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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 496, page id 175905688X:0518
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=518
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.87
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496
LOH ANNIS TIUDDENET FPIST. I
tineo y3 X + 20y - 24 + ∞ 0, PrOy3 -9yy - 45 y = spP ∞0
+ PY + 49)
(MaMI P ∞ 0, 4500, Y∞ = F2, 5∞ - 5.) quae dirisibilis est per
y = 4 ∞ 0, ita ue loco duarum x quationum habeas has duas
N X  2 N  5∞ C
e X X = 2 X = F∞O.
Similiter (i proponatur aequatio literalis
X + 2 a ∞ 3 2 a a X X = 2 a 3 X  a + ∞ O; CrIt P ∞ 24;
6
9~24a -- c6; r ∞ - 2 a3; s∞ a ideoque in locum aequationis
y3- 4yy- 4 f y - sep ∞ 0, Ceriben d a 93- 24a9y +- 42 266∞0
+ PY + 495
t C
quae diridi porest per y - 2 a a ∞0, ita ut loco duarum ae quatio.
tium habeantur hae dux
XX - a X  X V a a = 66, - ) A a ∞ 03
_C X X = a X = X V a a L CC, + a a ∞O.
Si verotae aequationes per y. L vel - aliquo dirisore ultimi l’er-
mini non fuissent dirilibiles, non poruissent etiam aequationes
Propoliex ulcerius quam ad 3 dimentiones reduci.
ZZI. RE O V F A.
Flacanus Regula, eus cradidi, respexerune ae quattones, i
quibus una taneum incognita quantitas, quam a nominari, inre
niebatur, ut meos conceptus diltinctius exprimerem. Jam uno
adhuc rerbo adjiciam: Quod in Proposita aequatione quamli-
bet coenitam pro incoenita es vice versa quamlibet incoenitam
procoenita respectu Reductionis considerare liceat; es quod sa-
pe compendio sit incoenitam tanguam coenitam es unam ex
coenitis tanquam incornitam considerare es sic Reductionem
inquirere. Nam primo in omnibus aequationibus, quae ex dua-
bus rationalibus oriri pollune, aeque per quamlibet cognitam,
eam canquam incognitam considerando, quam perincognitam
reductio inveniripotelt, de lape ctiam brerius, si ex Tolis irratio
nalibus produci possunt. Dein quod hoc lape compendio sic vel
hinc