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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 31r, page id 00068197:0061
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X,. X+b, X+C, aequode quadrato. sit X = OD- minzz+ Emnaz + nnaa
DD
Ppze2+ 2p9 a2 4 qqau
11
Hinc _ X+b, X+C, DE = aOD + bDD, aOO + C DD = aaC + + bc 74 + ab +4 00D
in hoc producto tollantur termini ultimus et penultimus seu g0 et gi
au
4 4
4
r.
pro tollendo termino ultimo, fiet aa Rre + bcag + a (b+C) a nngus = b, Et
ponendo g: n = a, r: a, seu nr = ag,  in  evanescet n, tet fiet.
e
aa a + b bc pF + a (b+ C) aarY = o. seu  seu 2 + a (b+9aaYqusbr)
= aa)) a a qu (brC) -qa b , : 9bbcc
et fiet rr = - a (b1C)
2bc
aa
E +C
u
3(b-C) = F -4 vel  a
edum
0
1n
Pro tollendo termino perultimo, seu Z, fiet  t
aa Amnannaa + b. 4pgaggaa + a (b+C) L
2mnagqua
bc ce
C nn
0
apgatpaat
L
e
et pro aq ponendo nr, dividi poterit aequatio per 243, et fiet
aa(btC)
a tat atm + 4+si 2 brp + a(bic) anta
et fiet 2am F 2b - 2(C: f) afrafp + aaC-aa + c)afM
sit b negativa=
Abole
rrm
Carp
  fiet W.a a f et rk  Yr~ -ab-aC
e
s
d
3
tat p
nXC(Bas et Petmaq) CF m + pras,
a
seu 2aam - 2C P raf, (b + c) fm+pVat) L
seu 2aafm a23
et fiet p: m = 2aa H b+C)f,: =(3caf + (bHC) Va
vel pem = 2 aa f et fanates )f,: 2 feras + ( aa + Cf) tas
seu = P. m = 204 af + (- a0 + cf) faS, in da fet +a 1aa + cf.)
e
e
 etgaa
seu = p: m = t aa + cf,., ba)
seu denique p: m = vaf: a
e
et  q. n 2
fieret p: m = quin sed hoc
x
evanesceret
id
fafi:ta.
evannisset et fuisset 9nq: nn = - a: b,
3
.ila
quam in valare ipsuus X
non licet 
e
ut primus ut ultimque terminus nempe Let
 variabilis.
et pp: mm = -a: C
) quod non prodest
pellet XX + ab _, XX + ac, et fieret XX = mn XX: aa, ut supra x: a
redisetus priordifficultat
-. odidet ide lane an C + bc D a (b +C) C
et prodicet eadem plane difficultas, sed si ex si osset XX=
fieret Xx + ab, Xxtac 
seu XX: aa =:) fieret xxt ab, xxtac, ut aute
A
ny
olli in aequo asurgente ad L
o. Tollendi essent
terneni pra primus et segundus ne
ad
7
at Ztah
afzF aaquut
vhs ssuid quui nveeret
AeZZ+ anZ aep
Pp Z2+ 2B9aZ + qqaa