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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 19, page id 175906937X:0043
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=43
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000043.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 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.
# 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.

eaer.
1IO1S0
2b5.
Cub. 272
Rad. 3 N
XL
32
9r1.
=~t. 1. d11.
L. PLuS.
MIAPHESEOS IINEVBRSAL1S.
 2.X
L27X  = 2X
2 X
2.∞ + AXX + 4. XX
34XE + 3X∞ = 2X
 12X4 - 8 X3
pet
36∞
BX X - 2 X
=6∞3 L. 4XX
9X2 LLa4XX
2.71 361L2bib.dCCo
+735~+- F 5 quocus secund. L 5
L 27X
B X X = 2 1
9X+ - 6X3
Ct
t 2
=3XX - 2 X
L
+ 27 ∞ + - 36∞3 + 12 X X + 7GXX- 5OX = 125.
+ 5 PeT 3
L135∞ + - 18OX3 F6OXX. + 225XX - 15OX
Cacerum si quantitates, ex quibus radix extrahi debet, cales
Fuerine, uc radix praedicto modo inreniri non possie, designabitar
ipla praetigendo quoncicacibus propolitis signum V. UE ad exErA-
hendum radicem quadratam ex aq. Scribo V aq; quo indicatur
radicem quadratam ex aq esse exrractam, vel ad huc esse exIra-
hendam. Sic et V a a. F b b designabie radicem quadratam ex
aa + bb.
Similiter ad extrahendum radicem cubicam ex a ag, fcribo
VC. aag. UIE de V C. a3 = b3 + abb, ad extrahiendam radicem
cubicam ex a3 = b3- F ab b. Oux quidem radices vocantur quan-
citares Surdx seu Trracionales, ad modum numerorum lurdorum
Seu irrationalium, de quibus Acichunerici asunt.
Cbinocandum, lignum V, rocari Signum Radicale, atque in
enere ulurpari ad denotandam quamcunque radicem, sire Ou2-
dracam, live Cubicum, sive Oundrato- quadratam, eec; sed ad il.
lam distinguendam; communiter scribir o, vel etiam Cimplici.
cer V, ad denocandam radicem Ouadratam: _ V C, ad denoran-
dam radicem Cubicam: ec V 9O Ccu rV, ad denocandam radi-
cem Ouodrato quadratam, dec. quae radices eriam (ic delignan-
TuT: Y(3, V3, Y (4), dec; acque ab aliis, hoc quoque pacto:
83Y (C, V88, ec.
+