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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 141, page id 175906937X:0165
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=165
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
# Lines: 65 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.
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# After the first blank line: the recognised lines in reading order, one per line.

X -
equil
equales, 
aquaeoi
POTCL
Dt~3=
quoque X
2qualotu
lingut no
et
i tuctIEpe
et Masor
lA aF I
Minot qu
AaEIONIS
+
linen
+21
aqualiset
nulla rd
1O PerE
-2LH 19
CnON L
13 +. 111
F CuBIM
IIuBG
n per cub
radicu
Itam
A O U A Y L O N U M.
24 L
major quamn, erie necessario inter hos terminos l L n ec n.
Muodlivero n tuerit vel aequalis vel major quam x, quia l x3. L
n x majus elt quam pr, erit d Innx- L n3 x majus quam pr, ec X
major quam Jun Fns. Ac proinde qualibet radicum aquationis
propolicae major erit quam minor horum terminorum n es
+
Inn. L m3d at minor quatm l. L. H.
C A P W X X
Delomitibus aquationum quatuor dimensionum,
in quibus nullus terminus deest.
erop. 2. X + - bX3 F. MMX N = 13 X 1 p+ ∞O.
DEecranspolicionem est lx3- L n3 x ∞ N= - L m M X X L pF, ideo-
L que lx3- Ln X majus quam xt, _ lX X L n majus quam ∞3.
Jam li fuerit propolica aequario realis, erit e x realis, et vel x-
qualis velmajor rel minor quam n. Ouod (i fueric aequalis vel
IMajOr, erit lxx Y B x x majus quam x3, hoc eAt, l. Ln major
quam x, eexminor quam n. Mulco isitur magis minor erit quam
l. Ln. Eroo x necellario minor erit quam l L n. Deinde Cx ca-
dem aequarione lx 3  n3 X ∞ xF m m X X J p constac, eAe
IX F n ∞ IajuS quaim p~. Sed inrenta est I Ln Imajor quaM X,
2C per conlequens II.- L Bn- L 2 ln majus quam X X, eC l3 N L InnX
 2 l. IB x ajus quam Lx 3. Ouare erir 13 x L lBBX L 2 ltB X
Ba
L B3 X majus quam pF, eC X ajor quat p. L Inn = 21In f. n3 3. 
quandoquidem cubus ex l -]n major est quai 13 -] - lnn. F
2IIn. Ln3, mulro masis eric a major quam p dirilum per cubum
ex l-) n. Invencus est itaque terminus unus major ec alter ini-
nor quam unaqua que radicum aequationis propolitae, sive haec
duas sire quatuor radices habuerie: Praterea, quoniam inveni-
us, quod l. J. n Semper major est qudim , SI PONAtuIE X quo-
que major quam n; manileltum est eam esse inter duos termi-
HiOS I-Ln ee n. Ouod si aucem n luerit aequalis vel IminOF quam
, quoniam est L∞3 -n3 _ majus qudin pa; exit LW n ∞ -+ n3 X
AaGUS