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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 14v, page id 00068022:0028
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Ut ergo redeamus ad scopum, quia summa haberi
potest hinus seriei.
27 + 1 = 2 Sy +y
Emret, omendo y  n fit   +y  y +em. seu m + m
ab hac siguo
suad trer
seques ))
itam
Y VCdy + 1 (- y) + m
sive Z 7
sive (2m + 1 + 2m (+ md s
2m
1+ 2m
V mo
1+ am
+ 1 X m
sue Z Y une q um 41
sumtis ergo m numeris tme naturalibus; summa quotcunque irrationalium
hujus naturae haberi potest. Mutando figua in +, fiet
2m +2 m +. 1
2m +1
Ergo s +1 5- 8 +1
sive 7
107
B Vme +
10 + 1
a +1
possunt, Eorum enim summa est: .y
X32 +1 sumuat
8+ 1
majore est auter
mininum y.
Est auter Maximia ext Nclusa, minima inclusa.
Jam YP)
m seu m. fiet dy 
2m 1+ 2m
proxime major ergo y est
minima autem est
1+10
25
seu ergo
13.
Sitem
imA)
m
Ergo in + 2m +1
3e +2m
in quo patet esse errorem.
resumatur res ab ouo:
Si+Em
m
1+2m
- 22
S0+. - 5
Ergo agle y + +y - 2Sy + y
cujus radix
S1
summae horum quatuor irrationelium
Res ob momentum sui resumenda est:
mti
5
aquantur
Ergo m +2m +1
m mam
3+2 m42) 1+2m Stma
+2m +am
7 Z
3 + am + 4m
+2m am
Ergo Z5 P2y+1- 2927
Pone 5 + y   y F0 - 2ym + m fiet: Y 5 m. Quare resumendo.
mer fer: S . - s m
1+ 2m
1+2m
1+2m
Ita A. cum
abseisse sint y ergut quidem progressionis Arithmeticae, nam differunt unitatib
vel minim
ite 1+Z A 5. ordmatae
sed prima earum, non erit unitas, sed 
autem erunt horum abscissarum radices. si im sit 4. Vum eut
2m +1  (= 2  m a 
+2m
1tamtam
- 2(m + m + 2m3 ram eut 
+ 4m +qm
H jam ex hac  quantitate signo affecta potest extrahi vidio
2 m
1+ 2m  1, - 2  m = m
et fiere 
1 + 2m HZ, riets 1 - 2m
ZV.
fiet ergo.
12
+2m
sive a4+2 m-Em;
quod conferentum supenodi Z p, E  1 - 2 syly) sivc 2n
um
) () 1(- 2m C-  m
1
Rusus eror in caleulo
3 + 4u Am