# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0545
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0545?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 273r, page id 00068201:0545
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 274v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=545
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000545.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 89 lines, status machine
# Lines: 89 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.

De irrationalibus aequationum Radicibus investigandis
-aq X p1 ayf (3) ba
r ibba.. ..
1fhaβ, bda - ..
(1) r
si jam ponamus fH g
duae aequationes insigni utique
comipendio inter se coincident, et
+3fg a(3bca. ..
+3 964 freda ...
+sfyta () ba .. .
a 44 = 3923) bca
+ a q - 6fg1bca
3f iB bda +5f H5 cda
a47g 10bda
pes..
ec
(3)7 0.
fur ergo Cer. 4qu
ex aeq. 2. h 
dis
+Ighabida 1.. rostitibia..
sufficit construi ex ipsis pi
unam.
Methodus nova
+ g 1( ca
(Dri
391cda
10 cda
At ex aeq. 3. habetitur
rusus h, nam fiet:
Quos duos valores ipsius H
aequando inter se, habebimus:
-9370 bca bda  X9 10) cda + aq
secda
=6 g3 bca
Sed jam comparet difficultas, nimirum necesse est omnus tres:
bc. bd. cd. fiari aquoles sumi pro cognitis, unde sit
sit bc e B 1 . bd ⊓ B.
cd p 7.
ent: Cr Z. et n Z. ergo Z e Z F Ergo dp 7.
idem dri . ergo Z p b7. Atque ita b. quae per ultimam
c et perconsequans ipsae c. 0.
aequationem inveniri debebat nale invenitur per hanc Unde postea
. 1. 3. T. g. ope residuarum duarum aequationum quaerenda
sunt, quod sec satis difficile fiorit
si qx e arsb tane, be
Bent HI
a ql . . . . . . . .
pX  bpse ca.
3pbe ( bca ..
(1) 10
ocae e 
9 .. .. ..
tap a.
43pbc 1 bca..
2770
_ b cbc bbe bebca
s0 b6c b e bc
ari
Bes
+bbc s0b
4HC.. ..
Cb22
aqB. (8b22
agc 6..
a9. bc
agias
te fta
(b c7 6bc b
10 b cbC a
1bcn 18bcan
ubi aequattones A et 2 coincidunt ere ipis st L bc Et prmndo bC r ya et quaelibet
exipsis divida potest per sC ba. et si ponamus 4 bE r Y. Ret ex aeq. 1. vel 2
sequens. y2 43
ubi malum illud, quod scilicet duae aequationes 1. et 2 non
coiaiint. Item quod in ullima habemo contentum b. erc sed et. B. 12
ipsae
+6 egha l bcd
la2 bsBc
bc3 (622 a( B2
+ b+
sit b4+ + b3 =+ b2 + 1
ba
 cae
+ si da
L aY
(4) A
2B 1