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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 27r, page id 00068217:0055
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In quarto gradu, indigemus veloribus: abc aequ. h. a, b4 ct aequ. f. ab a C +C q
ascendendum ergo est minimum ad aequationem octabi gradis: Sit ergo
X + ea X +  a X+ 1 X + 4a X + 5aX +6a X
eabX  +21abX + 3t abX +41 abX +51 abX
+M abc +2 a bX 13cab 142 a6 X
e
Y2abex +31 abCX + 411 a bCX 151 abc X
TEElaBck 133abX +43ab X
161 ab X
152ab X
+ 7 a X
n
+ abx 132 abCX +qua bex
MnaebeX +3314bcX
h2abex
1 aq
7 a
61a
= (2)614bC
52a
52ab
5245bE
=suNbC
SH1aB
430
CA3 at6~
434
3c
quabe
421a
Tt214b
3314b
 a63 
absoluta multiplicatione prodibit aequatio in qua extabunt formae omnes octari 
omnium graduumusque ad octavum inclusive quae tollendae praeter abcx. a X a at
quod ut fiat non suppetit satis arbitrariarum, nisi quoniam obs sunt arbitrariae numero
2. tot scilicet quot formae infra gradum octavum; in octavo aut formae autem
sunt primo etiam 29. dende formae octavi gradus scilicet: a
scilicet. a. ab. a V. a bc a b abc. a b b2C. a bc. a’bc b  numero je
quinqque
id est in summa formae 39. Quae tollendae ordine omnes, temtis his abc. at.
a bc ab quae si subtra hantur a 39 restant tollendae 3. Cum
tamen formae sint tantum 3 arbitrariae 29. Sed in promtu, remedium est
quia enim omnes termini octavi gradus reduci possunt ad simplices  (scilicet
ad. ab7) accedentibus inferioribus potentirs ipsius X. potentiis Ergo tolli poterunt
reliquae formae, etiam sine arbitraris, satis ergo arbitrariarum habemus
ad tollendum. 
aliae
Si ergo omnes forma sint sublatae, restabit aequatio:
abc X
X   re abc X + 8s a A+ ga
+ h a+b+
aequ. 0. comparanda rquationi
decte Xx GX + rX +s aequ. 0. etiam ad ad excitutae, quod fat multiplicando per
XY 9N’+ rX1s
arbitrariam formulam, X +x + lx + m. fiet:
it k aequ. - 9.
+l9 + KY aequ. 0 trgo Caqu.V.
+14 - gr aque teu laqu. Y.
denique M aequ. 2)
Ergo Q abc aqu. 2Y (. q  (+)) ae qu. fa
=s9 + p - 45 aqu. 9abc
Aliter XE C IX +YX
s’aequ. darhab
Eodemque modo et in altioribus quaesitae aequationes
haberi possunt nam ex data a tolli potest
ad. et superest tantum quaerenda a b+ in ultimo.
Xex q txam
ml etmgs nns
+x itentex AlsX
qr = qX
X + R +EXHS
X XKXLIX +M
ex mai x
+Ix ige rik HX
ed quoulam
rXX alq rtrXitSX
A +q ArX +sut
Xd + + teita tsa  as abet + ga
=habe