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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 90r, page id 00068195:0179
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Ravicis
ossumus scire quae nam parseratialis in data aequatione satis
item quae purs rationalis quadrati,
.Nam habetur
facientis sit pars rationalis.
cubi a liquadrati, surdesolidi etc ejusdem Radicis, iationaliter
b  nos
Assumi instar Hypotheseos, quae videtur possibilis, quod tradix
a radiciluss
na quaque
rationale
datur autems
proposit quaesita sit polynomium, v.g. quod radix aequationis
vinti gradus sit X = l + m +n + p, posito aequationem carere ter
meno secundo, quo casu nullam continebit partem rationalem
eno ubi l, m, etc. Sunt radices surdesolidae
Assumo porro istas radices surde solidas tales esse ut combinatae
per se, aut per suas p potentias non producant rationalem, nisi
 seu aliquid unee extralci possit radii surdesolida, nisi forte uno
casu, cum omnes quatuor ducuntur in se invicem. Itaque extra
une casum, uoportet haberi l, vel lo vel _ Er, vel lo mS, vel
ale aliquid ut prodire possit quantitas rationalis.
tac hypothesi assumta, sequitur quicquid rationale est in X, coinci
Seu inO
ere cum eo quod est rationale in 15 + m +n + pC; et quod est ratio-
114
t10
1o coincidesse cum eo quod est rationale in  l
CM + ex =)) Et quod est rationale in X coincidere cum eo quod est
stuin
male in X
aationale in . m +. lmn 66 et tandem quod est rationale in de seu ia
10 10 110 5C
20 +.. lm +.. lm +.. l mn+. l’mn pe
115
110
seu
coincidere cum eo quod est rationale in
nubi coefficientes vacui relict non expressi quomodo supplendi sint, suo loco dicetur
se qui autem quod dixi ex e hypothesi assumta ex eo patet, quod X
 ECinet V + m +. l’m +. l’mx +. l’mn +. l’mup, sed ex hypothesi nullum horum
o
15
dE paeter l continet aliquid rationale. Idemque argumentum valet de X, X, p
1.
et l’n possunt
erVempe in X. Soli termini
Aissumo jam novam hypothesin, suffecturam adque determinandum
20
de
15
x0
scontiant aliquid hationula
ubrs monxuXi
8, 4
s
est in
ipsis (
ilas l M, n, p; nempe id quod rationale in iptus (C, 8, 6.
aequari ipsis O, D, D, 4
atC seu irrationalea omnia in ipsis
c
d
EX hac ergo hypothesi dantur . C
constat autam Datur autem summa rater ipsorum X ratimaliter cujus quinta pars 1t quod est rationale
la XS, seu  es ( habetuo ergo _O. seu O est quiata pars termini secundi aquationis. Habet. ergo endem modo
ur. habentur ape Tabulac en valore
tp.o flabetur jam B3, et habentum
lm in 5
evanescere sive destrui.
Norum X. ex potito X = L nod e ldit G ip 15 et Pm datishalatur
et D ,e B, et B. sed confficientes istm
rcumdat quod fes
 caetera caburos
poto derivat
punt
3
e
13
2