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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 26r, page id 00068196:0051
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y = Nab +CX + Sad + ex N ab + CX +2 Sabrex, ad tex)
+ ex
videamus jam an data Yal + mZ + 2 +(a5 tagZ + an ZZ) =y ad formam secundi valorisipsius y
adce adeoque et ad formam valoris primi reduci possit. ita enim datus val nempe
tertias valor ipsius y poterit summari. Quem in finem assumatur Z=  P+
C
9(4) s X + t. Et ex valore tertio fiet fat + mSx + 2 + (af + agsX + hs5XX) = y
adaut + dhstX
 aret eux valere elefiet radices factrices atite
las
  jam ostendum quaerandur radices ipsius sorrationalis (aF . .. etc)
n
augt
eumque in finem assumatur formula generalis faopt aa(a Q+ _a DX + a0XX) cujus
ut quaerantur factre radices fingatur hac aequari nihilo sietq x dividatur
per dividatur per ad et fiet XX + aD x + da  = 0 seu XX + aX + aa DD = aa D D- qua O
4OC
200
seu X +∞2B = a+ 3D- 498. seu X raa D  = aar (7- +84). Ergo duae
20
eC
2ac
radices sactrices possunt esserX sac +M a D+ au XCDB. ad, et  la+na
d
 sao
2Vac
tis enim invicem ductis, fit aCXX + na D + L a 32 - a DD + 4 08 = aex x + au d + 28
ad ga
jum   1 SaC + Sa = mE  id est = et e.
et fita (N H Y) S Sch: a) = R mS: a et sublato S, habetur n, ubi
met h, sunt datae Rursus et fiet  (n  (nn+1, :n) = m B: tat seu
nn =(M: Sah) n mm tah aah) + mm: tah = mm-aah,: +ah et
set n = Imm- +ah +m,: 2lati, ubi m et h sunt datae.
Rursus (n + 1) aa Z  + (n - ) aa r(D -408) = al + mt
un
seu
m: vak
2Ya0
2an0
n + L = m: tah) CR = ( um- 4ah: 2 Lah)  m: L Jah + n
ergo L- = imm-auh  m 2 tah. Vrgo  = = smm -qah +m + Tm tah- 
2 Tat
smmdrat. Ergo  m +eum Bah
gat
m a maD + atmm- 4ah (DD- 409 M
 Vatue Ed HOXE
m
sed si tode mus D 0 fieret 4- n ag: 2tr et fiet
Wah sah Wtat
(vel D =c
ubi non licet facere _.
quia eensi invento
, evanesceret 5
= m mag contit (2mhF- mag Esit  + 2alhe
2tra
d
ja mm.+ah DD- 408.
mo
sit compendio ra Eth - mu: tCmm - 4ah) = +
(aho = Lhssia
(hO = h5: a
aa W= aagg. + Ihht
eritque D) - 40 ∞ ZsR R: aa ubi K est mere cognita, sed sevaneset
e aague + paghto + eshitt ces  4 afh + Taagt h x qal tCh
a
a
a a
3
il
Ss = SsKK.
seu aag9ue (+ 4a Zh+ L 4hhtE) - 4aafti = 4 alue tha r Ahh tF = aa KK
ibi suspectum est hbnemorabile eonesceret
s et filis 4a = 4 fh = KK seu gg- 4th3 mm dahi = Ellht- et hinatum
D= (mmgque mnfk 4akg + 16ah et habetuo f vel t e
 d +
et fit
seu f Lagg -9(m +hll,: quh
de f= Al (+ 4a996c:3 16ato- tmm quod an
17
poressimus
ac=ms ac =hS
e = ms - aC3: a = hss: ac fit msC = aCC = KBB tk Ess, sqF
Aliter comparendo 2 et
seu Gh = u aa Cc = ams C + ahss = o seu alt nace -a msac + Lmmss = 1 mmss -al
et ac = E Imm- +ah + Lns et ac = =ms = = 5 nn-tah habentur ergo C et e
ab + ad = al +mt abe + ade = ag5 + 2hts, hinc d = altmt = ab, : a = ags + 2hts - abe.
e
alc + met - abc = ags + 2hts F aber fit  ab = lac + met - ag-2ht, : (ac. a-) 5 sum val
pt ad tac + met = ag- 2ht.: -esmm- +ah
rursus aabd=af+ aagt + ah +F
 compendius um. Fati P M Etque sit aabd= sal +mG ag- 2h_t + (alF int) P, sello mG9- aage - 2hi el fatrmt) 
niemcalculus absolvatur ut appares
astan tahH
mm 4ah) L- et p
 erogultigno, et  qui ante prodetat valor ipsius f