# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/1060/text
# Catalogue record: 1060 — [Aufz. zur Logarithmenrechnung und zur Kettenlinie]
# Incipit: β = 1/2 - 1/[2.3] + 1/[2.3.4] - 1/[2.3.4.5] + 1/[2.3.4.5.6] -
# Date: 1690-06
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1060&katnr=58610
# Work: https://leibnizlegible.com/work/00068056
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 11
# Folios: Bl. 3–4 (from the shelfmark LH 35, 6, 11 Bl. 3-4): 4 pages, canvases 5–8, page ids 00068056:0005 to 00068056:0008
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068056&page=5
# Lines: 328 recognised on 4 of 4 pages, mean confidence 0.74
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 3r — 00068056:0005
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 4v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068056/jpgs/default/00000005.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 154 lines, status machine
3 = 2 = 13
23.4 2.345 2345. 6 2.3. 4. 5.67
L = 90.50000000000000000000000
L = 0. 1666666666666666666 6666
= 0.04166666666666666656666
245 = 0.0083 3333283339 333333333
dE8 88888 8888
L 4.5. 6 = 0. 001 3 8888885.
13. 2.5.6.7 = 0. 0001 984126,9
=, 0.0000 2480158
23. 4567.8
2.3. 4. 5.b. 7. 8. 
velo minus quam
10000090000
+G
-0.000000000V1605
3= +0.3690794394(2632
(V1 24 234.5
 0. 17520119348242
0. 175201193498477
= 2+ = +  +, 11 555 1
1
ex
h.3 23,4. 5  2.3. 45. 7 Y 2.3. 4. 30 1. J. 9 2ete11.
00001841269
00000627
00000
00
D. 17520119.
6
54308003271
718
c
ne bq2 dB L10838
282180171828182619845
23.4 5. 6.7, 9 = 2345. b. 1. 8.9 2ete 10 hetei =
24F
asesie
0. 16.66666b. 6 6b.0V
000
3
2.71828161d232
12 c4209aqac
000000000208763
+0. 54. 3080632924 70
+0. 1252011434984
9. 71 828182642320]0
2. 00000000160000]2
 + 23 4+ 21, +5. (2 1 4 5b 1, 456, (281826423C6)
15. 4
2.7182818264) 2b B
2.718281826
idem 2. 7182818 etc. prodibit, si dividamus 1. 00000CC per o36787 et.
2. Ptc. 12
1.0000
4ZY6
1.0000 (367
2. 7182 28 p15 = 3 = 060646 = 28
Se 13.5 = 4-17B172
223.3 = 27453071
60
33
19
d B
22
5. 5. = 6- 1264 264L_ 20.
6i5 =
5.5 = 8-
E12
(0666009 6B0000000000000000000=27
83647443422 in giu. propetsne 11). une isica
By gg4
X 36.73
60
56f208767
A
= 0000000 02505 21083854417187750521
23et2. 3 = 0. 00000000016 0590438
3= +0. 36787943923361
+0.00000000020876
3
000000006001605
f  1
0. 3678H
qcet
ex 5036787943944632
858906525,573
2. 3 Ct12 =0,0000000B,20976715698
0.0000248615873
32 2 262439
+ 1
RL
et error est mino deficit
30158730158730158
L+ 1, 4 = 3.3,4. 5. 6 =2. 3.9 5. 6. 78 = 2.34. 5b. 18. 10
0. 5000000000000
0. 00 1. 3. 8. Y8
99002755
est
-6. 1752011934824 3
e
18158906525157
1922398
2.3. et14 = 0.00000000081 1 ege
L
lC
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41 269921269841269
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-0.60000 276573 1922
23. 45. 678. 9101000000027557:
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0. 04 16 6r66666 6.66
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c
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aliaa
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138338712
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13618

## Folio 3v — 00068056:0006
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 4r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068056/jpgs/default/00000006.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 84 lines, status machine
WN 2N 2 qH
7V 8 9
1
1
e
18 1 -1 -0
∞  0 
O
aad Ce X 1 16 ∞
36,7879 = 1N. L
9 271. 8281 = gN9L
308.6160
WNc  pr. 1 54. 3080. 4x mery roc
F
247, 2181
8 211. 7000
258. 9181
2MC. 81BC+ 12 9. 45 90
3 60, 6550
164. 3721
225. 5251.
2113 C- 7ayC. t3G
qu
 Xx
17. 9800
6 1 28. 4005
206. 280,
L
+540
(64. 7295
6. 381E
macababedt GX. C4∞Zi (51. 8E 81
x
1000000
5 1000000
2000000
1090000+50.
722
5NSL vel 5N5C = 1. = 1. 00000 eH
INIL = (3 = 0. 367879 etc. )Hoc funda
9NgL = ) =2.718281 etcS mentatia
3N3L =NiLin 5ASL = D 50b53OCK
4N4L = Y3Nm SHGL - 0. 77800 etC
2N2L = S3NL im 1N,L =047218I et
7NIL = 1SFLingr9 L = 1. 648721 et
8NBL = LINILin gN9t = 217000a.
b45L = 15 N5 L in N7 L = 1284005 etc
in figura nosera lineae Calenaria ( β cadit
supra T. posita AR = OA Nam seu Cd (Bp OF Rem si probo
46) β= OD + (3β. sed CB =AM = BC nostro in casu = y. et n seu arcus = 1. jam
+i
s. 2,  + 5,4.1-
3. 6 2
l  su y =  n - = n = 2 n - Y 5. n + 35 1 - 53
jam si n = 1. fit y = 1 - + + Z -2 et. porra 281
a
1152
1. 3.5.7.9
1
1. 3.5. 7.9. 11 n3
pono (D = y et OBCB
( (= e si A(= OR, A) = S2. si AR = OA = 1 fit 4C β = yt S2, et Oβ- y+ 12
comparemus Oβcum C)T, seu cum OB - BT seu DOB - BC (non in calu hoc. BC = BY) seu cum 12-y
seu compatumus see y+ N2,:4 cum 2-ysseu t 4yum y + t2 am 412 -4y, seu
+0 in fit  14 141 7: 1690
57 cum 3(2. sen  25 yy cum 18 si el faciamus y - - - = + 3-
cujus quadratus multiplicando per 25 prodit 17.  88657 seu 0. 84345238. si
e
2
t
1152 2916 fit
y =e 6g8 37 f C quadratum
08f146216
cujus licet justo minoris quadratum 07249878 et 072498781 divisum
et magit accedet ad posterius, sed umamus minus, nempe o.72448790 id ad huc  e alio
capite eit justo minus, quia sumsimus y =  -  +Z - 3
40 112
+ 35 -63 quod est justo (minus
7157 2816 V
et tamen hoc quadratum nulluplicatum per 25  seu quod ide est mulliplicatur
per 100 et divisum per 4, dat 18. 12 etc. atque ita plus quam 18. Ergo in nostro caasu
2579 est major quam 18 seu 5y p 35.
seu y+ Mr p 4 12-4y, seu 7+ 1B,: 4 p 12-y
seu 0B p cF quod propomebatur

## Folio 4r — 00068056:0007
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 3v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068056/jpgs/default/00000007.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 88 lines, status machine
+
154 01d 10 e 4076182879
s
et
166
4
ad (ar 1001000f0761B
6) A8 6456666
+ 8 88 88
35 = 63
203 = 400080097
1152 2816 25349
20300000600
LBBA_  4
2
26
e
olo 3 tr
20300516∞960.00800978
253A44444
203000070008
A2x B44444
a a 200
L 5
20000
76985376
6
7.
O. 7610279
0.0086097
0. 7bG
: 2
46190256
53888032
57 3095128
e
58.7008
09285384
46. (90256
388562
S B. Ab, A993∞3 376F 14816298259.
34
A A A+ 4 A AA 4944A4V
C8224
200770900070.
11
422
48
I6
a) (4A A86800008A3452
880100800c
XCN X,
0851 462 166
b p
ol1
222243
5926. 293. 3037
1000000000010000
B
249878099118656_= 1812
A4g4
618279(4
76182794
n. d: 3. B. l. 3
. 327. 953
1523.655e
60946232
279
69674
95
45
14 33
1803817492184117
8514621616
8514621 6)6
108772C
851462 1b
0292432
510 8 77296
340584864
4257 3. 1060
60110944d
5
146216
425731090
81189728
987 809911865b
d

## Folio 4v — 00068056:0008
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 3r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068056/jpgs/default/00000008.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 2 lines, status machine
5181 i
agn