# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/60563/text
# Catalogue record: 60563 — [Aufz. zu quadratischen Gleichungen in x u. y]
# Incipit: 100 + 110 x + 101 y + 111xy + 120x² + 102y² = 0
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60563&katnr=57461
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 198 (from the shelfmark LH 35, 13, 1 Bl. 198): 2 pages, canvases 391–392, page ids 00068196:0391 to 00068196:0392
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=391
# Lines: 91 recognised on 1 of 2 pages, mean confidence 0.74
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 198r — 00068196:0391
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000391.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 91 lines, status machine
1nt WX +1By + InXy + _ 120X + 102y =0
200+ 210X + 201 y + 21Xy+, 220X + 202yt0
20g+OXF,V
multi pl.  per 202 et 2 per 201, et producta a se
invicem auferendo, fiet:
10 242 na a iotamxge
HIEo
w txtOXyt. oX
tot 2o Wove= i_2. Woy - W UIXy -102. 27025 =0
adsit pratere a aequatio tentia
Amsus ex ag. 3 quia y  + 310X: 301
h
y = 300 + 310x; 301 fint y 30nt 2gau
or sobdit tung in ang. Ex aeq. alolla
tur y per aeq. 5. et siet
1100. 20, +110. 202E, X
VI. 20
= 101. 210 X
+120. 202  X
=102. 210 X
20
30d +  rvo X +11I. 202310 X2
102. 201. 300
101
set
101
= 102. 201 310X
+III. 202. 300 X
301
102. 21. 300 X
10
10t
102. 211310 
301
sed et per s valorem y in ∞9. 5, et valorem
eig velo
2002+ 2. 300, 310X + 310 X, : 3
potest tolli y ex aeq. 1 et ex aeq. 2.
Nam ex 1, 5, 6 fiet
Ho +HO X + 1207
rioiz0
301
Tugo. X + M
301
+1141OX
3
2
+102. 2 420 3 +318X.
301
100
301
301
Hoed
100
448 pro
in nota late
penultima pro 1
Scribendo L.
Ope 7 et 8 tollendo X, fiet: mnoo notar
7 peo +1d 7 220
110.300in en  + (∞1. 210  11. 2
301
301
(12
o in guere
or d
30
n
3os
qu
r1II. 300
301
210
201. 2
301
211.300
In
301 L l
5. fabua trunt X et y
301
3
top
120
Et similiter
eodem modo dit
G. ausu
llm et
nullo
e
quos dons culo
dis solti eodo

## Folio 198v — 00068196:0392
# No recognised text on this page (recognized).