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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 3
# Folio 15v, page id 00068216:0030
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068216&page=30
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.87
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# After the first blank line: the recognised lines in reading order, one per line.

X aequ. a
X aequ. a+ 2ab
X aequ. a+ 5ab + 6abc
rad 1b 3 ab. eab. 10ab
X aqu a + 42 b + 6ab + 12 a bc + 24 abcd
Naequ. a + 5a b + 10 a b + 204 bc + abc abed abide
X ab ab ab abi
ael abque aebed e a vid abide abedet
(2) aequ. 2 ab.. seu ab. aequ (2). abc cequ 3)
 ab aequ. (2) a aequ. (4) - 6C3)
(2) quod pe rationale in X. (3) quod est rationale in X esc
nonlicet ponere rationale totius potentiae esse tantum in forum aessuiformi, nam
alioqui nihil foret rationale in X. spositis a. b. c. etc. itratio nalibus alterius quam
Eti gradus  et non existentibus pluribus quam 4.) quod est absurdio
abap 2+ (ab). Ego 12) a + Cab) a mgo 4b. + 3abe rgo X - a - a1. Ego qud ruto ate in 41) a son in ab a est in  - a
e
ab= a g ab + abc
2
rursus aa aqu a + ab
4
Xa a equ.t abur n aCd aeon
a + b + C aego X
peaequationum valorem ipsius y inveptigares
May mute
ut et ipsius 7. per solas cognitus, accedente
ac cedentibus 4. a. a. a
~. etc,
id est quaeratur primum y per solus X (a. a. a.
eodem modo et Z per has solas. caeteresque omnes
formas aequi formes. Ita cum sciamus quid in X. X.
 sit rationale et quod in  a. a. a. etc. sit nihil
ratiomale, sciemus etiam quid sit rationale
si mille; eamque sciamus aliquam
ex his formist esse totum rationalem eo ipso
an una quaque
buo vatorem invenimus.
uia in a nihil est rationale
 Hinc quod est rationale in
Z et yx aequatur ei quod in X
eq ap. X -. yx. a
 vanqu. X ax Zrqu. x.. . aX.. a k Z dividatio per X
y aqu X- 4
Sed nova se offert difficultas circa a
a x. cex  ax aXeC. in quibus
si scuiremus onnia essent
quid sit rationut difficile
itaque ipsa a ax. aX: aX. erc
vado
1
item aX. ax. ax prius inveniri debent
ac tolli ope aquationis datae et solarum
quantitatum a
X
1. a. a. erc.
p qu rre
ax aequ. h
h aego a X ergo a p + in.
X aequ. a.
ed difficilis haec sublatio