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# Piece: https://leibnizlegible.com/api/records/1117/text
# Catalogue record: 1117 — [Aufz. zur Integration einfacher irrationaler Ausdrücke]
# Incipit: □(r√lm + s√np) = rrlm + ssnp + 2rs√lmnp
# Date: 1705
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1117&katnr=58667
# Work: https://leibnizlegible.com/work/00068071
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 26
# Folios: Bl. 7 (from the shelfmark LH 35, 6, 26 Bl. 7): 2 pages, canvases 13–14, page ids 00068071:0013 to 00068071:0014
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068071&page=13
# Lines: 49 recognised on 2 of 2 pages, mean confidence 0.73
# 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 7r — 00068071:0013
# Source image: https://digitale-sammlungen.gwlb.de/content/00068071/jpgs/default/00000013.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 43 lines, status machine
(CX + 11XX+ PXFB
1a+ HX t 13 XX F13X
10+2, 161
1 et Ex + MXX +
13X
10
t
AIX +10
+2.10.  tE. 101 t 21011XB
ex(m + Am)- Imamnt 2 sn
(2 (e Im + np) mnp +2 lmnp
El  r5 + Slmnp) = erss Hlmnp +Er5 Amnp
ergo oportet esse rrss+ lmup=rrlm +ssup. Eo jam res redit
renfiet se = rrlm Immp,: rr np ut Y et s habeantur
latana
rationaliter _ 55= en q In (rr- np) e: (rr- np) Ergo vel
erit S5= lm vel rr- np quod est contra intentum
Et praevideri polerat non posse aequari r5  Ctunp, et rilm +5 sup, quia
e
F una est Ambigua duorum, altera qualilor casuum
XX (X alXX + ~C) = y. yxax pendet ab  xx dy
X + AbXX 1  aabb = gyXx
X + ab XX + ac = 0 seu X + ab XX +  aa bb + =y - Labyu = = aabli+  y
c
yu
XY + abXX+aC, : XX = yy
= L abgu= aC seu XX +  ab - =yy - ((e - 2abyy + aa bb)
aC
Ergo datur (dx V tabxx +aC) posito dari (dy s(y- rabyu +aabb
e
a
=gaC
L + ab XX) 4 aC = (X + abXX + aabb + 2aXXZ + el aabZe +qyaa
a
Cportionis fmra
Quando quadratura aliqua reducitur ad quachaturama simlli
ut eo casu, quo partes figurae comparari
interdum possunt inter se, ut in circulo et hyperbila, et ellipsi
ita prodirent aequationes quadratoria.
rbZ + CC =  AR ci + 2CZB + 7Z on fit Z + b = 2CV + ZVY
=2CV
ov- 1
dq A(22+ b7 + CC, 2) = s dze. C+ 20, M

## Folio 7v — 00068071:0014
# Source image: https://digitale-sammlungen.gwlb.de/content/00068071/jpgs/default/00000014.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 6 lines, status machine
.
ERSÄCHSISCHE LANDESBIBLIOTHEK
eeee
mnat
3, 6, 26.
-70