# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/35151/text
# Catalogue record: 35151 — [Geldrechnungen]
# Date: 1673
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=35151&katnr=39660
# Work: https://leibnizlegible.com/work/00068195
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folios: Bl. 131–132r (from the shelfmark LH 35, 12, 2 Bl. 131-132r° (=39659;39661)): 3 pages, canvases 261–263, page ids 00068195:0261 to 00068195:0263
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=261
# Lines: 195 recognised on 3 of 3 pages, mean confidence 0.73
# 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 131r — 00068195:0261
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 132v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000261.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 72 lines, status machine
ac + b
b
e
bd +c
Ebc sa cd cd
bi ac+b
cd vc Xd
acd + bd + bc
bcd
In tali ergo casu, cum fractiones summendo sunt, q ita comparatae, ut
se nommator praecedentis sit numerator antecdentis, fiat fractio, cujus
nominator, sit factus ex omnibus terminis demtoprimo numerator compositus
ex tot terminis quot sunt fractiones, et quaelibet pars ex omnibus terminis ita
it
ita componato, ita ut prima constet ex omnibus terminis, demto se secundo, secunda
ex omnibus terminis demto tertio, et ita porro. ita terninus pri pars prima numeralori
differet a nominatores quod loco termini 2di, habet primum, (quo nominator caret)
pars 2da Ao, quod loco termini 3tii habebit idum C.
dam ut talia: acd +bd + bc  4 + h +E
d
bcd
breoder symnes ita orinor agendum erit: differentia imer acd+  b
uud sic potius; nominator habet ses demito primo, primus numerator habet oes
demto, ido reliquinumeratores habent suum terminum bis, et carent praxime
ante adentet proxime sequente. differentia inter acd-
summam ita investigabimus: acd + b d = ac + bd
bd + bc = bd +E b
Hini apparet si b. sit media proportionalis inter a et c. vel C inbib et d. tunc
ad summam inundam, tantum primum terminum multiplicari possi per numerum termonorum
et facto velut numeratori subscribi posse nominatorem factum ex omnibus terminis
dento primo v.g. acd + b d + b facilius perveniri posse, quia ac = b et bd=
1 2. 4. 8. 16. et sit  q l B ibi mendi poterd oes temminos esse
Quid verd si temini siil Arithmeliae proportionales, ita stabit:
a + 2aX
1+37
act, t a a atir, 4 at or  atr, atn aror, f an acin atx
a + 2 X + 3aX +6 aX
a lax + ran = 3a X + 3X  6aX =
= a2+ 3X +5AX + 7 ax
atx a + 2X a+ 3X. (bd) arxat
Ar  + = +  + . sintque a. b. c. d. e progressionis arihm etiae.
a +  = 4t +b (B huc aequita ulilis observatu ad reduchines) i 
B+C
ee
a +X.
a +b, 1 ab + bc + ac  + - abe + abd 1acd +bed. Et (hoc schema unversalcest
ab NC abc.
abcd
in omnium fractionum additione, in quibus Numerator Unitas. Cum jam numeri su pr termni
sint progressionis Arithmetuae, sunto a = a. b- a + IX c = a + x d = a + 3x ex
1+ = = a + b = a + a +X 2a +X
ab
a aIX ara
+
1 E
L. abtbetac. arax + a + Er FSax F a trax (3 a 1 6ax 1 2
abc
quod si jam X- a. erit 3a X Ha et si a = 1. erit 1
ad + 3a X F 2aX 9 a +3aX134
math. X1B 2 131
ac + b +, bd + c acd +bcd + +b d tbC-
cd
DCd
acd +bd + bc
bca
Ca a a +2K =
a + 2aX
abc a aFL atEs
= a + aX  a + 2X.
+ a X + 24
F ax
30

## Folio 131v — 00068195:0262
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 132r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000262.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
2o(20
CZ+
50 
44 16 50)25
24.
24 12
250+24 274
24 _ 120
+X 2
2.
qu
120
25 + 1
12 F.5
125 + 12 137
60  60
11 96
a ia Ba a sa
5
it rto 1Bo ta 1o
10
240 60 14 12.
14 2.
a:
duasis assantis sequbiamons iu
iat
120
3
n5
(7 psa
720 , E4
120 (1445
siB
5er452 234+ 15+
239+ 234 
nortoiana:
 26id
264
i  l it L - 2 , 1 + e2 +, 1e 1 ( + i
2a
X7 4 X2
pt1 44 +6- 50. + 1 250 + 24- 274
A29 720xab
B)F F. 9 i 2 + 1, 3 + 12
a
1t vi
2X3 = 5+ 2+ 2+X5
d. 129a . 1644 + 120 = 1 b4 ) 2 ~ 24 (h Z f2
120 26
1
 4
e
manet.
nos
1etes q5 er 34b.
1et + 12 +1 1erZ + 13+ 123, 1- 11334 1 24 +14534+1254 + 1
220324
1
20 Eto 60 120
+2,: es+ 2 + 3+ 23 , 1 = 53+ 24 154+ 234, 1 184+ 2551 145 (454 5 45 + -
1128
25345 26.
12 2
gro Cuso  240 + 380 + 14 4+ 120 = no b+ 
425.
240 120 9660
o 60 36
et
11207)
(3) 3ea5o. 
2545~346+2356+2456+ 5456+ 23456 Hac ut sum menus opus graeguiture
r mn β)1ise
eorum seu reductione ad aequalitatem per mutuas compensationes
e3 45 4 2346 = , 2343+ 24, Y   56 = 23
23545 + 2346. = 2345(2) + 2334... + 2556= 23545() + 236 +(2) 254. X...
n + 2456. = () (4) 23+5 + (3) 2341(2) 236 + (1) 256.... +3456 =
(5) (23545+) 234 f(3) 2326. +(2) 2516) (1) 456. .... +23456. =
6) rerae 5+ (5) 22 3 4 + (4) 2e 3Cb + (3) 256+ (2) 4526+ (1) 3560
-20
20
I atset
t
436 560 8120
12o jaqe
100
240
360
ppe
(13) 23 45 +() 54 (3) 23 43 (1) 2345.  e 1
(3) 2545 (2356 (1) 3(456
Arta
(3) 34
23 + 29+ 34 + 23. 4.
la
d
2
vil an
2

## Folio 132r — 00068195:0263
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 131v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000263.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 25 lines, status machine
de 
i e) ds
e a
720
0 5040 25 2 vssop q
st
1680, 420 1 84
12602
nl +
620952
1008 10
840
10
ee -1
b intt
n eta
e15
417
el
=H
0
Es
8
I
lo