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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 129, page id 175906937X:0153
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=153
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000153.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 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.

GaM H, u.
mjor qui
1udC
, d CC
L1BDta
aF qua
 L. MIBO
1a) et qu
lel quo
acionispe
quamp
1aI
Tinc dii
de rmin
PP, dC PB
onteu
eguem
quatu
2IM X.
2quai
1P.
ei
AE Q U A Y L O H u H.
C A P U F VI.
De Aquarionibus quatuor dimensionum, in quibus tertius
es quartus terminus deficiunt.
Prop. 2. XF - lX3 X X L p4 ∞ O.
Eccranspolicionem eAx + ∞ L l∞ 3 = p , ideoque X3 major
quam. AEvero eC etiam p + ∞ lX 3 - xt, e consequen
ter l major quam x. Inrenimusisitur, quod unagua que duarum
radicum aequationis proxolitae est major quam V C. at minor
quam l. Tinc quoniam lmajor est quamx, _ L X3 majus quam pr,
habebitur Ilxx majus quam pr, de consequenter xx majus quam
73 e x major quam.
Prop. 2. X 4 - I X 3 X X = p+ ∞ O.
Pertranspolitionem estxt =lx5 ∞pt, ideoque x major quâm l.
Similiter eltxt =pt ∞ lx3, ee consequenter a majus quam pr, e
x major quam p, ac proinde px3 majus quam pr. Sed est etiam
IX3. F p+ ∞ xt. FrgOl a 3 F PX3 majus eric quam x, dc l. L p imajor
quam x. Inrenimus isitur, quodradix x aequationis propolIEX
ajor eA quam lec p, ac minor quain l. L P.
Prop. 3. X + -f.. L X 3 X X = p+ ∞ 0.
Pertranspolitionem est xt ∞ p+ = lx3, ideo que  majus quâm
23. Similiter e(lx 3∞ pF - x+, ac per consequens p major quam X,
_ pX majus quam x+. Aequi est etiam x L l ~3 ∞ p+. FrGOIX3
LPX majuS erit quam PF, _C X3 major quaM JL. Quare inve-
nimus, quod radix x aequationis propolita major est quam
V C. F. Sed minor quam p ec Y C. . Facillime vero evitan-
tur extractiones radicum cubicarum, sumendo terminos paulo
IMaIOreS AUEInOreS, Prout necesitaS requirit. Atque in hOC Ca
Tu