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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 22
# Folio 14r, page id 00068235:0027
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De terminatam Methodum perveniendi
ad resolutionem omnium aequationum cauc
video. sit X a + bX FCg + dX + C X aequ.0
fiat xaequ l+m + n + p
Et concipiendo. X. l. m. n. p
tunquam irrationales, tamdiu attollatur aequatior
donec non gisi surdesolida horum extent, quae
aquatio quocunque demum assurgat, nempe ad
sexagesimum forte gradum, ninl refert. Illud
 potesttanten relinqui Imnp. ut eo minus assurgatu
25
20 151000
Aequatio data 1. altollatur ad X _X. X. X. X. X.
per Recbi Tabulam excillationum; et producta
aequalio multiplicetur per ordinatium doneo aequalis
fat doe formulam arbitratiam; donec ipsi
aequationi 3 frat similis. in Aequatiar3 ta
autem poterunt omnia reduci ad 1.+ m+n etc
m + len en. lmat eu. Quibus habitis
instituatur comparatio, et invenientur tum
piterae arbitrascae tum valores ipsam lam.
modo i non assurgant ultra debitum; possent
enim assurgere si
gradum 12.
im
e
equat esset gradus 66) u
+2 5omi ad gradum sextum
ad itum
siu 2d
mio debent esse nonhamum
rectanguloru citronale
lam + a+ p haberent summas rectantuuloru
et tricestagnulorum etc. rationales n seu si sunt
I
radices aequationis gaticae ascendetur ad gradum 20
en
10 1151S
 +.. B. X +. Vm X + ninx hit
omnes
et habebitur X
foret enim X radix a quationis quaduto quadraticae verum
deferet coeffraiens ipsius 15
ita Y valeret l. itpu quia
esse summa omniam sl( + in an +p. quae exprimi pe per l’an
n+ P quinquies, una cum rectangulis brrectangulis, ete
etiam quinquies sumlis, quia dantur intronatiae nam ins
his consentium diverscetradices in quibus ad rationales abeunt
2
Ergo si ponimus dant l’am vlc. es interioibus iler