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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 5
# Folio 1v, page id 00068218:0002
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prodibit alia aequatio quae postea cum data vel saltem cum data exaltuca
comparari potest. st n 1b X a 1b I. Id se
sit X - b - c - d- e aequ. 0. quae exaltata assurget ad
X
Jam ex aequa data
sione
.. b ∞5. fi0X . l XE
e
XC
bé - - b e5-
. bc d -
. 155 
Hc
a b10 10
M
 655d 
X x +qX +r X +sx + t aqu. 0.
15. 12. 8.3. multiplicando per X AX X, x ac. habebitur aequatio D. quae ut comparetur
E0. 17. H.8 Cum aequ. 0. ita explicandi arbitrarii 2. 3. etc. ut omnes termini
praeter 15, 10. 5. 0. destruantur. Sunt autem termini isti
octodeuim
novendecim
nempe 18
17 crc. 3. 2. 1. 0. quorum destruendi quindecim
867 8 9 10 1 12 13) 14 15 116 17 18 19
D. 1. 2. 3, 4. 5. 6. 7. 8. 9. 10. 11. 17. 13. 14. 15. 16. 7. 18 419. 20
tantum enim quatuor restare debent
Opgergo quindeum
arbitrartis. Sed nos non videmur habere nisi qualnordecim
derum felici remedio nancis quia in frimula:
X
A 2X + 3X etc. utique solum 14 arbitrariae. Sed
Jam video nos felici remedio nancisci arbitrarias 15
si scribamus:
1 X X, 2 X + 3X eI. non quae
est formula qua multiplicari debet
X + 4X+ YX + (X + tsequ. o
habebius) aequationem in qua sunt arbiliariae 15. nempe:
1. 2. 3. eti. quas explicando
etiam 15 terminos tollemus
deinde invento hoc modo valore ipsius 1. perque eum aequationem
totam dividendo, poterimus jam
comparare aequatione
cum aequ. 0 adeoque effectum est, quod tamdiu quaerebams.
Eadem methodus servit et ad compendia invenienda, sit
enim X + a + bFC ete aequ. 0. utcunque sit compositus vale, semper
po commodissima ad aequationem revocandi ratio apparebit
si sint plures iirationales diversae reducantur ad communem
exempli gratia:
Sb + ac.
scribatur rab + Vac
si fuissent b+c+dte non suffecisset multiplicari per b - bc + 2bid productum
enim fuisset. b - 2bc + 8bcde. quod ducendo in b2 - 265 - 8bede habuissemus:
b + 6b2 + (67 d + 24b ce - 4b seu b - 4bC + 6bt + 4 b. d - 401 42
abted) -64bcde et