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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 12r, page id 00068197:0023
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et licet haec aequatio ex duabus novissimis ducta
suffecisset ad habendiam f considerandhm est d
jam haberi ex praecedente. Et ita aequando
eis ralores haberetur determinatio in datis contra
intentum. Batodempe hhg: p unam constituunt
quantitatem, nec g et p aliqui habentur
Resumamus
calculus nonsconus
se Quaeritur fdx (ex tab, XX +ac)
Xx + ab = aa sus + ab -1 3
est N + ac 13.
ExSN  = ffOD+ aa 42 + 2af210Y
= ab, 0D +  + 2t il 3D
+55O5 + abOD, 2a52O)
erit ex tab in Xx+ aC, + al 74 ab q q 2ab
f5OD + aCCD, 2a57) ()
aa 2 + act + 2ac ti
Sit ras 2 + 2act, = - 2a52 - 2abt
estaf -a(b+4)q seu  act+C
semf = 2f7:, b+c compendia sit 
-2afi,btC= 9. fiet at- 4
Sit a1l + a) (O) =9Z = gVOD Et primum
Ergo ex pa ita  ita 3+ VD in 1 -1(OD erit
idem quod 3 +  SOD in 43 - 2 105=
433 = Q OD aqu. quadrato s
ob identicitatem nuperam, fit, 2=
seu 2a54 +2acZ = 9 2af2 + 2abt
seu (ab + ac) +HF (a+9) 4. Atque
ita  = -  f(a +9) 2: a (b+C) = - p7.
Et e ob a TI = g3, fiet:
gff0D +9 aa 44 affOD + a24
gab ODFgab B aac ODa CB
ff ducitur in (aqu (b +au =Q qu(b+C) aatib
(ab anca qu brd) acaab iu (b+C)
Ergo f uanessit sportesua
ab agu (et d) raba- ac aqu (b+C) 2ab
Corficiens ipsus f. et gusbtc) - aqu (b+e
(ab anetua Ac aabtna)
itaque evanescit f, sed non ff, seu
Tollitur egno terminus secundus aequa
superest coefficiens ipsius
(a, qui est. aqusbte) ab = ae u(btC) ac
(abaaC 4a (6+) acaab ta btC)
(qu bC) rab =a quo rerab)
itaque aequatio sordinata
+ quexe
Etri (t) p qaequbre  I5 - rabi  f alijpestas eu
quae aequatio sividi post potest pen. bdc c- b
et fiet (4f = a a qu (+ C), f + 2abff +a abb
A) 2 ft = +a (b+C), B+ ab
_f = acbrc) f + aagusbed
aa qu (b+C) = 8a (b+C) ab
+3. a CbtC) tat (rebct  ebbtu
seu= = 2a (b +C) t (qu (b +C) +8 (bt96),: 4
quod vilstm sucedere semper, hatem sucedit in fonicis
cum Xb4 C)  minor
im 4 4qu C0FC) sit minr quam
seu gD = 3 3B =b5151
D = 31 (9. a) -51, a.
posset Z sumi constans et posset esss 
fiet g=a +aa cpi a + abpp = afs taac, 
pbsolutus in pigisi gaxitime
ubi f alcendit ad
nequit, nisi ii casu quo b +c
qu (b+ C) tq aac ueta
est coefficiens termini sum seu
cb. iad nec hoc tolli monesteu
ouihilo aequanicusosse umstuqe
at Bforet f20
ata sit pp= Haat ss ggt 2ssag
issicaque res non semper succedet eaes rsto min
fiet, aou (bc) + aa Cff qu (a +9),: at qu brc) taabfs qu Catu)= sftac; 1ff + ab
porto p= F
qub++ Ebteb
fiat  = Zd9. a) + 51, q.a (i
ub destuotur se licete ta Mutetur haec imbyc se
aequatio in identificationem, et fit ob ()
fiet g = afftaac,: f5 + ab Et ob 27
vedendum an possit tolli fb et ff
 compendib  x B ++ to pro Numeratore
3+7 OD in  1I - IYOD
X= Pa. F10+ a 4 = as
ubi prorsus pn a+g ponendo valerem 2af5 +aa (b+C):, f + ab
fit a que brC) ( qu (5ftab) taac ff qu (2aff + a a (btC)
aqu ( b+C) qu (1F +ab) F aab ff qu (2aff + acb +)
oportet autem
ita fE vel ac surgit ad aequationem biquadraticam
esse gsf ut mujorem qua fF+ ab, et fs +ac, simul affirmativas vn simt negativas
itaque si ff possibiliter inveniri potest, res est absoluta
e hs clipiis
quod si utrumque evitari non
A+ac  cum ft tab, ejusdem signi
aesolbendam prxinam prituam
datoe ut Ss sit affirmativa pollilili ss eatu 
Non ausim fidere adhuc blondimento Entus
successus quia hinc duceretur quadratura abso
nte rationalis, cn 10) possit aquau quo
t l
eubbusor1) ab  aabb su b) 
a)b)
3be asbis) pb.   unis
i
 L i BEP
Mputram ipsaum Z et
 ponendo equalem
Au liot facere fftabu
nec ff + ac 20