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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 18
# Folio 12v, page id 00068231:0024
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Sed res omnis proponenda est distinctius.
er X+ pX gX X+ SX + =0
sit aequatio, cujus radices quin  HE, L, M, N, O quarum quae libet vocatur X.
radicis unius partes irrationales quatuor h+l+ m +n, compendio h = X
H + L + M + N + O = p
H vel L vel M vel N vel O = X
HLMN vel dc = 2
h + l + m + n = X
HL + HM etc seu HL = 9 HLM = Y HLMN = 5 HLMNA. F
HL vel HMvel Adc = Y
ALMNO = TI
hl + hon et = hl = y
HLm vel HLNecc = Z. HLM NoelSC = 2 HLMN- 
hilm = 3
Elium = co
hlumco in veniri potest quid sit rationale in qualibet potentia ipsius 
ut in X, X,  etc.
Inveniri etiam pt quid sit rationale in  vel in qualibet potentia
ipsius Y, ut in V V etC. et ita quoque in Z, 2, et
. Sed non aeque vid etur facile definire quid sit ravate in ipsis
qu
ex h, l,mn copositis seu in y, Z
ie invicem et cum X.
Xx = Ah + 2hl
co, et et horum poteneris atque factis in
h, C, in n = sa sb sc B
ergo quod in X est rationale erit et in 2ab
X3=  + 3hl + etm
erit ravale in 3ab r abc 3h C+ 6hlur
illud manifestum videtur hi, h, tc. nihil continere ravale
jam htrx eliam nihil continet rationaleSa + sb + SC +Sd inta tbd
dat sa + sab
videndum an in generalo calculo unquam aliquid ravale prodeat ex formula
je
tale, eut forma maequaliter se habente in exemplo, ut Sao vel hat
Nota. Quae farimus pro X, e ex p, qr; eadem facere
possumus pro _Y ex 9, seu HL ex HL. HM (cujus valot invenori potest)
ex HL. HM. HN (cujus valor etm inveniri pb quae et eunt HL. HL. HA MC. Ma. aV
ad tactand habendum y crsque Y,
Y1
e
is
loco
Vecum illud in quaestione est, an
liceat inde transires ad y.  seu an possit haberi ontor ipsi,
y et
eigue quadrulorum potcabiar, itat ut coincidant y er Y. vel saltem, ut
quoad rationalitates ut se X et ejus potentiae habeot ad P, q,r, ec. ita se
et et ejus potenliae habeant ad qseu HL. HC: HM, eC.