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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 386v, page id 00068196:0768
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X b
(Xt C). - xe 
erent X2  + B, e 1, C-2X 3 3 +R. C -1, C- 2, C- 3 X C. 4
2
12. 3
sit C- 0 fiet (Xt C) = x = + E -   +  - 4 4 + etc
=_ C jam CsI - E + CC  8, + C  etc ∞, et X = c - cc 4 3 -
D
e
X
1. 2. 3. 4
e L C etc + X. C4+ G
ergo 1 - = + cC = C etc = X et  ce - 3 +C ete = X - 1 + = seu = - C
XX
XtC
et + C -  rete = c logxe = c logXF9 et log (X+G)- loge =  C - ce + 8 etc
XtC
XX X3
Ergo (X+C) - X = log(X+ C) - logX. quae conlusio es
et
3X
2XX
Hinc si pro opona,  1: 1000000 potest compliobari logarithmorum
8
Hinc si X sit mod E modo E+C modo,
d
(6+ 25)(8)C 4
C
ec
I ErC 3EC
8+3C) - (X+ 29 = 1 -
Ergo
c
= 2
353
+ e
32+C
+
4
4
e
1512c 2erC 381 4 81ge
E + nC + C). -
5 
seu
  loq
logsy + nC +C) - log5
quae sequantur in alia scheda melius explicata
seu sum l proxinus à maxe it
2XX 3X
tialiidatur
log (8+C)
logE
= log (25 +2C) - log (8
+ a xre
+
ad
ce
+
+
03
e3
- 
ter
ce+ 53
34 etre
25129 3(2t 1 4(5 1C)
ete
1 Erne (5+ nd 3 (5+9: 4(5+4C)+
seu log ipsius X proximi a maximo) est summa omnium
E
2(1. 3(Zt C. 4(5+C)
E+3C
asque ad
cC
B
-
c3
3X3
e
472
pplcalmmuo  ad maximum
quae sequat rema fenerate explicata sun Ca Aemnorum
aminos
Generatem regutam hanc invenio sit = summ reumer. y
eometricae.
ta porro
rentin
etc = log (Z+3C) -
+:
numerica
demito leq ipsius x mipimo melius
nter
C
b infiaite sigpato differ
 etc
c
2
quae addendo omnia simul fiet
etc
Sne 5
s
memorabilis saltm
a bulmper cuna c
+2C, modo
Hie es sc cet c iasi quitassamaist
Dinfinita
fiet (5 + C) = . = =  = 24E
1
Genetanis regulal y
etc
si inter summas Nnumericas Terminorum, differentia Geometrica, est
si summqe Gemme Numerit summae Numericae
summa Numerica differentiarum seometricarum inter terminos.
1. disferentiae Geometricae, dy,
summae Arithmetica
omnium y sint v, fite do seu v = summus siet du = summ. dy
positis semper dx constantibus
sit sint Termini
erit fyda = v eANia ; X jam inveniamus summam numericam quadratorum
XADM EXXC sint termini XX   = y
a 0 usque ad aliquam X, quae est Xe XFI - X - 1, :2 seu XX + 2
2 = XX+X ,: 2 = v 1+4 -5 - ++2
_ C diff XX _ seu XX L nhC XX + 2XCt CC = XX =
jam inveniamus summam Numericam quadratorum  ab 0 usque ad maximam
seu XX F 2X +
quae est Xt posito differentiam ipsorum x esse C, fiet ea 2(x + Cs - 3 XFCC + (X+ CG 1 bc4
 2X +6XXC+ 6XCC+, C3 - 3XXC = 6XCC -33 + C, : 6CC = 2X +3XXC F :bcc
  ZX L3XXC+ XCC,: 6c0
eu erit D 2X + 3XXC +X CC,: 6CC posito c= esse differentiam
L XCC
et o esse minimam. Hinc deD.  6XX +6XC + cc3: 6ec
Hinc  = Et  quia y = XX, fiet dy 2X F. jam omnX = X+C- XB,
et debet  de seu erit omn. Xx  sive
posito X esse maximam X
(V) = omn. (y) . du -(1)- v = Omn (y) -omn. y
du = (V) - v = omnly) - omn. y = omn (Cs) - y) = omndy = de
(3) -y = dy (V)- V = do  v = omn y
50 - 4v = 4 y. Eo
nn. XX = D = 2X + 3XX + H, :6. du A=XY + OX + ix, dx
Ergo 50 - 1V = 1y + 29 +39 + 4y+ 5y = om 26 3d 5d d 5v. - dm d1v
30 -20 = 2y. 4v - 3v = 3y
ax+2xa 
Ex. gr.
Ponamus omnus y es h d5v - div = diy + drgs + d3y + dr.  (X+1 .2 - (x+ B. 2  xp ax . 2
tam
C ut iritque L XX 
omn dy
cet cede 1++A) d (+ 00t 20) =
ert
2V - 1V =17
( +    ( t L(1+1 60040- (
sit primium
B= N ZXX + LX
L(2 + 2) - = (.1 4G = 2
2(3.313) - 2 (2. 2+2) =3
Exx+ LXN C -. X Y X - L - 1X + L =7
L4 4 24) = 2 (22 +D a. saet etc.
xrt xie tax  seu
CE+HI) = 
Ergo
ce unner 
aarg . 1behb3