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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 135, page id 175905688X:0157
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=157
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
# Lines: 61 recognised, mean confidence 0.78
# 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.

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NV O Y A B R E V E S.
33
ee iplius cubum y. pro x3, atque mulciplicando secundumtermi-
num per h, certium per hh, d quarcum per b3; eandem consecu-
curi simus aequationem. ut ex demonstratione superiori tacile est
colligere; e omnes quidem termini x que multas habebunelite-
ras seu dimensiones. Lc tantum de operatione per literas.
Ouod autem spectat ad operationem, gux fc, cum radix inco-
nita per numerum aliquem est mulciplicanda; ipla cidemr de-
monstrationi innititur.
Fsto eadem, guae supra, aguatio: X3 = CX X  d d X = b3 ∞ 03
ee oporteat radicem incognitam x mulciplicare PeF 3. SupPOna-
TULy ∞3 N, CxIEGuC ~ X, e ∞ N =, NCCHOH, ∞ ∞ 3. Oui-
bus, ue supra, substicuris, Aet 13 -cY 2 1 d27 -- b3∞O. AC
proinde multiplicato totOper 27, exturg et y3 = 3cyy L9d dy
27b330. Oux aequatio etiam invemIEuF, Si in aequatione
propolica substicuamus y, quadratum ejus ry, de ipsius cubum ys,
loco x, quadrati x 2, _ x3 cubi; atque deinde secundum cermi-
num per z mulciplicemus, certium per 9, ee quartum per 27, cx
praelcripto hujus Geometriae. Oua quidem operatione termini
omnes, ob rationes supra allataS, aeque muleas dimensiones ac-
Quirent.
Idem intelligendum est de exemplo in hac Geometria pro-
Polico, X3 = ∞ x V 3 + = X-
e
e
2, V3 ∞ 0. Etenim suppolitO
y∞XY 3, erit ∞ X, e = ∞ N =, neCnON γ ∞ X3. Vnde
siin aequatione propolica substituamus quadratum ejus
_ iptius cubum v in locum x, quadrari x 2, e cubi x 3; inre-
nietur 33 - γV3
261
27V3 27V, 00. Atque adeolcocum
mulciplicemus per 3 V 3 habebitur y 3- 3yy. L 5y - = 30.
Fadem nempe aequatio, qux obrinetur operando juxta hujus Oco-
metrix methodum, quemadmodum supra fuit ostenlum.
Non secushiet demonstratio, (i de radice incognita per quan-
cicatem aliquam cognitam diridenda asatur. Proponaturnamque
RquatiO X3 = CXX L d d x  b3 ∞0, Cieque x diridenda per B.
Sup.