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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 2
# Folio 69r, page id 00068202:0137
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Nempe sit n =  1. 2 f quaeritur (1- M dx
I-  dx = n5 12 3usqe ad e
3, 4, 5 usque ad 2t
ee usid e
m+ 1, M+ 2, m + 3 usque ad M + e
2; H2 etc qui sunt recipqved su
Mrangularium
Ergo in hoc casu redimus ad modum ex primendi generalem
qui procedat et
2 sed hoc non procedit cum e est numerus non inleger
1, 23 4, 3 usqe ad e
.  Y dx = 4, 5, 6, 7, 8 usque ad 3t e
Ergo generaliter si n = B  et m intiger, fiet 1 id X- 
X- x ax  nunc similiter investigabuntur
est e.-1 Z et3 C. (- 1. (- 2 et 4 et
SX. X Bx = eie crvil ersiu
X - X dx = 1  e  e. (-1 C. 2- 1. P-2 et-
et 1 et 2;) et 3: 1. 2 et 4; 1. 2.2
si c = 1, vel 2, vel 3 ek fit = 23 2. 5. 4 5
ex , err. ets rodem
1. 2. 3 et usque ad e
2. 3. 4.8. 6.) etc usque ad 2C +1
X. X Ax = _ = - e + B. C. 1 - 2. P- 1. 2 2 et =  21, 2. 2, 2. 3usque ad 2e
et1 et 3; 1 e+ 53 12 et7; 1. 23
2.p - C = e. 8.1. 22 es =
etz; 1. 2 = et 10, 1. 2. 3
et si scudx. 1 fit = 2 - e -
etI etIHI;1 eta Zh. 1; 1.2 CH + B -1 ; 123
1etI, 1e +m s C+ 2n - 1, e+ 3n - 2, usqe ad e+ en - )
in in, onusq ad en-
e++ era+ et R I, etH On
et et F, e+ t_tn 1, C+ HEN- 1, et
e+ 1, et 1+ n- 1, et 1+ n- 1 + n - 1, usque ad et 1pt e n. 1
un, in, 3n, usque ad en
et 1, e+ 1 + 1. n 1, et 1+ 2  1; clusque ad e
e.e-2. e.3 1. 2. 3. et usqu ad e; in R.2
isque ad X=1 Ees 2. E) HAHs EErtenH; 12 2C3 +3nH Det A, 22+1 + 1 n. Z, 2et L+2E 2 ey )
similiter se - , n ax = . - e
AX - X - a X - 2axX  X
7 et 1, et 3C, et5, usq d +1
et 1, et 4. e+ 7, ete usque ad et 3e+1
2.8-, = Y. C. 1. P-2 et
+ P. C-1 = P. V 1. 8-1
su ret tris 1. CZrnAL 1E3 LnFI
seu = 1 1. 2. 3. etc usque ad e
e e.  ma c. e. 1 X Fertuur. P. B. 2. 2g.  s ani
=ret reI +MI) rEZFEH;L2 TEZ+BnHi IB3
ret1, Vet1+ In.T, rent 2nY  d retirenr se
ernotius Atque in hoc uno via prioram omnesque Tabulae Waleisianc, e ocentis interpolaholibus
confinentur. nec refert utrum Y et n st integri fracti, an crracionars
Modo et sit rationalis rateger. poust
, 1. 23,  ad  12
and naprolateserale
teri et B Letit read tera BC
=2 resse  ouo qstrobalio succedit
  1+2 35
rpr simbliser ergo investigandiam ubi duae te dignitales ub a sibi adduntur
t prellieai pondum hic habemus casum, ubi potentia minor sex conentis detrahitur a minor
indsim alta sit te L p  sibla 4. 3
= L4 + 6 - 4 + 1 3. 6. 9. 12 et 5- 2 et n impar
ium, uom, von et sq ud en: rt I 
si e -   , et fit 2
si n = 1: fil seu M- 3 fit
onis t   item ubi detractiones vel adiitiones sunt recipiocorum.
2  d N, 12. 3us ad e = s, XB dx
(1 - X1X dx -
e
Cpruitter sx. X M = ett erepravi exirmasa
 spo nei
+ = 2. + = = 2. 4 L -3 + 2 - 1 - 24. 6 ralifer (X- X d
 X  in =
quasismuz sit n
ex partibustribus.
demqus perjendum esset ad compositum
vxe YX- X ax dat posito X Jgy hat 2yy Si- ist X y sed et
gituo maa es
gYt alia facta ex vel factum ex progressio vel factptimorum, quae finiatur
quae exprimat fadum continuorum, 1. 2. 3. 4. 5 etc usque ad , si e sit numerus integer; sed abeat
haec in nostes continentur
st
= be + C_. 5 = e. ent seu L + ar e = ent sit bsegbh+ ce-c = se. f ahe -h. lu 1s C 2G et bboc-
in terminos, in finitos di e
sit fractus vel sur
quod si foSiet B ex b. debet autam besse posse = 1, C
pva
bh+h +sshf
pursus bes cerea
is s f bt e s h+ = L
’eli eco e   
se +bt ce C b miojam
5X2)  s = b. e
prodit ex bs ee, quod nuspum loclitur. vert
 
eutt
X -ax- ex
_ P. ert. 62  e3+6
ser X.X = x - 1X er 
XX = X. ex B et 
Bixp5= X. ex eses en
(e 1+ en (ett 1- n
(X - X = X - 2XX 2X
1i 2 X - X = X - XX +X Xh
X. X = X . X r. X X -. X X
 ren 2BItRFI 2EI
 c= f -bf =
etis =  c-0 it
nitatum progessus augo
eom quo erratum