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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 41v, page id 00068197:0082
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XX - bb, XX = CC = 0
XXD ab, XxHaC = aagus. sit X - m nun VVt aupV aq:, Yer 1 exat V aat
Xx+ ab = uM V+ 2man B + naa pV +2maqu
 taannv + ranaap V Lap aequr
sit X am v nanV + C; ro prratotunt +  vo 1 aap aqV + agq
xtab, XX = X1a =
quiar
4b-
amv taun- p
H 
X: a = mo tan: pV tar
=X + b = amvtan + bon + abr =0 et
sunt quatuor radices nova aequationis am V + aat ZBN (,V + aah -bpr, v aat + Cpr L nat 
D.
au ex
aptus
a bP
Et afes
si esst aaR +Vp = aa _ - Cp fieret (a R + abp = aat A = bcqr) = ( B - A N + aabk b cpd
a+b
a - c
fietque a(brc) pr  = na (b+C)h et prodirent duae cadies.
t abcar = aa (bC)n, quod inutile
itaque non possunt fien duae radices aequales, 
quaeritur ut silut ut tollatur terminus ultimus et penuttimus, pro ultimo tollendo fiet aan = acr =0
oralis f sestruatur
temantur termini primus et secundus iptro primo destruendo it sit am-cp =0
seu an = CY. sit tercinus renulli
sut p: n = a: c. si destigatur et pe selundus fiet summa omnium
aequalis nihilo, fiet Nan +b +  anbr + an + Cx + an -er =0
amtab
amop
am+cp. am-
an FbZ + an -br = aamn (t ambr - bpan) -bpbr + aman an bu tbpan) bpbr
am tbp am-bp
et an +Cr + an -a =
amcp
am aamm = bbpp
raamn- 26 pr
aam = cepp
et omnes quatuor dabunt + 2amn = ZaabCnmpr - 2aa mublpp + 2bb ccpr 1 =0
amtep
+2mn = 2aa bbmmpY = 2 aamneepp + 2bb ccpY.
i po qponendo a, prossaenc, fut 24a Cn + a 2bbccar aa ctaraa enbbaa
seu divisis omnibus per C sit
Haabbccr Paannccaa
Casiet 2Cen + 2bber - 3Y = abbn = 0 = cetbb,
finqus sen: Y = + bb. = CC, C, :, 2 (ce b q (bb- c1), seu nn: Y = C: a = m:p quod heliet
sit X -
seu M: y = - b: a
v mrotanvtaap,: quotarv +t a
bquotabirt
pabe
a
bber = acen
si terminus imus sit o, potestfieri  ap- et =0 seu p. t = c. a
ut tolatur pe secundus fiet Gan. + 4b +.... pl quam quatuor, partium summa
eadem quae ante solum pro  ponendo q
am + bq
frit. 2On 2accn 1 ibe C, -4a mase tm- 2a ammor (bb +CC) traamnqq bbtC) + 4bb
et pro M porendo b, proq fint 4 4abn (bb n) + 2aabbar (bb + CC) 4 Elaa bnaa (bbrcC) F abbccaeY = S
ta
et firt -r: n = 2aH H  - ( a (bb +CC),: b (bb +CC) - 2bcc
seu _ r: n = a Cbb = cc); b(cc - bb) firt r: n = a : b = - q: M.
pari jure si destruamu etiam penultimum fiet r: A = = t: p = a: C, sed ita fieret a = b contra lyp.
sit tamve tanno+ ap quadratus ob D + aan tabrx + a p, aabt quadratum
superest dispiciendum an liceat habere quadratos
11, 6,5, 1, 3,2,t
am +bq
cntba
+bquo + bYV + aabt fiet 2 qu aantabis- aep + abbt
am +bq
amtbus
seu aann + 2aabur + bbir= Lamap + ambt +b gap + bqbF= ap+ It, amtbus
aann= 2aab nr + bbrr L) ’amaxt an ab -bt, am -ba
qu (an +br) =iam +b9, ap +bF) fiet  4abir = sab t gabpus
m seu enrntiva
du (an -br) = T, am -bg, ap- bt et Znann Fbbrr =4 aamB + bbat et  L Y nanniblrr a
unde fiet, ac r, aap Ipgaax =aannt tborrt bbqet, et sit dg  a n Tann +bbrC 2aan
 bbIt- aapp
et m = a bb arttZaanrpp) Laanh ebr) Ea: bb t3-napsit
 4
marpor
seu mD (aann +bbir) P = 2bburt; Aaapp - bb H
superest una aequalio acun -Zaaeu 4C qu (ap - er)  Aaamp- acmt - ac qu iccqt
ex 1 et s siit an qu (antbr) gul an cr) a nc   amtaco. ot (b+C), bc
bbm alran cer reran   2apt (b+C). Et nom q
 ubi absuntg et
pro m et substitueno valores, habebitur aequatio in qua ns t afsurgit ad qua t: p assusgit ad
ut rusus Iqu (an +bi) aump, b qus an CY)+ qua
datu et tabatur, ipsi n ir manentitus. sed oporeat rem absolvere