# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/11728/text
# Catalogue record: 11728 — [Math. Rechnungen]
# Incipit: x[Formel]
# Date: 1694
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=11728&katnr=45214
# Work: https://leibnizlegible.com/work/DE-611-HS-958803
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folios: Bl. 18 (from the shelfmark LBr 57, 1 Bl. 18): 2 pages, canvases 35–36, page ids DE-611-HS-958803:0035 to DE-611-HS-958803:0036
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=35
# Lines: 93 recognised on 2 of 2 pages, mean confidence 0.77
# 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 18r — DE-611-HS-958803:0035
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000035.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
qu X = 1+Z Cx = 1 Z - 1 y2 + 1 yd.
2
+Z7 etc
y = bFC y = X = b + cX + d7 + es etc
=dy = 8c ∞2dZ - 327- 45Z59Z- 6h2.
1
+ ytx = b + cZ + dZ + e 73 +fZ4 +97
+ ylxex
cb d= B2b
1bZ - 2b 7 + = b 73 - = bZ + +b
+ LCZ = L C7 + 2c 54-
+ 1d73 - = d 77 + 10
c = b d = 2, b = + 1b = 2 = L8E 2
e= L - L + 1 P: 3 C =- = + = + 1+ 1
eto
3E
F= +  ( 3) +  B 1st L B
9-
a
2-
2 = 1 b
+ 1 (- - - + ) + 5 3. 5 =-
- + = = 1 + (. 1 +  + - : 6
3
2
2
3
2= +  - = + L - = +  +  3 : 6 = = + 2,:6
a =
a l y = 1 + v
y = v - = vv += V
3
1215
2. 3
1
= = b
24-
8 - 4
3, 4, 5
8-3=3
3. 4.5 d
12
27 5.

## Folio 18v — DE-611-HS-958803:0036
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000036.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
e
y
2
seu og X logX = logy. seu
e
X tg X sax. x = fdy  dy: y- sit
 fit dx + ex sax: X = y dy: y
sit y sit g  a + bx + CxX + dX et
et fiet a +bx + XF et dif sit ex constans
1+ ax. X
fiet dxX =  day: y =  ddg dy: y
seu _yy dx   + ax du = dyddy
sit y- a 4 bx +  ex + dx + ex etc
sin pruatur du constans, fiet
dx: X = d, dy: dx. seu siet
et fit
dx: X = ddy: ydx - dydydx - dy. yddx
gu. dx
yy dx
(. seu  dx = ydx ddy - dydydx = dy ddx y
sed puoi calenlus brevio r.
Sit loqeme sit log y
sit loque Y = a + bx + Cx + d exere
C
Sed ecce aliud arciticidum
=x logX = Vaciabiuus artes.
sit X = a+Z. sit log. y = + bZ + CZ +d83 + 0G etc
siet CC fiet lege log. X -  Z + = + = 23 = 1 q+
et X logX = a logX + ZlogX.
Ergo prrodit aequatro
f+ logu = t+ nx + pX + qu + rX + 5X eter
=log. X =  - aZ - Ry - 4Z - _y
= Z logX =
22 3L
e
= 1 7 -.
2a 2
+
G
de
fiet n a g - p = 1 + = seu 2 p =
fiet n = 0+ 1 seu 1. p = = + L seu 2 4= = +  seu =
e
6
r = + + = seu Z. Ct
12
ergo log y = 174 37+ 5 2 + 7 et
L 12L 23 3.4
sit Y 1V ly = vae Lrr + EB   erc
sit X=