# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068022:0060
# Permalink to this reading: https://leibnizlegible.com/page/00068022:0060?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 30v, page id 00068022:0060
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 31r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068022&page=60
# Source image: https://digitale-sammlungen.gwlb.de/content/00068022/jpgs/default/00000060.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 98 lines, status machine
# Lines: 98 recognised, mean confidence 0.74
# 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.

fiet. Za
+
+ 8
V
+ Fpga
fiet: ponendo Y() Z+ d, et
et V  Z + ed Z + da
(+  fe . comparanda y + β7
+ 2)ga. L + 2fgad. cum for. 
+ fBd
+ gr a
+ fβga
X
( f
4165 d8
H + 16d f + 8 4fC + f V
F 0, sivi (+164~ (- 9f dB
Uende patet explicationem y per Z1d.
nihil contulisse
+16 d ( ((+ 165 3d)
32 d fy
2
8a15B
4 51
+8df quod est impossibile
=16526d hac ergo methodo solvi
problema non poteste.
si Z Explicassemus per 8 + h, et Z per y + 2hy + ti2, feret.
3
confecendacum y
Uende 9 r 2 4 (+
+ dhy + t
Y
β.. 
(+ 2f94) +gra
+
(+ sega
fB - f2 -. (t B
2 f a
con
4hf - fB
+ a
et g 16h f~ - 8. h f B + f2 . Unde Et his suloribus in
16 av
ultima aequatione collatitia insertis,
fitr:
h + = eh f  (16h f- 8hf B + f.3 +f Bah - fC
~)
seu (+d Bhf2)
+ 8hf B)
6 +g
mula: Ergo ed f + 2fga rs P N = β.
sive 4df 143a + C (, (FB
Ergo g⊓ -4d f s P.
quot valores inserendo in posseeriore collatitia, fit fiet: 6 a
16d f g
(2
6
Y fB - +f B 0 quod est absurium
Scilicet ifga a f, et g a + fBgai
scilicet generaliter: gisi Y ,2fga y s+ g a  aequentur y lV + ma
16534
et sumondo l. er in, quasi coqutos, fier: 
81 fel - f β. e g F
ea
es. +f
+
210- 2frlβ + fr
4a1
quo valore
in postenori collatitia inserto fier: (FI (+ 2f C   A f ma
et deletis caeteris arbitrariis, fit aequatio: (-B  ma. Unde fit ut quando
e
cunque ma abest, fiat Y l β id est fiat progressio driangularis.
posita autem ma adesse, series haberi potent, modo sit ma l- β, et
senec hujus summa haberi poterit.
V + ly + l  samtis l. et B.
-
pro arbitrio sed constantibus et B differentia abscissarum.
Y
itaque seriei hujusmodi.
 quodsi l et B, aequales oitur series Triangularis, si inae-
11 4+C quales, fiet v.g. ponend. l r72. er Br1. fiet:
112+ 4- 1
6
4 +4 + 4-1 9+6+4 -1 16+8+4 -1 25+10 +4 -1
18
in
ad +x1
2
25264
ad 2
c
(+ 2fga V
+ se.
2df2
t5
3 .