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# Piece: https://leibnizlegible.com/api/records/27893/text
# Catalogue record: 27893 — [De discerptionibus]
# Incipit: Uniscerptiones (1) 1
# Date: 1676
# Other printings: Knobloch, Kombinatorik 1976, 266-269
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=27893&katnr=56634
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 169–170 (from the shelfmark LH 35, 14, 1 Bl. 169-170 (=41759)): 4 pages, canvases 337–340, page ids 00068201:0337 to 00068201:0340
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=337
# Lines: 223 recognised on 4 of 4 pages, mean confidence 0.71
# 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 169r — 00068201:0337
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 170v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000337.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 25 lines, status machine
Unisecipsiones (1 1 (2) 1+ (5) 11. (4) 11. 1.1 C1
Biscerptianes. (1 O. (2.)+.
niscerptiones (1) 1. (2)2. (3). 3. (4). 4 ek.
iscerptiones (1) O (2) 1. 1. (3)2. 1 (4)
3. 1, 2. 2 (5)4. 1,3.2
5. 1, 452, 3. 3 (7) 6. 1, 5. 2, 4. 3, e ere
Triscerptiones. (1)0. (2)0, (3) 1. 1. 1 (4) 2. 1.1 (5)3. 11, 2. 2. 1
(6). 4. 113 3. 2. 1; 2.2.2. (7) 5. 1.; 4. 21, 3. 3. 1,3. 2. 2, 8
8) 6. 1155. 21; 4. 3. 194. 22; 3.3.2; (ansic. 64 1, 5. 2. 194. 3.1; 42. 2 2L
9
bd ut 3 sit majuscila effici
non ut, quia in bisceratro
 7. 2.1, 6. 2. 1; 5. 3. 1, 5. 2.2; 4. 41, 1. 3.2,; 3. 3.3
nibus residun E occurrua
l et. 2
a
31
2122
2 ep
a ab ab ab abc. abeadenc en
nin perpl
biscerptiones
iscerptio nes
itaque nrumeius formarum est idem cum
numero discerptionum

## Folio 169v — 00068201:0338
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000338.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 72 lines, status machine
s.
rr
, I= p=
invenige bielectiones
rielectiones, eu
abC divisibile per
a
e
1 1 (2
IF
X
(E IF pi B 1E
D JE
Ll+
1=
I2
 
a
d
e
1F ex
e c
u
 e
+ ∞e- = F
=E X
 ExS
 11
Ebielectiones a b in at b+c  abac E1.
b +aC + bb + bc. et hac a in
F i E
2F.
puti
aa bb ab ac dis untelectiones apbsc
a in a+b+C + b in bFc, etc
2
u
=
 EdGC
2
a
5 W p1 =
C
1
d
 = -  = d 1
+ Y, 1
 F ∞
Restmet adhrce
C
s5 F
C= 0
3
22(2
merectines: a in a + ab + ac + bb + bc ) s seu at abra ct ab +, ab c. b) +bC
b in
bb + bc
sunt trielectiones
quadrcelectiones a+ a b + ac + ab + abc + ab + abc F b  B3C
quimelectionas +ab+ C + ab + abet ab + ab c + ab + ab b + b
seuielectio abc
dd
a
dc3
Id
e
e
553
8 e c
 
e
unveshes H auc s

## Folio 170r — 00068201:0339
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000339.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
Jala. d.
1 aa
a la
abiaa
3+1 b b. ab. ab. ab
V3+1 b b ab. ab. ab
si X respondent ad b
(X) et
ad C
fiet (x +I n = (X)
an
3tusA +C cctaetaCttberabeta be +2b +bEtaCtabe ab
Nu
 L
en
a
l. n n
am ab c dete
 b. I= m IFI + R l+ met 1+ p limintu
1+ belm lma
m + mn
n
seu x nX = d ()
13. F2. 3C (C + aCtaC+ a C+ bC+ ab C+ abc + abC + bE + ab E + ab C + abC
F
ab
=
In
 itLB L Bi +L+ itImN- F + l+ it Lm + 1+ L + Et LM N
l+ Im + lmn + lmns
m ln Imp
est
Ix Lnp
m map
mp
np
et
ti
 
X+ 1+ l ip itm  1+n  1+ p
sit a bc 4O = 1+3. 1+2. 1+1 - 1 = 24 -1 = 25
Hinc numerus partium prrttum abC est O seu  1Z. I2 EFI -,
divisorum
linoh
et untius
Et numerus divisorum numeri abc est Ori seu est 1t3(er 1t2 per 1F 124
4312
(C Numerus divisctum numeri ab ed est, 6. 5. 4. 3 = 360.
quae consentiunt cum numeris shotemi pag. 379
ictionum Miscllanearum, sed non cognoral+D
Gecrema tam pulchium brevs et generalet
ususque est dia illa prolixiore additionis videantur lagen
et conferantur quonschoteniu habet de mebi datus electune
vel numceri ce dcclam  divisarum umtaludine habentibus
C
s

## Folio 170v — 00068201:0340
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 169r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000340.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 70 lines, status machine
Res
Etemnes electiones data multitudine rerum
a 
iores
b. ab, E,2
C ac bc. ab A 4
F d. ad. bd abd. cd. acd. bcd. abcd
a a d
et
ubi patet seuem seenlinam equentem
estinere praecedentes omnessumtate
auctas. si autem sit serres
l M n p, qlibet X
x
(X
sit xSX + 1 = (X). adeeque e fiet X = (d X). unde
patet esse seriem progressionis eometricae.
b.ab. pb a. ba2
(A
Va
sa aa
Sa aa. a3
ab ab aeb
2 Jr est e
babab ab
C AbCbc abc abc 2
Numerus eleorioum ex a b c,d abc. 
ob Raa prodeunt tres forme a, a, ale;
ob C prodit 3+3+ 1+) ob C prodit 3. 3+1, 3+3+
st
a
C ae ac ac bc abc abc abe bc ale ab. b2. abc a a bE b
b ab ab ab b ab ab ab
at 
L 1+(1) 1+C9 1C a
1+()
 3
ob b prodit 3+1 rursus ob b prodit 31, et
seu sic
a
1+ 1+(1) + (1) 1+ 1H(1) + 1+ D+ (1) + (1) + (1)
Il 113) c+ 1+ (1) +()) 1+ 1X(9 Y 1+ 1 + () A(1) + (1)
21C)1 1HC= (C))1 +1+ (1C1) + 1+1+ (1) + (2 (D) + ((1) six t) lti
si omnes unitales vt (+ (1) significat mihi se de primon
u
at 1+bC1) )
Uunitatem additam (2(1) secundam. etl. I1 X 1X C C1) a it 1t CC) do oCo
si omnes additae mutates valeant aliquid, tunc
Modeunt terminus progessionis duplae, sed solces non ontent quotiens
nonvalet additific unitas seu est nihilo aequallis quotres
 non adest nova res Omnis unitas valens repelilus
progressione cieome Vrica dupla sic ipsa I prima b
Non ila.
in secundo occunit simel in tertio bis
in quarto quater eh. a
1 2
D
34 5
0
6
a aa
si ergo adsit aaa bbc habemus sist 1 L. 11 C a aa aa a
2
e
lum es
a16
32. + 7 + 1 =40
utu paneus
e
Non ita