  pote
7 6mn 4 mY + 16 mn + Q n. vel
s neque 
sire
6mn X-gnen X
maner a quantitas sit jam equatio. X  
vel generaliter: X B ida X+
Apa..
-+aq X
3 d’a X=
-2pd a 
aq
Quae aequatio D. conferenda est cum aequatione
+
+ aY
+ 4343
2
0
quod ut fiac tantum opus
est ut sexta pars termini secundi quadrata, aequetur nona termini tertii
3da +  (, sive Dd + 6dp +P  3d + 2pd  + at q
5) 4
sive. 3d2 + 2pd + 4aq = p   sive d +2p d + +p  10 p - aq
Alterutrum ergo necessarium, est, vel ut sem tertius terminus aequationis cubicae propositae
ecima octavt
completae sit regatious, vel ut quana sais te quadrati a secundo sit major quinta
() m n 299, n rn + 16es mn
162
multiplicata una
66 comprehensionis
parte, et divisa altera
Nota character
Sive distinctus ab
aequatione, quando
scilicet aequatio iden
tica est.