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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 273r, page id 00068196:0541
# 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.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.77
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

pro reductione quadra
s
furarum ratifualum (eptembr. 1690
pusgeneraliter invenim
X. a+  ax
huc enim postremo revuci possunt omnes
ratinales quadrature. Habetur autem
A
e
vel t: X ux
Xla (X: Xta d
quaretur 
fia porro
d: +adx Ntam sit
I: X dx et (X: Cea X+I dx
sit jam C Proposita (XX: 1+ X ex.
pat X+ 1 = y. et hab ebimus X = ya et fiet
S  fi dx = dy et XX = yy a 2y +1
ergo. PXx dx = sydy - 25dy + sdy
+x
seu (XX ax = 2yy - 2y+. Sdy
1+X
similis Methodus, procedit pro
modo e, sit numerus rationalis
1
uam
 de
+7
ex
sed qui
e sit fractus, veg verb. g1. moe e c.n
faciamque m: ni faciamus XIin.
Fiet X = Y et f
Eogo
Ergo to  et
habernus
m
M. n
a
u
m
y
et
dy. Qualium jam datur
reductio. ex hypothesi
Hinc jam artiticium nuper x me
vipioredite
pora enim