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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 104r, page id 00068194:0207
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de Roductione Sexti gradus ad Quintum
sit aequatio X + bX + CX + dX + eX +fX +
ex
os
sit Ket b sit X+AX+ SX 
si X L HX+ A X L1X4 I4X +15X + 16=0
240 n
suciessit
formetur formularcubica sexti gradus generalis; facta
ex cubatione hujus 10X + FIX + 12, quae dabit
10X 12O. H X = 3. 10. 12X + PIX
+ 3. 10. TI X + 3 222 + 3. 10. 12 X
+EBX +3. =1. q2 X + 311. IX + 12
articuli
Farmula 3 addatur utrique later aequationis 1. fiet inde ae
firuula vel aqu+. quo est aequ artic. 4. Cujus pars sinistra
aequanda est cubo generali alteri ejusdem gradus nempe
excitato ex aquatione hujus formulae,  20 X F 2IX + 22
ex
fursus
cubatione quae dat fiat
2
20X + 3.28, 21 X + 3, 20. 22X, + 2I X
3 20. 21 X
+ 3. 20. 22 X
foe (5)
E)
+ 2t X + 3. 25. 2 X L 3. 21. 22 X + 224
et multiplicanda esset   artic. 1 per  aequatio
in l. per form 207- 10 deinde addatur ei ab utroque
per
latere formula ex 3, fiet equatio in artic. (6) quae incipiet
3
28 X + 20
= 10
X ere  10X + 310. 11 X ete
quae ut sit utrobique extrahibilis, cum sit in latere
dextio, debet comparari sivistrum, cum form. 5
+ 3,10.11.
sed video nos tantum habere literas arbitrarias sex 10, 11, 12
20, 21 22. imo revera lantum 5, ob laves notas, quia omnes
termini in arbitrarias ducuntur et ideo cum tamentermini compa
raudi sint 7. Res igitur hac methodo non procedit. Et
tamen aliunde judicare mihi posse dibvideor, debere
procedere. itaque Methodus hoc sb succurrit, aequatio 1
mulliplicetur per _(220= + 20 X + 31 X F 32X + 33.
ut ffiat aequatio L3) graduum noven. 110
ibus (
et proformilis cubenter formulae () 10 X3 + ( 1X +. 12X + 13, quoal  mbus
quaeratur (4) imbuforinntae (6) 20X3+ 21X +22X + 23 quaerata () cabus
cubus  ponatur ab cubus ex 4. addatur utrique parti aequationis ex 3. cuius latus sinistin
dextrum ideo erit cubus, simistrum erit aequandum cubo ex 7. Habemus terminos aequando
numero 10. arbitiarins vero habemus , in effectu aequi valentes 10
et comparatio procedit.
10E
verte