# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/59604/text
# Catalogue record: 59604 — Tangentium calculus
# Incipit: [Fig.] y²+bxy+cx²+dx+ey+
# Date: 1676-02-08
# Akademie-Ausgabe: AA VII,5 N. 067
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=59604&katnr=57559
# AA VII,5: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-vii-5
# In the Akademie-Ausgabe: AA VII,5, p. 139 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/VII5B.pdf#page=139
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 391r (from the shelfmark LH 35, 13, 1 Bl. 391r°): 1 page, canvas 777, page ids 00068196:0777 to 00068196:0777
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=777
# Lines: 53 recognised on 1 of 1 pages, mean confidence 0.67
# 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 391r — 00068196:0777
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000777.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
tangentium calculus
+BRY + CN +d1 + Cy1
1bxy  2cxt - d
et fiet denique: D
+O⊓ = 21 ∞bt y adt
N
-V y - d
+2dY tibtdy +a+
+2by +bt..
+ be
+ cd.
C
.
EriscXM
ota
s  bxy Lat
D7 b +4b +y +4 e+
eH -
et
=e V--
absys abetsus act
-bey= 4bete. 4et e
-1- abet .. - 4cF.
H 47 + 4 bt y + 4 dt y + = lFd y + d+
+ 4 C
+ (72.
+ 2 Cd+
ut calentus facilios pro altioribus continuetur; explicandum datam +2bte.. 
aequationem prius explicando ita formemus, ut altissum (uno demto +C2..
ex ipsius X termini tollantur, et facilius veniemus ad progresionem eamque simpliionem.
a - 2y -bty - etc by +2c+
. erit cOxp QX Y.
et 2P1
P-c0
Ergo pro  40- c02 45, 70.
rer
R
+)
61
+A4 167 +abetf yiaet
le +4cFC. cd
261914c+2. -2cb1d.
=4utc. - 2cedF. +dF
(2t2. +2btd.
e
=ed.
es
41214 +bC y
-4. (+4bcF
aeb
bC
e
+ 1b