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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 7
# Folio 28r, page id 00068220:0055
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A
de Modo Transformandi aequa egones, deprimendique ad proximi infericres. Itrc noca
sit aequatio 47 16 es
1+ 4Z +6Z + 4Z+
aego 1+1
inde peri potest. 4 + 52+ 4Z4 Z3 a9. 0. Sin pro 1+Z scribas X, fini
ret a aequ X +2X + 2.
Tentemus generalius:
1+ 9Z +6Z +4 27+ 2 aequ 1 + a Z + b Z2 +c
13
at
sin pro _ 1+Z scribamus X seu Z aequ x -1 fiet:
X aequ P a + a  X.
+b-2b X + bXX
=C +3C X ( 3CXX + CX
qua comparetur datae
+N
X
a pX
+
4
seu
fiat: y aeqi vX +r
6
6 Y X. n 4
+4 B1674= 
seu a.
= b. - c. 
fiet  aequ P. b aego B+ 3p
a aequ A- 3p +. 3A+ 9s
seu a aequ M + 3 +6
ruisus 
a aeqo 1 + p - A∞3p - 1
fiet M - 4A - 9p - 1 aequ. 0
sit aequatio Y aego l + m + n + p13
 aeqo Vy +Y siet
sit
+
2
Laeqo 1 + M + 4 H + 9 p.
X-
ues
singularis hoec videtur
hhoc tamem
alia obtinendi tales
aequationes collati
quod sic sima tias, ubi non servatur
plicitui dolffilex hom ofenecrum
unum adoinur sed lilerae coeffi
cienles simpliciler
simul adduntur
Videtur ex hac methiodo
nimium sequi, unde dini
suspecta est sequitur eam
ita et cubum de paitur
posse ad quadratum
eit sicet incederemus
in quadraticas impossibiles
tamen id salis mirum foret
et sufficeret ad deprressione
quo ad rrationales, cicet
imaginarias
X
2
aqu
aequ
rpo
colerm
prronen
fuit rve
notandum
cientes n
rergopotentia
assurgunt
ullimelinen
hujus pagine
deprere
enor
aego
 unanom absolas . seu mutate contineantur
et Laequ 1 + M + 4N +9
aego
dividatur aequatio  in duas unam, in qua conteneantur omnes termini in quibus est Z sine ulla
alia ipsius r vel Y mentione; excepto summo termino rC. et habebitur aequatio uno grabu inferior, cujus ope
inveniti potest Z. valoc ipsius L repertus, pro quo substitui t V potest h, substituatur ubique. et ita subtaa Y. munebunt termini
qui oanes erunt sesibices puet. et ita deprimetum B ad quodum inferiorem sencetiam ad Tubum. am videt
in quo deceptus simo explicande , 
puvatione emo cossat depressio