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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 90r, page id 00068201:0179
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 91v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=179
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 100 lines, status machine
# Lines: 100 recognised, mean confidence 0.83
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

aea nontim depreh ind
 pontum deprescad
(13)
2duatum incognitectum, quae in se non ducuntur
y + eY - al + fX - 2
Vy) = b y) + coy - al + fX - X
(5) srrst tar (al - al) 1fX L X p o.
X +4 + Xt + ax9 + fX - x 10
e p = bY + co. Erg per (4. (5)
eri = br = b + s + a. Ergo per. (9) (0)
(14) Crj - bx9 - b + xt + a Ergope
(17)
(19
XF, e + b xq + b - a. p 4.
(
bxq  Xt b+ a - e.
X  Xtq + + + ag + f. ex 14. 12
(5
() ∞7r + 1. (So sta coy oristraeral
0 5H Xt (gr +) va
X t
jam quia Cp,- b7 + Cd ex plicando Y et Co,
sit Ea Idem peane calculus
serviet, ad si adsit terminus
VX., est enim yXB X 4 + XI
Unde divisis omnibus per X. i aequalioni
Jungantur Aequationes 12 et 14
es
12 acedet X9 + l. quae sane
nihil turbant, valor enim ipsius
Xg. puus, per meras datas in
ventus, in ejus locum substitui
potest, C. autem est data
Habemus ergo Methodum
Generalem exhibendi
suc pere6) eo) (ai ne aq ( f aqudta
Jungantur inter se aequationes 12. et 14.
utraque ante conjunctionem per arbitrariam
multiplicata:
1 P
in Numeris. Aequationem
quadraticam quamlibet
quodcunque incognitatum,
modo id fieri potest.
Si unius in cognitae esst, semper
sciri potest an fieri queat solutio
per extractionem radicum, si
βxFg + tβ + aqβ + f β- Aβ 7 0, Aequatio 12. per abbitrariam multiplicata
eY + bx + b) = xtY = a) 10 Aequatio 14... . . . .
(22) Cntq Xty + ly a te n-
C) err. bV+ c
Item per 14.
+ p X - f - aq - xt 4 ex ae9. 12.
es b9+cd
divisis omnibus per X
per 14
XEG p X - f - aq - + ex ag. 12.
(22)
quam libet
1 0
70
(12) xtg , t + ag + f - x 1
(2)
C
--
duarum incognitarum colligo
ex datis, semper in numeris possubi
lem esse nisi ipse calculus praesens pluda
quod escib aut fieri queat Ares in cognitae
β X +g + bxgV f xt7 + tB F ag C X β + fβ + C) + b7) + aY 0
aequiparabuntur
Habemus arbitrarias  =B. γ. X. t. q. Numero quinque
unius exhis tribus
F nec aliud jam quaeritur, quam ut inveniatur valor purus ipsius l
Bo Et iptiu X. vel C2 vet 9., quem vlltr quem una tatitum
Cn
ex reliquis duabus ingrediatur.
Caterum it ipa fieri quean com–
dmodius, nec attollantur dinensiones efficiendum est ut sint duae quaedam ex his
 tribus, quae in se invicem non ueantur; quod ut obtineatur termini omnes
E
tnon nisi per arbitrarias assumtas multiplicati in ultima aequatione
destruendi sunt, ponamus ergo:
Enficr
f ( 4 ex + b7 + ) 10.
cY + b7 + a7
et restabit aequatio:
BX +4 + bxqV  X + ) + t B + aq ( = x (3 pit 9  in qua si B. Epi
Ponan  n + 18 4, fiet
 frocus
3
quia cognidae sunt
 Pagr + bX4Y q X + nd + noa (+ 2B , 6 (( age r agB rl
12
e ita potenno onnia divili per X.
(20)
duabus.
aetu destrnetur tam
quam
Ergo