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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 453, page id 175905688X:0475
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=475
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.76
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d
500
DF RE DRCTLONE A ORATLOHUM. 453
∞p ∞ 2 diridendum eAt per X x L y X F Z ∞ O ∞ X K L 2 X -
DO, invenietur que pro quotiente x+ F F 2 X X F 3 ∞ F 1∞O. FF
manifectum elt, nos etiam alcerutra tantum duarum illarum e-
quationum uri poruisse. Facilior itaque ria eligenda erie: non
enim Cemperilla per communem dirisorem brerior est, neque
Scriper longior; rerum hanc haBCE PFarOgatIVAI, quX PanC NON
parra est, quod inuriles radices abscindat. Ouemadmodum se-
quenti exemplo clarius patebit.
FHOxquatio PFOPOLIEA X = -2 X +- F 343-3X N - 5X- 1∞O.
Ouoniami hic p est v o, reductiorentonda erie per B, D, 5.
Incixiendo d B, invenietur pio + md y 3 - p yy- + q y = r ∞0.
LB
AxeC Xquatio y 3- = y7 - 27-3∞0; d PrO 2dà yy-
)
0
- 030O,
haec yy . = 2307 - 305 ∞ 0: est enim in hoc exemplog~ - 2.
3∞3, (∞ = 3, t 30 -- 5, _ v ∞ = I. IInde, quaerendo carum
communem dirilorem, comperietur nullum dari, ac proinde
dirisionem per B tieri non posse. Hlinc eranseo ad D, ubi Dro
ma aequatione qu3X. f s y -- + ∞ O invenio - 29 3X 1 1y - 1∞O,
+94 + Y9
e PrO 2dd sy + - + y3 + 295yy - +9y- + 99(∞0 invenio
 )
3 yt = Y 93 - = +2 7y - 207 - 24 3 O. OUarUI a quatiO-
numdirisor communis est y- f 5 00; 2d coque Z ∞ y y - F 93 -- 1:
ita ut dirilio sic Facienda per X X  L Y ∞ -f Z ∞O ∞ X ∞ -- ZX -- 1,
exitque quotiensx+. L L ∞ 3 X f + X F + 50O.
Eibi nocandum, modum hunc quaerendi communem dirilo-
rem in altioribus praesertim aequationibus permagni esse ulus.
non autem eantiulus, cum aequariones, quarum dirilor commu-
nis inrestisandus eAt, Tolummodo Tunt 2 dimentionum, aut e-
jam erium, quoniam cum dirisores taciles sunt inventu. CE in
3
_qua.