# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175905688X:0317
# Permalink to this reading: https://leibnizlegible.com/page/175905688X:0317?run=74
# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 295, page id 175905688X:0317
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=317
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000317.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.81
# 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.

140
eujus
alic AB
lI
_; AM
BCOI
uS. Quade
se habor
lidutano
u 
evectert
DOret, 
erta lunI
derdiete
ubiind
le exipla
nplo du
oris pele
0000
00
CORTAFENTARETRTD BEBEUHHIL.
295
eR hac aequarione, irethodon Victa tradica in eractaeu de Nu-
merola Poceltatum relolutione, inrenietur Z Iaj Or quam 15052
_minor quam 15053. Ouibus dirils per 1000 (quia praeceden-
eisradicem mulciplicarimus per 2000), herr major quam 15, 6
de minor quam 15,558. 2dco ut differentia inter hanc veramque
inrentam d veram millesima parte umicatis inor (ic. Quod erae
inreniendum. Porro quoniain a quatio propolica y 3 ∞ 200y p
OD duas adhuc admiEc Falsas radices, quae Similicer sunc irratio-
nales, quiaipsa per v. L vel-nutlo rumero ultimum terminm
dividence diridi porest, possine ex eddem ratione inveniri, mu
catoraneum ono  in  Ocaruni equidem major excedee
13,385; _ minor deticiet 2 2 53 componentes simul veraim in-
Ventam 15,25. Cacerum, sicur aequaciones ope mulciplicationis
a tractionibus liberantur, acque ad Faciliores reducuntur, ita quo-
que interduin licer iplas Beheticio divisionis, quando cam proli-
Kosnumeros continene; ue earum resolucionon hisi operolioreim
industritur requirae, in Paciliores etansmutare. IIc ( Fuerie re qua-
tiO x ∞ F. f203125 ~ F 23.437500, e ejusloco alia delideretur,
quae minoribusnumeris exprimatur, diridenda est ip la por nume-
r05 proportionales Y. 125, 25625, 2953125,
hoc pacto: N 3 8 O _ = 203F25. x = 23437500 30,
1es 3e . BR _X, KF arrer L. 2 5~,. 13F5625(3cVer. 1495, 3.F. 2.5 ur ua
e prodibit aequatio 3 8 oyy  139 F + 2005 vel y3 ∞ X +Z y
F +2 cujus radices lune 4, 3, 8  L, quibus per 225 inul
ciplicatis (quoniam prioris radices per r25 dirilunus) exlurgent
radicesprioris + 500,  3753 d n 125.
Ibi porro notandum, quod spostquan aequatio quaelibet a
tractionibus aut surdis numeris est liberata, atque in faciliorem
eranmutata, herinon possie; uculla ex hujus radicibus; sire fal-
Cis live veris, Cenumerus aliquis tractus. Ouemadmodum Facile
ex 7no Flementorum libro demonstrari potest. Aded ut, hilla
deinde sicur pag: 7q est octensum diridi nequeat, concedendum
sic, nullam exradicibus sive Fallis sire reris pumero explicari pot
se led omnes esse irrarionales.
5 Qu 2 ) L sua al 2. 3
Ouibus ita constituris, ut pateat quo pacto hae radices lurdis
numeris sint exprimendae, vilum tuit ea, quae ab ingeniosistimo
FTuddenionostro circalxc excositata sunt, in medium adducere.
Tinc ueinrellisetur quo pacto, exempli causa, radices re qua
tionis