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# Piece: https://leibnizlegible.com/api/records/402/text
# Catalogue record: 402 — [Aufz. zur Integration irrationaler Integranden]
# Incipit: Quaeritur ∫dz√(z4 + abzz + a³c) M : N. posito M et N esse formulas
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=402&katnr=57978
# Work: https://leibnizlegible.com/work/00068199
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folios: Bl. 130–131 (from the shelfmark LH 35, 13, 2c Bl. 130-131): 4 pages, canvases 259–262, page ids 00068199:0259 to 00068199:0262
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=259
# Lines: 50 recognised on 3 of 4 pages, mean confidence 0.82
# 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.
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# 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 130r — 00068199:0259
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 131v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000259.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
Quantur ( (du ((2 + ab7 Z + aC) M3 N. posito M et N
esse formulas rationales integras utcunque p secundum Z. seu quaeritur talis
Quadraturae reductio ad rationalem. Reperi hoc praestari rationem ex formula
aggregatum duarum
quantitatum radicalium, ubi radix non sit extrahenda expenore, qui assurgat ultra 23.
mula
VL
Ponamus Z = O + D et sit O = L(10 a 2P + 1 aa) et D = (20 a  + 21 aa)
=(0 +60ODD+ 490505
abzZ = ch ab(00 + 3D) + 22ab 09
aec =l
quos duos valores coincidentiando, fiet ob O8 fiet, ar = 2 (001313
12. 12
et aarr = 21284 1. 2
12 12
aarr = a  -12. 1OOD + ab 00 + ac
4
HHine et comanude venin posit ad extractionem feat
ubi non licet faere 4: 12. 12 = 1 alioqui fieret 60D) aequalis constanti. Ut
aarv = ( 12. 12OBDD + 2. 12 ar6)
egol rttamu aequationem extrahibilem, faciadiu
+ 12. 12 -6 (() + ()C
3t + B2. 12
54
DD
+
aarr
Ordinata aequatione fiet
ut ergo ad extractionem pervenire possit non explicatisoD et DD,
73. 12
aabb - ac
+ ab
12. 12
1
ponaturse
+ 12. 12 -6 =4)- 2 et fil 12. 12 = 6
sed video hoc non licere, sic enim O et D plane in aequatione
12. 12
seu 1h. 12
aestruerentur, et fieret
aabb- ac = 0 contra hypothesuu
13. 12
4 12(2 - 6
12. 12

## Folio 130v — 00068199:0260
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 131r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000260.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 4 lines, status machine
eeeeeeeeeeeeeee
TFRIED WILHELM LEIBNIZB
DERSACHSISCHE LANDESBIBLIO
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

## Folio 131r — 00068199:0261
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 130v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000261.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
-
435, 13, 26, (261] - 1311

## Folio 131v — 00068199:0262
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 130r); this page is its left half.
# No recognised text on this page (recognized).