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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 9v, page id 00068217:0018
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Ex hoc calonlo sequi videtur amnem aequationem
quae unat altiorem v.g. gradus X. quae uno
tartum termino differt B X6. X3 X. deprimi
posse, Nameiusmodi aequatio generalis
OX + pX + qX +Y aequ ninilo
0X3 + 1X + 2X +3
+ 3X3 + 3pX 3_GX +3Y
e l + bX +c4 + d aequ. 0.
companni poest, cum excitum ex XCLpX No 2X + rp. +2g + 2rR
+1X +Ip. +19. +ir.
tax +op. +09. +07.
0
1.
+r
aequ. nihilo
fiete Tollamus jam terminos X. N X. X. ope 4 arbitrarieru
nempe. 0. 1. 2. 3. 
fiet: Op + 1 aequ. nihilo 09 + 1p +2 aequ nihilo.
2Y + 39 aequ nihilo
1r +29 +3p aequ. nihilo
eugat aequ. sed hini jam video literam 0. esse inutilem, nam si caeterae
omnes lexplicentur per ipsam, ipsa evarescet. Sumamus ergo
perindeae si non fuisset ascri, ita, sed fuisset unitas et fiene
aequationes: p + 1. aqu. 0. 2Y +39. 6 qu. 0.
9+ 1p +2 aequ. 0 1Y + 29 + 3 p aequ. 0.
pro qit 1. substituendo - p. fet: in aequ. 3,54 - p + 2 aequ. 0. et in aerqu 2 fer -rpt 29 +3 paquo
e
porri 2aqu. 34 substituatur in aequ. 5. et 6. fiet q- p = 34 etqu.o er - rp- 3 +3p aequ. 0
Ergo e ex aequ. 7 fier: qY P aequ 3. et ex 8 fiet 3 aequ. YP
ergo fiet
sive
-
1- p pr - 4 aequ grp. sive
pr- qu
p9 -9
(9pr) = 93 - pr + pq) aequ ( qu p) seu fier raequ.
Heud quo casu aquationis cubicae radix erit radix culica ex radice aequa
tionis quadraticae. Nos autem aliunde seimus eo casu fore rationalem
sihil ergo hinc duci potest ad usum nostrum.
Hine autem apparet unam saltem arbitrariam deesse, quo
minus hoc modo solvantur, aquationes
X + B B. X + 2b X 4 b p0.
X3, aequo pX - 4X - 7.
X ago p X + 2pq X + 2pY X
X + b
quid Liaidas ad aequat productam
vides nihil lucrabimur, quia nihil plimusest
ac si pro  3. scupsissemus 3 +(1) seu multiplican
tem flcissemus: 0x34 1xt + 2X + 2 jam 3+1)
una literm exarimi posset vig 4.  ergo eodem reditet
ot 1 aequ. 0. 0q + ip + 2. aequ. 0. imo etsi quadrents hinc X. philile pX - qX - Y
atque inde faciamus novam aequationem, sclicet
sextus gradus ut attollatur ad 30. opus 3 4 aibitrariis Jam _ 30
prX 2pqu escLaqui0. eamque
addamue pricriproductae, nihil lucrabimur, quia hoc aequatao tiam per illam
N+ pX + qX +Y. est divisibitis, ero quotiente exeiente formula rationali
24
quae ab imsio addita multiplicanti generali, no  on ad unam mulsiplicantem
componendam, utique multiplicante generali non constituet generaliorem: Itaque
haec ceddita nihil  novant, vec majorem dant comparani libertatem
X + pX + q
pX +X
N  + 4X
ppsam dat