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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 145, page id 175906937X:0169
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=169
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

D0.
xloremas
pajus qui
IaGuco
opoa
am M O
inclaet
verice qua
IC X realiS, C
veric aqu
V MM +
UC X M
equalu
ecRuNO
00.
ellext
A Q U A Y L O N U M.
Prop. 8. Xt -= L X 3 - M M X X - 13 X = p+ ∞O.
Pertranspolitionem est xt = l~ 3 ∞ n X - p =mmx x, id-
Cogne li tuerie x = ∞ lx3, erit x ∞ l, _ ln ∞n X, ec 13 X L pF
∞mMXx 2C proinde BM3 = p + ∞ MM XX, _C X D V Ln3. + p
Unde paree, Situerit l3 V Ins. = pr
mm
mm
 hoc est, Sihabeatur IIm m
∞In3Lp; radicem aequationis provolita Fore aequalem sin-
gulis cerminorum aqualium L de V In3 L pt
min: ac idcirco, substi-
turo in hoc casu in aequatione proposita ralore ipsius. Pr, nempe
UImm - ln iplam esse dirilibilem per x -- l. Quod stueritxt
majus quam. lx3, hoc est, x major quam l, erit quoquens X. L p+
ajuS quam MMXX; e si fuerit lx majus quam x+, hoc cAt,
lmajor quam x, erit _ mmx x majus quam n3 x -L p +. Tam
quandoquidem aequatio propolira est realis, erie x realis de vel
xqualis, velmajor, vel minor quam P. Ouod I Fuerit equalis
velmajor quamp, sicque major quam l, quoniam tunc 13 x L pt
quoque majus est quam mm xx, erit d n x = p. x majus quam
MMXX, de
13 + p7
nn majus quam x. Frgo in hoc calu eriexmajor
quam l, ee minor quam
23 t B3
mm. Duod liautem x minori exi-
Stence quam I, ipa sic aequalis vel major quam p, quoniam er
EunCnx  p minus est quam mmxx, eric limiliter n3 x ( p3 X
13 = p3
minus quam mmxx, e consequenter
um minus quai X
Tgitur in hoc casu erit x minor quam l, de major quam n3 = P:
mm
Ouare univerlalicer apparet, aequationem propolitam non ha-
bere praeter unam radicem realem ipsi laequalem, cum estIlmm
∞ ln3pt; modo quaelibet radicum, sireunam, sirecres ha-
buerie, tuerir semper necessario inter maximum ex minimum
erium cerminorum 1, ni L p3
M
de V n3 p = p+
MM
PIOP