# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068195:0182
# Permalink to this reading: https://leibnizlegible.com/page/00068195:0182?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 91v, page id 00068195:0182
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 90r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=182
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000182.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 recognised, mean confidence 0.76
# 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.

l+ m = -Y Im = = q.7
 M3
x+l+ m =0
fiet M = - q. 3l
 et 27l + 27Y13 -9= 0 seu 16+ rl - 1=
fint l’+ M = Y
X = - l, m X = - l m FImX, seu X lmX + 
jam X+ gX +r =o fit qu lm. 3 et r 1= m lm = - 9: 3
1+m = Y = lA , B = Y. fiat 2716 - 27r12- 90 seu fiet
2
6- rl - _ =0 1+m.
Pulem Hypothesin sic faciendam ut omne sit non nisi
per 1 m, erc. fine rationale excepto max. seu totali
= X - dm X + lmin XX +. lmap X + lan lm. b
(10
Hinc si 15 contnent aliquod rationalem
necesse est e valorem aliquid rationare
conficere; quod si lnqo ema lmup nihil
deberent. Nam cum  X ex nostra hypothesi, necesse est id solum quod est
in XS rationale, Equari ipsi 15 ut supposuimm sit Im = B Emn - Imup- S
.
D
5
3B8
3yP
eIS
3
Hic ex hypothesi quod rationale in 10 sumi debet ex eo quo rationale est
et in dd XX, et in (5. posito omnia praeter 8 esse nrationalia
sed in fallor res meliis deducitur priore mores ex 
+ 23C
+B3p,
+ βd
u
et in SX
 X= P = Om + Vmm = le mn + l’M + l mun = lMap + ar Cminn. mmnpi
p
=lm + Vmn + B mnn + Cm ap + Pmmnnp + FMA ( m n+ lmnp + l’Nn’H mnp i
m
continerent rationale, etiam ta saltem line tm. lun aliquid rationple confaere
Urum
= X + Bx + yX + ( X + BY X + (3  B X + B2xx +  X +
+M nP + P mnp lX  ubi infaller statum patet in solo 
10 et ln laere ravale quod est in r quia lmnp hic cum aliis non combinatur
sed videndum an secundum hanc hypothesin posito immp esse rationalem conscn
+
tiaut quae du rationalia quae ducuntur ex l = x + BXd etc. Et quae ducuntur
d
ex (10 = (d Bm etc. Nam in priore occurrit B3 cortmens aliquid rationale est
autem B= composita ex Cm  n B et ita resoloendo ad modim ta 1. patet
quad ratiorale in B, non posse secund hn rothesu assumtam esse nisi in BM ita
pidebimus auliceat facere _ d rationalem, seu an ita habeatur consensus.
Un
anes si liceat assamemus prd pro rationali incerta, quae demutur
altinia aequotione deferminabitur modo ibi non occurgal
20
aqualis difficultate cum quaesila, seu 8 +.. d + et
et aequalio
es ois in itio et quiulo gradu prius bene excilcenda est
ex ab ab ab etc. possunt haberi per B, V, S, etc. sed i non tamen plane sine x simplice
est
abC
2aabc7 = 2abX
albc
atcC
jane XX haberi potest per X et aa ab= B aa bb + 2aabc + 2abcd
Hinc mo licut facere ab et abc, et = datis quia sic con passent haberi ab, atE, et sine X
t