# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0011
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0011?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 6r, page id 00068196:0011
# 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.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=11
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000011.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 82 lines, status machine
# Lines: 82 recognised, mean confidence 0.86
# 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.

ubi signo diffirunt duo membra, quae unum habent factore commutm, seu notam
posteriorem eodem loco. Et quodem omnes pro formandis membris adsunt combination
ba tantum lege semata, ut in quovis membro reperiatur quaevis ut quodvis membrum
sit trificum ( seu brium factorum) et in quovis membro quaevis nota tam prior
quam posterior orepeniatur.
porro harum quantitatum numeris fictitiis bi-notalibus designatarum,
quaevis quan multiplicatur per 1 habens notum posteriorem I, multiplicatur per 100
et quia in quovis membro est una habens notam posteriorem 1, ideo omnia  membra
explicata dividentur per 100, et 100, quia non nisa semel est in quovis membro
evanescet, eodem modo evanescent hic 290, et 300 sed hoc praevideri
poterat, nam adhibuimus solum 100, 200, 300, ut ipleui ubique eadem esset maltitudo
numerorum fictitiorum ideo eoanescunt cum p, q.V
+10. 2132 = (1  +12
31232
LV2. 112. 113. 112. 123. 212, 217, 223.323
+112. 1237212, +112. 1231313, 4212. 232123
312.323
(- 112. 113. 123 212. 22. 22. 213,223, 323
+212. 2237113, +112. 1137323- 7 112. 12. 113133
9 -31. 323
212. 213
112. 223
) 2312. 313
10.2231 =
Sed quia is calculus prolixior, et videmur abundare arbitruriis, ptupideo pro contrahenda aequatione 14
8112. 10∞ p. - 312.380)
10Or = 1L = 31
100p 312 113
123,100p = 323. 3001
1e0p 33
nam fit
ponatur 113. 123= 313. 323. Et procontiahenda aequatione 16 ponatur 112. 113 = 312. 313. et fiet
312: 112 = 113:313 =323: 123. Unde ex aequ. 14 fit 300r: 300p = 313. 13 et ex aqu. 18 similiter
fiet 300r: 100p = 31X0113. Itaque hae duae aequatiores 1g et 18 hac duplici suppositu
ad unam. Revera ergo non nis unam hypothesui consumlimus. Superestae quatio 10seri qua pro
300r substituamus (213: 112) 100p, et pro 312substituamus (13, 313) 112 et pro 323 substituamus (113: 313)123
itaque ex aequ. 20 fiet (multiplicatis omnibues per 113. 315) fiet
+113 33 2t. 232 uL 100p + 1 aIZ  32 2 uE. 100.
-112. H13. H3 123
1(3N212. 223.3132112 1p
-112. (113 13. 1 23C
Fil2. 223
1sL. 13. 13, 1
f113. 100p
13B. 222
   tur 127 313313 Z(I ZEt 2009
113. 113.l13, 123
sed resumamus securioris calculi causa es ex aq. 30 faciamus
+ 1. 193. 313 3( 0op = . in n G e 213. 209
seu multiplicatis omnibus per 13. 313. 313
112. 1232 313,. 313, 313.313.100p FHIX 123. 313. B132 113. 213. 2009
+212. 223. 313.3132113. 113 100p +
2. 113. 113. 123 yihi Zt
=112. 113. 113. 123. quae aequatio dividi non potest, nisi coefficiens ipsius dividipossit per
ipsum autem ee s coefficiens est, 313. 3e3 (113H,. 212. 223 ta sed hoc video non litidefier
si esset jam H3 H) 2(3. 33. sera divisis opni omnibus per 13. 113. 113. 3 fiere
+2 +AAS oOp =1Z)  2. 209 adeoque 123 = H~. Ergo 312~323
Et quia 13 H3 = 313. 313 fiet etiam H12H2 = 312. 3R et 123. KG= 323.323
ItL 13
H2 123
itaque conjungendo valores ex rgo primum et itium ipsius ak, ex aequationibus V et 12
fiet 100 100 pp - ab  700 g0 rr-ad. et pro 300300rr substituendo valorem
fieret 100, roopp - ab = (313. 313 : 117 1) 10. 10pP = ad, id est 1 roOpp- ab - 100. 10 pp - ac
quod non licet. Ergo non licet contrahere aequationem C faciendo H3. 113 = 313. 313
+212. 223. 113. 113 +112. 123. 113. 113) 100( = (1. (20 +113. 1137112. 113. 123,213,2009
-113. 113
ium aequatiop duccedit ine ieq a  nova determinatione,
recimus.
seu aequatio
= 212-223. 113.113
112. 123. 113. 113
dividi potest per 4 213. 313 = 113 113. Veum non licet facera 313. 313 =113. 113. nam fiere
neque adeo ponendo 113. I13 = 3(3. 313, quicquam proarbitrio
etiam 112 112 = 312. 312, et 113. 123 = 32 3. 323. Unde conferendo duos valores ipsius ak, primum etterti
ex 2gg. 10t Z, fieret 1 100pp - ab = 300. 300rr -ad. sed posito 113113 = 313. 313 fit 100.10pp = 300. 300rY
ergofiecet ab ab quod o non licet. Itaque aequatio O dividenda est per 313.313 - 113. 113, et fiet
EIL ECG. 313.313 (313.313-113. 113) +112. 123 (31373+11313) (313313 113 13
3100p = 112. 123. 113. 213. 2009 (313.513- 113. 113) actoque aquationem C dividendo per 313. 313- 113. 1
fiet 112. 123 (113. 113 +313. 313)=212. 23. 313.313,: 112. 113, 123. 212 -,2009: 100p
ubisi faceremus 112. 124 = 212 (23 fieret 113. 43 = 2009: 100p. ita revera hactenus duo tantum pro
bitrio assumsimus
2133(313313- 113. 43)