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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28
# Folio 44r, page id 00068241:0087
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divisor X+ tx =mX+n
X+ bX + CX + d F 1
X  x +mxtns
ex Imx-n
X+ b Cx + dx + et x N+ bX + Cxdx + ex+f E
(X + x +mX +n
X+bX C d CE EXFGE+
=n -bn -1
ba eln ta
+Im rem +bn
c due ln
m eb
+b1 m
X + X +MX+M
alx-dm-du
+al +mn +.
ebim +bni +bum
almne flum
+c12 +ctu
em alu
Cb13
bum
an
+a +Bm ben
e ex pmxn
te
+
m n
dividendi: X2+ bx + Cx + d
Quotientes:
Residui
-
Ab X + CX + d
mx sux
ib. 1
+ lx +mxinl
blx bnbn
u enx
+cm
-blII
+d. n- bu1.
ect am
+bI2- 17S
C-bn +mim
in +bim-em
faltultbem
temdaerem
4b13 +14.
+ Ix Em X + n
-IX-m- nx
Xh + lxF+ mX +n)
Divisor X+ lx + mx +n
=blx - bmX - b X
+ll +im sin
+G. Ix
tc
am
= bl
(X LLX +mX +u+U
LelxcmY-cut
+m +m. +ia
+b +blm bln
13. Cm. in
X +bx3+ ex +dx+e. X+ bx + Cx+ dx t ex+ f, X+bX Cx derexfatu
X +b
+cX +dX +e
mn
-bn
bi bu ila
Fu um
X + bx + c. m
iblel
td X +e X + f
um
+In
+bl2
+(3
bn
+in
=en
em +mn
+
+bin
ibtlin
m
 X+ GX +C- mGXtd - n. b
+l4
-birie almde
ut progressio appareat, Residuue unus AX + BX + C, proxime sequens: - ALX - Am X -A
Regula generalis qua residui proce
Divisor X+l. Regula: Residuus unus A.
xflxtm
+B.. 4
sequens - AC
+ v.
ex regulis specialibus:
Resinus praecedens AX + Bx + C. sequens
sequens ). AI
A 
c=
+C.
Riesiduus unus AX + BX +C
proxinio sequens- AIX = Am X - An
+
 + C. + y
1b(2- B
etun
er
Ingbm, ben
Ihu.Bn
te-bnolu. X +F. cn X +g- dn
emenebim. minebin. nabu
emdenl. Tn, dn
Ablmiem +mutbui;
)+cl m- bB. Citcns lnin
n
habebitur
XHXEmXIN
finitas
AX + bX tC
Unde jam tale Fheoema generale:
sit divisor quiunque X + CX = A etC. et sit residuu L+ M X + N,
+ P,
X etc
tunc mona se eadem divisore, et assumto dividendo, qui sit  sit divisor finitus quicunque X +1
2+
a t lx
tantum gradu altior, cuit residuris
sit divisor finitus quicunque ab
e
Et sit residuum divisionis. A.  1d a
co
X
+C. ∞
e
et
m.
x2
+n. X
lX X Enx
ere
st divisor finitus quicunque X + l. X + m. X etc. + YXIS et residuus: A. X + B. X1o-1 + C. XC ete + F tuncmanente
eodem divisore, et dividendo assumto qui sit uno gradu altior, Eit Residuus: Al X = Am. X   An. XC etC Z AY. X = A)
C.. + D
C An
=A
ot
+ x
=Am