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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 129v, page id 00068124:0260
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si p3 - p X + 4yX = P. et (X3) sil radnle irrationale in X. etc. fiel (X) - p + qq() = vd - P 93pgi. 3 N 29,
est aequatio identica ordatur else de
et y: abtac He  Z abe   2V  - 5 9 p
si sit X = a +bicere tanc quod est rntionale in X, X. 23, et, in y. 9t. 9 etc. oritur ex F, gY ides ex x
posito p = x Es ex etC, et 9 al v + 9 etc, uti se se se sy sx, Sx sph eu, sy su syd er 
quae
est x+ p:  + xV X; X + 83+ Xh; (.d est )  XG + XX +  et oritur, ex usdem B4, Y et
(hoc
hos solo discrimine quod ravale dividendum prodit, summae valo rade raoate in singulis prodist summae omnium
vatorem dividendo per ipsorum numerum radices se habent ad p ni demoe radites rempe
X Y xeM. se hadenl ad P, g, Y etc. ut vartes radicis, a, b, c etc Se hiabent ad X. y. 2. et
N illa formita estius non facile inveniamus partem pure ravalem possumus quanilibes reldere pur rationatem. omni
et sola formula quae aequationis alicujus omnes officiets praeter ultimum continet est cola ravatis
dividat
elmula per aequationem fundamentatem  ut Npx +qe si residuum est ravate tota formula est rationati
sin residuum nonsit puire cogmsum, patet quid apddere opuset tt tae fras quantitas corrationatis uni
mni dicotam cm losum quod in illa est sub uno vigento continet 
 est quantilas pure irrationatis inaequade cuu semp
ui sublatus hinc et a b, c etc. purs iratonales. Si a vel a v et aletc est potestas secundum exponente rit
s
euspartum ravalis partum; rrationalis possito quia id quod in vincuto sytenetur tale est, cumsit radix aequatione
uti naigamem
mt s erupt ompe
infenoris generatis, adeoque secundo Termino non carentis
eltae aequiliter pariter et inaequaliter ex a et b epositae irrationals exeeptis ceteram
protubeante esse o omne)
ce
s
copotitam