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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 194r, page id 00068195:0387
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=387
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Hacaccuralius vestiganda
cujus terminus,
Sit Fractionum summandarum senies (
e
exyy + myt nn
sit seriei summatricis terminus . et sit dy = d. itaque differentiando
ey+,
fiet:  + + -
eys eyred seu ted
ceyy + eed 9 + effd
1eff.
54
= D, set
porro () multiplicetur per e D seu per ed. et sit 1)d = d. et fiet
ed
cegy+ eedy + efd
cegus + cemus +eenn
= 4
+2cf0 4 f4
unde comparando siet ed + 21+ = em, seu f = L em = L ed et f+ = e, m - 2md q
rursus etsd +s = eenn. Ergo  edm = 1 ed + m- md +. est dd = et nn
in datu
ita evanescit e, et sit L mm - Ldd = nn seu mm = 4 nn + dd seu dd - nn tu
unde patet etiam datis in et n, qualo
tebe
jacu sniapta na quarr seu sit
Retque
sit jam GV+ q+ rr  et fiat v = y + p.
yy + 2p y + pp et debet esse ( Ep+q = 4 nn + dd = 4 ppt aqpu + arr + dd
seu (a pp  4 p4) + 4q = () pD + (4 q p + 4 rr + dd ita nil b
+ 9 y + qp
+ YI
a=
lucramur
ergodu d
it ergo  L WD + qu +rra siat hY + p = V (et do - hdu = d
misus
ita variatur ipsa diffe
et fiet: hhyu + 2hpy+ pp quodividatur per hh et fiet yy + 2Py +(AP
+9h y+ qp
11
 hy 79p
rebet esse: B ip + q = 4 xp tqp 1Nr  taudd ethi
 hh
ergo 4hupp + 4 pghh + hb q = 4 pp + +qp + 4rr + dd sit
tk
th
h = 2 fiet  1pp + 12p9 + 499 = 4 1r. + dd. se 3 prt 3pa t4q = rr + 4dd
quae cerras impossibilis
pt h=  firt (16p B + 16p 9 + 49q = 2pp (3) pp + Cd qp + 32rY + do
1 16
16
seu pp + p9 + 449 = 449- 5 99 -  Le 
fit app +4gP + sit p 16 p p + 169p + +q = 4 ps   ZL 32rr - dd
a
seu 4p + 24 =  app 1899 - 32rr - dd. seu p =  894- 3rrr- dd- 
sit ergo  v = 2y +  899 - 22 rr - dd +  4
videtur his successum aliquempondere
nuncericarum
nisi sit error intcal culo, ut liceat serierum
timmas eec nmeri investigare
sit 1. rn  . fiat v = hy + p de =  1 fiet dy = 1: h - porro
Ergo ex ve fit: th gy + 2hp y 4 pp dividatur per  ha, fiet gu + 2p. h y = pB. h
ebet esse nim = 4 un 4 du seu mai = + un + 1: th hoc loco, ideo gy + my + nn
fiet 4 pp: th = 4 pp: hh + 1: tih. sed ita _ 1: s foret infinite parva, quod
absurdum sit. 1: v0 +1  et v - hy+ p. ub ante fiet yy + 2p. h y = ppitihi
my
un
sit app: hG = 4 psi: hh + 4 a +  1: hh  seu a = = 1. 4hh seu h =  it-a
Hembrevus resumta formula eegu + eodus + eff fiat ey= tiv  her
12 T2 eff y +f4
et fet rrcico +eribco + d b
+ ed Y co + ed
+2 ff Y co +254
ner P. edt is
cd + 4
st formula data in qua deo = 1 = ed: Y
haec famula  Coco + hed + KK. multipl cetur per
fet rrcoco + retco + rrkK, fiet
494
2it + ed + 2f = rh et  4 + ed  4 2H V = YYKK
seum FS s = 17 = 4 bi + B5 + 4sL,: th rh+1 =  P + 2  
hal. n
seu 4. k LV Y a 92 EXsi + fAL = hh H +ohtit( 4 A atous Ed ilta
e
v