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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 75, page id 175905688X:0097
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=97
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.85
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

ae
M
OIMM
1
L LB E R T E R Y T U S.
minorum ejus lint replera (ut ( locOxS X. K X K -- b ∞ O, Aquasioni
desideretur AEquatio, in qua incognita quantiras (ex di- sini comple
mentiones habeat, et in qua nullus terminus detic): 0-
POTTeEPrimUM PEOKS X X X X - b ∞00, SCriberCKS X X F X
bx∞0; deinde Facta p = a ∞ X, habeBIEUE
96 - 6 a y5 + 15447 4 = 204393 + 15a+ yy - 6a5y + 46
= a b∞ O.
Vbi liquet, quod, quancula etiam suppolica Fueric quan-
citasa, omnia tamen Equacionis loca non delinant el
Screpleta.
140
Praecerea pollunt quoque radices alicujus Equatio- guomodo
nis, etiamsi sint incognieae, mulciplicari aut dividi per mulciplicare
quantitatem aliquam cognicam, quam libuerit.
Duod tic, supponendo, quancitatem incoonitam, quarionis
mulciplicatam, auc dirilam per quantitatem, quae muI radices, ipsio
tiplicare aut diridere debet radices, esse aequalem ali-
cui alteri. Deinde mulciplicando aut diridendo quan-
citatem cognitam secundi termini per hanc iplam, qua
mulciplicare aut diridere debet radices; e per iplius
quadratum, quantitatem tertii; a per iplius cubum,
quanticatem quarti, atque ita porro usque ad ultimum.
Id quod inserrire porest, ut ad intcoros e rationales dua rario-
numeros reducantur tracti, aut lape etiam lurdi, qui in nefracti
SEGUALIOML TCrINIS FCPCLIUNEUE.
VE BhabcatuE
X3 = X X V 3 + 28 ∞ - -
2
Y3 0O.
dciplius loco alia delideretur, cujus omnes cermini per
MUMCTOS FATIOHALES CXPPIIANEUE, OpOrceE uppOnCIO
y∞ X V3, d mulciplicare per V 3 quantitatem COgni-
cam secundi termini, quae quoque est Y 3; ec per IplIUIS
Quaclratum, quod est 3, quanticarem certii, quae cst; d
per iplius cubum, qui ett 3 V 3, quanticatem ulcimi, vi-
delicet
r3 id quod TaciF 93 - 399- f 259 - 8∞0.
in
2
Dein-
Vel divide
possent A.-
incoenitis.
lmeri oli-
cujus A
quationis
reducantur
ad integros