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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 396, page id 175905688X:0418
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=418
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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 0.86
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# After the first blank line: the recognised lines in reading order, one per line.

A D D E Y A M B H X U H.
Cocicetur d. =F 3 abc esC 20, _ 3 a a F bcV bc eNeV 392, ita ve
 a 3 + 3 a s
L 3abc.  b V bc designec datum binomium 20 = V 392, 8
radix ejus cubicaaVbc iplam raclicem quaerendam, cujusm-
or pars (ica, ee minor Vbc. Tum opcrare secunduin regulam.
2
20  V 392
2C
subt. 5 +00
392
relig. 8,
2 radix cubica reliqui, sire a a - bc.
Adde 2d 20, partem rationalem binomii
 19, praterpropter ralorem partis irracionalis.
_ Ft Z9, ralor dati binomii inrarionalibus, cirei.
cer. utpote à rerounicare non discedens, quippe
qui incer 39 8 40 consiltit. Unde radix cubicatie
ajor quam 3 ec minor quatm 3 =, Ita uF 3 radicem
reram non lupra= excedat. Sumatur autem quali
esset rera, ee aqualis a + V bc.
Ecdirid. 2, hoc est, a a - b0
per 3=, hoc est, a + V b6:
dcHC =, SIVC a = VbC.
add. 3 =, hoc est, a = Vbc,
dc tic Cumma 4 4; sive 2a, duplum parcis rationalis, radicis.
supponendo 3= esse veram radicem. Sed cum 3 = sIc major 12.
dicerera; Ita tamEM, UE dIFCTENEIA nOn SIE (UpTA Z, HC, uC 4=
quoque duplo partis rationalis major existat, e differentia mi
nor quam c. licut inferius ostenturi lumus. Unde cum eadem
parssicnumerus rationalis interer, sequitur duplun ejus fore 4
UEpOce aximum inceorum numerum in 4  Contentum, adeo.
que iplam diccam partem Fore 2. Oud invenca, Faeile et reli.
quam invenire. Frenim, (1 a 4, quadrato ejuldem partis, subdu.
Catur 2, radix cubica differentia quadracorum parrium dari bi-
nomni, relinquetur 2, quadeatum alcerius parris: Ita utradixin.
venta (IT2 - F Y 2.