# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175906937X:0159
# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0159?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 135, page id 175906937X:0159
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=159
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000159.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.77
# 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.

Undecor
de
 eritt
1b bHC2
0, lec
labsticu
X - hc
ecam P
Clnc
eu
Aicurd
ideogul
Mot
NF O: U A X I O E W H.
major quam l. Sed ee per transpolirionem est x 2 =i M X X D LX3
p+, idcogne x IajOr quam m, _ m X3 ajuS Qua m M ∞ V. Si-
militer pertranspolitionem estx+ -p+ ∞ l∞3 F mmx x, ideoque
xmajor quam p, de px majus quam pr. Praterea per eranspoli-
tionem propolicionis cst L~3 L mmxx F pr ∞ xF, ideoque l x3. L
M X3 + P ∞3 MajuS QuaM XF, ee l. L M. L P MajUS QuAM X. OLaTC
invenimus radicem x aequationis propolitae majorem esse quam
l, m, e P, at minorem quam l. L m- L. p. Denique per transpoli-
tionem elt x ∞ lx3 Lmm xx + pr, ideoque xt majus quain l ∞3 +
mmxx, _ xx majus quam la L mm. Aequi demonstracum est (u-
periusamajorem esle quam h ac proinde il minus quam lx. MuI-
cdisitur masis xx majus erit quam II. L m m, ec x major quam
VII. Lmm. Non distimiliratione demonstrabitur, quod x Ma-
jor est quam VV 1 + p, VV m + P, _VV mmpP + P.
Prop. 4. X t - - V ∞ 3 -] M M X ∞ X - p+ ∞ O.
Pertranspolicionem est xr- L l X3 ∞ pr =mmx x, ideo que mm
majuS quam XX, X  majus quam v. Similiter est xr. L m M X X ∞
p+ - l∞3, dC per consequens p major quam x, e PPX N IajuS
quam xt, ec llpp majus quam lx3. Sed perrranspolitionem pro-
polucionis elt etiam xt L l ∞3 + MM X X ∞ PF. JuacCPP XX L IP X X
LMMXX majuS erit quam pr, e x x majus quat pp. Y Ip. L mmo de
x major quam V 
pp. = Ip L mm. AL vero existente xt L l~3 1
mm Xx ∞ pF, eric quoque pr majus quam lx3, ideoque, majus
quam x3, e V C.  majus quamv. Inventaigitur est radix X X-
pa
quationis proposica major quam V pp. F Ip. L mmi aeminor quam
m. V C. , e P.
Crop. 5. Xt mat X3MMX X 1.
es transpolirionem eA mmxx L pr ∞ lx3 = v dCDsCIId