# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068217:0037
# Permalink to this reading: https://leibnizlegible.com/page/00068217:0037?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 18r, page id 00068217:0037
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 19v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068217&page=37
# Source image: https://digitale-sammlungen.gwlb.de/content/00068217/jpgs/default/00000037.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 89 lines, status machine
# Lines: 89 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.
# 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.

X +9X + Y aqu. 0.
X = 34bX - a aequ. 0 posito, X aequ. a + b,
ponamus: ab aqu - 4. et a + b aqu. = Y  et per 4.  ab aqu =  hinc
1
6) + 93
per aqu. 5. 6. fiet: a + r a = g aequ. 0. Nam - b aqu 2743 per 6. et b ao +Y + a per 5
Erip duos valores aqu. 8. et 9. aequando fiet: a + ra - 2 aqu. 0.
17 (10)
Scribamus
primum ejus loco:  f + r f .s. aequ. 0. ponendo, f aequ. a. et Saqo +
fiet f + rf + F aequ S+ 7.  et f + Z aqu. + 15 + . seu f aequ. - 2 + Y4 + 
5)
Pogro aequatio Ergo per 11. ot 14 erit a aqu. 3- Z + V2 + vel etum
auts A aqu.  -2 - Y 4 + = adeoque a + b aequ. Y- Z + Yqu a  + Y- = - Y 4 + 2
Verum notandum est aequationis 11 ad huc alias dari padices praeter Yf.
Ivela
Nam si a ∞f dicitatur per a- Ys. prodibit a f a Nam si dividatur
a-
a+ af + Ypi
+a -Yf
per a = Yf prodibit  a + aY + Y s quo probari potest multiplicando
ergo si a - f aequ. 0. dividas per a - f. quotiens etiam erit 0. adeoque
habebimus aquationem a + f a + Y5 aequ. 0 Quam aequationem
extrahendo, fiet: a aequ - Ys + 2s- Y5 + Ys
Sic
sive a aequ =  + f.3 f. Qui valor duplici modo explicari
potest, etiamsi f non varietur, et quia f etiam duplici modo exprimi
vel b
potest, hinc a vel b quadruplici modo exprimetur, imo quia ipse duplex
valot f. etiam significat a vel l. Hiur  habemus valores
ex sequentes:
et
aequ.
aequ
aequ. -  + 57 -3, 5--
aequ. - + + Y-3,
aequ.
-2 - 1. 3, Y.
2
aequ. = + - 1. 3, 3. ~ - Y
Ergo a+b aeqo L+M. quod coincidit sum, seu Y. 2 14
a  seu - 54
N
aequ P+ R seu -
agu N+ P seu 14 , Y- Z + Yq +
aqu. er H. seu 1 (3, Y. Y + Y8+
4
X + q. X + Y aequ. 0 R= qR - Y aequ. 0
suspecta haec
inquisitio quia
video plerasque combinatio
nes non procedere
2
haec itaque diligentius
excutiend
G
R aequ Yf
+X + 4X  aequ.0. dividatur per X 2R fiet X + RX + R  aqu. 0
e - 9f
2
Ratio cur istae radices
procedant traecandeta
e quia cum ab aqu. 4
extartda  issumtae
aor - 1
10
1b9
+gr
iia omnes
combinationes
ex valorum
aut L+ N.
L+ p. 8c.
dant
+
hinc investiganda ratio
et accurate inspiciendum est
negotium valiorum ejus deu
aequationis
valorum
en
radicum
amlignarum
Estt enim res
Subfilissima
eroribu
xposita
1a a1 at
LH 36, H A, 1.