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# Piece: https://leibnizlegible.com/api/records/767/text
# Catalogue record: 767 — [Aufz. zu Exponentialkurven]
# Incipit: 64 32 16 8 4 2 1 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256
# Date: 1680-10-08
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=767&katnr=58345
# Work: https://leibnizlegible.com/work/00068033
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folios: Bl. 23 (from the shelfmark LH 35, 5, 15 Bl. 23): 2 pages, canvases 45–46, page ids 00068033:0045 to 00068033:0046
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068033&page=45
# Lines: 136 recognised on 2 of 2 pages, mean confidence 0.79
# 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 23r — 00068033:0045
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 108 lines, status machine
S. Series:
+
64
4 2 1
16842 1L 1 1
e
L 1
1 1
48 1632645L8
primum uest ad
2
secundo primum
f. +ad
15
48
24 d
16LF 256
san
92
64
laequ s
2, 16
27
3
8, 2-1
256
vel 1
sumtis quotiunque finitis ordine. a. b.
22
15
ut = ad 270 ita Ex
item
a
2
32
12- 1
aequ
2 = 1
1
2
9E
L, 2 =1 minus differat data
si esset 72 2
2) nunc erit opinor a
a
C. d.
2
Videndum quae sit quanticas a qui
ista
, 162 - 1
quem ipsa sola ingrediantur haberi possit
= 2
2
169 f2 - 1
l aequ. 
( 2, 16-1, 4, 4-1 8, 2-1 16, s-1 32Z. uavis.
le quaeritur serici terminatio. Videamus an
unul
abscissae vero
3840
4096
a
 ad 1, ut L ad 3 seu + aequ. =, mox t aequ.  
12
2, 16.) C item aqu. . item L item 1
et generaliter
C aequ
4, 4- 1
aliquo modo ex ipsis idem componi possit.
2+4
E
V
a Z ad Var -a et L ad  v - Jrav, seu 1 ad 15 vel 240 a 151130
secundum
5 12
e
erit = ad 3 vel 12 vel 48 vel 192, id est ad 4- 1 42
laequ L
est autem
vel
e
terminatione, ubi a. b. c. c.
2 162t -
1
a
esset opinor
aequ
1627 -1
62
_ aequ 16(2) - 1
vi deamus an calculo aliquo in 16
il
aliquid in quo non extet Z. hoc enim posito in epsa
sunt aequalia habebitur quaesitum.
= 2. Fingatur curva cujus ordinatae sint ipsae + id est avel berc
videndum quae natura curvae talis.
aequ.
ponte sufficit etsi non ex solis a. b. cad componitur
adhiberi e ita, ut impatae poni possit aequalis sinfinto
e
1640
2 ad pita laol
L
4
2
 mance
ec
a+

## Folio 23v — 00068033:0046
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000046.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 28 lines, status machine
011OII
a LX aequ. 24
X = X a
C-dx
d X aequ. X - X. dx
2
a  X
91dy
CX
y+dy
a X + bx + C X + d X et
X aequ...
yedy
lX aequ d X + x rdx. jam X + dx H X +
d
ytdy
dx + Vtdy, ytdi 1 gedus 2
2
videtur Lgis esse aequ. y, X de. Nam quod dus attinet, non potest ejus ratio, haberi
sed quid si sit ex aequ. 0.
re
sit v.a
Hoc verum sed na inde dfo
C V. aequ a fiet: do aequ. 0 et quod
(simum est si 1 non ingredietur quantitatem sed haereat in exponente tantum
non video quomodo pose postea dus ingrediatur calculum
a
ae 2