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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 133, page id 175906937X:0157
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=157
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 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.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

P’ mjo
RCNO
+des
Dec tont
adIX XpI
IMOT qua
eOGVEMM
X + PX
ralereaet
rajus qu
amlibet 1.
ideoque
XX, de
(M XX.
1X. 1
BebIIa
O
IIndet
AE O U A Y L O H U M.
cet, lixx aequatur iplimm, hoc est, x m, candem xtore aequa-
lem iph : ac per consequens, situerine terminihim _== 2 qua-
les, eric una radicum aequationis propolica ae qualis lingulis iplo-
rum; e E inxquales tuerint, neuera duarum radicum aequatio-
nis propolita poterit esse inter illos duosm e. Fodem modo
pertranspolicionem eAt x+ =n X Dmmx x -p+. UInde Cimiliter
dilcimus, si x3 aequatur ip(i n3, hoc est, x ∞ n, Fore ctiam
X X D  n hoc CA, x ∞ . Ideoque sihi terminin el fuerine
aequales, una ex radicibus aequationis proposiea aequabitur sin-
eulis corundem terminorum; sin rero inaequales fuerint, nul-
la radicum aequationis propolitae inter illos duos constituta crit.
exaterea per cranspolicionem eAtxt. L p+ D mm X X L n3 X, ideo-
Que mmxX Ln X majus quam x+, _ mmX F n3 majus quaim X3.
Porro, (i propolita aequatio est realis, erit n realis, et aequalis,
vel major, relminor quam n. Si tuerie aequalis rel major, erit
mm X. L nnx majus quam x3, CE m m: F nn majus quaim X X, hoc
est, xminor erit quam V mm- Lnn. Si fuerit X minOr quaIm n,
minor etiam erit quam V mm- L Bn. Guare patet, quamlibet
radicum aequationis propoliex neceslario minorem esse quam
mm. Lnn. Denique existente x +-L p + ∞ M I X X L n3X, exit
Timilicer mmxx Ln3 a majus quam p2. EF quia inventa eAt
Vmm. +nn major quamx, erit conlequenter mmx V mm. Lnn
Majus quammm XX, ideoque mm X V mm LnN, L B3 XajuS
P
quam pt, ee xmajor quam
mmrmm Lnn. + X3. Ouare inven-
cus est terminus unus major a alter minor quam quaelibet dua-
rum radicum aequationis propolua. Atque ita modo seguenti
capice obterraco propolicione seprima demonstraripocest, quod
x major est quam minor horum cerminorum n et in mn. L. n3