# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068022:0032
# Permalink to this reading: https://leibnizlegible.com/page/00068022:0032?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 16v, page id 00068022:0032
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 17r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068022&page=32
# Source image: https://digitale-sammlungen.gwlb.de/content/00068022/jpgs/default/00000032.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 95 lines, status machine
# Lines: 95 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

eiiem reapse non esse siniem orrationalium, sed senen
rationalium, per quandam rationalem constantem SF di
visam, nam ex fa + y y riyB1 ( - 2 f3 -2f7 (3.
per +f multiplicata, radix extrahi potest, fiet enim: ejus radix.
tractent ihil
etgi in sunis
ciclunenum
f + ya 9+ B,
Nondum ergo met hodum video, per
quam summae niri possint inatio
vosers haec. smatium simplicium seu naturalium
273
4,5
arc. seu 
series ommin
y est c.
1
anplitibunire
stigausis sed jom
V 2y+I
. Momentum eorum ex
y+ 1 est L. momentum autem ex y + 1, a momento ex y.
differt fign serie in y. Seu serie cylindro. Differentia ergo
inter A idem moment set series omnium F excedit
senem omnium at
maxima serierum. 
maxima L  seriei omnium 1
v
Ergo
Eadem methodo omnium habetur dimensio quae sunt ejusmodi
vig.
D. Nam cylinder eorum ex y est +
y yes y
Cylinder eorum ex V +2. est
ex y +2. est 
y y+1 1
&et
momentum
yoy1
Nam cylinder corum ex Y est
est VH, y +2. Colin
ergo uptus t cytinde quae duo momenta
differunt suplo serici cylindio: differunt vero et recta cognite
seu primo tenmino seriei gega, qui non continetur in terminis
seriei yryer, id est primo.
momentum ex y + 1
est
Sed et praeterea idem mo
Quod momentum a priors
ytr
ex y +2, dif cedit etia figurae cylindio simplici. Quem in
venimus.
Datur vera et momentum ex y +2 absolute seu
Y yCyn
 seu u
_ 1, 3
habetur seriet:
et
y y+2
series
Ergo datur et series omniumi
2, 4
1
3,5 4, 6
 a
Datur ver  et senes
y v y13βB
V,ver
etc. pr. 1. pore β.
5,7
y+β
V, vep, yrest , 7r2
et seues 1
90
168
103
Ex hac autem inventarusus eodem ratiocinandi modo, datur) yap sena io 
d do Dabitur per datas 3. et 1
Ex data 4 eodem quo modo quo 5 dabitur et series.
verie,  yr3B  1, 2, 4 235 34,8
Gineraliter ego dici potest, omnes series quarum nmmeratores sune
30 i
constantes, num nominatorum vero factores starithmetice excedetit perpetua progressio
ne factores nominatoris fractionis praecedentis, esse summabiles. Quid ergo in
oc serie 3
35 99
mpcord Broumker dedirsumma hujus seriei:
646.
9 11
V B VrB,yeb3. C feriei
Y, t B yAB
dabitur ergo et
1 3,4 2, 45 3, 5,6 4 52
+0
Esta aus sout in pursat uum otpussera