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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 18
# Folio 12r, page id 00068231:0023
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luppono
De Radicibus Aequationum inveniendis
quod
Certum est  in radice aequationis generalis rationale esse potest
id esse terminum secundum, numero radicum divisum ut si sit
tunc
aequatio X + p X + gX + YX + 5x + + = 0 erit pars rationalis
radicis generalis = p: 5. Oportet enim esse X = p + etc. quia
erit
sola litera p ipsi X est homogenea
itaue quod in Xx rationale, est pp- 29 dices divis pers
p= 3p9 + 3Y
divisper
p2- 4p 9+ 4pr +. 299- 45
p. 5P9 + 5pr + 5p qps-59r +S
pono autem sublato termino 2d0 p, esse X = Va +  +Yc + Id et ment
= h + l + m + n = sh  = RC
constat esse XE - 5yX +5Z
eehh
sit hl = y et hlm = Z et hemn= co
+ syH X 5yZ. = _ h
=sld XX - 2y
X3 = 3yX + 3Z
X - 4yx + +ZX L 2yy-400
M
C
Amn
X- 5 yX + 5ZX +syyx  - 5yZ
5CoX
Quoniam autem h seu 1 + P+ m +n seu a + b + C +d sunt rationalis quantitas
ex hypothesi quod sunt radices aequationis quadrato-quadrntriae ravalis:)
Et eren si sintequanttas hinc pateb etiam quod X - syx etc. sit quantitas
Nobis id agendum est ut inveniamus h absolute. Quod utique inveniemus, si
rationalis
sciamus quid sit rationale in X et in 5yX et in 5ZX et in SyyX et in 3coX et
in 57Z. Deinde quaerere etiam debetimus quid sit SCE. His enim rationalibus
in unum alditis debet conflari valor totus, quippe rationalis ipsius h5, et oportet
destrui quid quid irrationale intercurrit.
ex Tabula alibi coepta
Eodem modo quaeremus  h l absolute tantur enim aequationes
pro hl (seu y) XC, h. m tim similiter inveniemus hVM
a
12
et denique s lmn horum autem valoribus habitis, utique habebitur aequatio
quadrato- quadratia pro h vel l vel m vel n.
Verum quia prolixum foret nimis investigare quid sit racale in yxd in Z
altinibe
in yyx in cox in yZ; et ita magis adhuc in aequationibus pro h3l, vel hFm et
Rideo reperi insigne compendium, cujus ope sufficial solum nosse quid sit ravate
co in aeq. pro h,
in X et ejus potestatibus. Nompe tollantur tliterae Y, Z
vel alia; ope equationum paulo ante positarum, et Hh h h  vocando O, D, 4
supererunt in valore ipsius h, solae
X, O, D, E et quidem hae nihil continent rarale
sed an nt facta ex ipsis, et estum potentiae