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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 30r, page id 00068197:0059
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Nunc ergo ad aequationem nostram primariam redeamus, ibique ualores repertos
ipsorum 40, 60, et m substituamus, reperiemus autem omnia posse dividi per am
Et sit ex ea 30. 30 avv 
O= 3030 av0 + 2. 30ap L Z - 2. 20. 56n aY - 2. 56  f ) t. aZ
et fint Z = 30. 30VV - 2. 30.56nV + 55. 56CC, :, 2. 30b0. - 2. 560 (n +b)
Et 30 = sC = 2r, firt  ∞
A+ Er 4
= vV = 2nV rcC
-bv + DCn + b)
ipsias Z, fiet
2gu(rt ) B
sb o a alui + (n +b) CC
ubi ulique evarescit Y, et faciendo p +b = p. et n. b-9 pV + 2 b n) V
utmunte sic lompendio b + n + b sit pet nab situq. En firt D 
lh.
st
ut m = n +C et n = YCbbAce)
_, ibum D =-
+2r
2 E fit v DxbuY L 2YbpB
jam C = m D - ab, : m = mB - cc, : D
vv - 
= Apr VV EBAB p
rvo I CC
A 2tbD + 2rbp
= bb v + 2bbq v
+
 2bp N. ton +2ce
= bbcc
an C
2bp
quo = 2qu + pcc
sid redeamus ad aequationem mDD - bbD - mm D + mec = 0 vel ob mm En
mvb = 2m V + cem
+ 2m bP
sint, AD = 2nD + cc =
qpqu + 2 pcc v
.
tbn
 a(pju =qp cCv  pp C
+2n 2p9V. - 2n pcC VV
tant -qurqpp .. +2n 2pKC
=2ncc_ on LEnCC
= 2n 2bp 3
ob
+ ce VD = 2CC4
av
pa ccip.
 ACCH
e
Ex v sis abb abb t Abn + sum Hoba CG + qon Alt C abidC tud- qtn Lbb c
Ex v sit 2nb (bB-Bbin =) C) c) + 2nb A cc= 0 suvedit
Bg esse nn - bb = ce, unde lotis termitus divi di potest per ac
Ex V diviso per p, fit nn Z_nbb + 8 anf _nb - 4cC = 0 succedit
et D fore constantem; idque praevideri poterat ex natura aequationis
nt -cc . debet ex identica depue hendi inventis valoribus ipsorum Teretur t 2
n v, ut nonaetit Conorutamus, novandum est q+ p es = 2n
 tecai
Fqu
+ mvo - 2mpV + mpcc Am on = Emp V + mpcc
+ sem
aee.
tepe.
2nqv
ten
mun
 2
+56. 5baCC
D2brwV  2r(t) V
(2tb) rWG= 2 (ntb) u V + (n +b) reC
Arv- 2ArnV + arcc
82rbV t2urb (ntb)
+pcc
topec
bo - 24  Esp
3 = Z: 2
tit mhrt - bb, D
= in E- Cc
nt-bl in GbEH t. Z
in hk bbHE- inti - nCc
42 =
-2nt
Encepcc
F2nEopipq.  2n
+ qccbp
= CC24
-45
Hoc
aequatio
debet esse
identica
per V, abcunque. sscondant si sint vjusdem gradus
Sed video dandem totum ioc nape
rao uatet
redigi
et quidem
deber debere et ipsius e binos hos valores seddi posse identicos it est si sut op
et et habere eundem denominatorem et numerptorem, vel saltem divisionibus. t dibersi
taeu maniteste petent in nostra aeg. N, quae cum sit identica, debet etiam in frrma fractionis ilpalica ostendi posse
per constantes, si sint ntrobique ejusdem gradus; v per formam rariantem
at ide
 inqrdec  pie 
ilt od dls
Htine _ cum sint
imus et nus ternim
iet cem + embp. :M = Bcc: q seu ccD + 2bpq = piC. quia pu = Ct
ejulda grodus dividatur aumeratur verter per m, et simiter per. 
ailet rem contingere et
e
s  ttrae
b.  sed hi duo denominatores sper constantes
ix itatu abre qurote utu sestaorm
identicae, nam aequatio
Nempen
asiore