# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175906937X:0163
# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0163?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 139, page id 175906937X:0163
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=163
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000163.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.73
# 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.

le i d
eropolta, 
CMINS. DEE
u equaler
2 ln loco
habere
de consta
oY
DA dr
i
racta XGL
quabiur (in.
Ie necellarie
11, de Gt.
Oeud i 1
dC prent
ell.
15 Gu 21
a.
jor qua
2Idcem
1 L1
D ex hul
Inorem et
nulto min
(N + P.
Es
one denio
AE C U A F E O ET W H.
Prop. 4. Xt - L l ∞3 X -. n3 X  pt ∞0.
Pextranspolitionem est xt  L l X3 ∞ p+ = n5 x, ideoque Im2-
jus quam x. Fodem modo est xr L n3 X ∞ p+ = lX3, ac proinde
majus quam x3. Similiter est l∞3 - L n3 X ∞ p+ = x +, _E per COn-
Sequens pmajor quamx, _ p. x majus quam x+, aC lp P a majus
quam lx 3. Sed per cranspolitionem propolitionis est quoque
X= + l ∞3 f B3 ∞ ∞ pF. QuarC P3 X F IPPX L B3 X MajuS CrIE quam
pr, de X Major quam pr. L. Ipp L. n. Et sic inrenta est radix X X
quationis prOPOCIX major quam p, f. Ipp F 153 at minor quâm
m. Y C. ep.
Prop. 5. Xt - lx3 X, + 13 X + p+ ∞0.
Pertransposrionem est n3 ~ - L p, ∞ L X3 = Xuy ideo que l major
quam v. Deinde eA xt - L pr ∞ l∞3 =n3 N, GuarC CFIE X N ajuS
quam7, hoc elt, xmajor quam V =. Sed est quoque at L n3 V
∞lX3 =pF ideo que v3 majus quam7,  n major quam V C. .
Duareinvenimus, quod quaelibet duarum radicum aequationis
propolix necessario major est quam V  de V C. , at minor
Guaim lo
Prop. 6. X t -  IX 3 X - B3 X F p+ ∞O.
Per cranspolitionem eAt xt L pF ∞ n3 ~ - l ∞3, ideoque, m 2-
JuS quam XX, hoc est, _ minor quam V. Deinde eA xt L LX3
∞n N =pr, ideo que xmajor quam . Praeterea eA l X3 L pr ∞
M3 x = XF, _ idcircO n3 ajor quam X3, hOC CA, X INOE QUAMIH.
Eroo invenimus, unam quam que duarum radicum x aequationis
propolica majorem esse quam, at minorem quam V de M.
PrOBo