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# Piece: https://leibnizlegible.com/api/records/761/text
# Catalogue record: 761 — De incognitis in exponente
# Incipit: Ut illae aequationes reddantur tractabiles dividentur in plures
# Date: 1679-05-23 (79-05-13)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=761&katnr=58339
# Work: https://leibnizlegible.com/work/00068033
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folios: Bl. 16 (from the shelfmark LH 35, 5, 15 Bl. 16): 2 pages, canvases 31–32, page ids 00068033:0031 to 00068033:0032
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068033&page=31
# Lines: 102 recognised on 2 of 2 pages, mean confidence 0.83
# 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.
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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 16r — 00068033:0031
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000031.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 43 lines, status machine
13 Martii 1679.
de incognitis in exponente.
et illo aequationes reddantur tractabiles
re dividantur in plures fient
tolidem aequationes ad Logarilhmicam
e X equ. VX + R D aequa e - y
positu se ago xta
c aequ. - y.
Xna
oex
ed
fectal ex facta ex hac
Oxra
X + V.aequ.   (et eaequ
quaa facta hae tres. ex qua haetres
ex
pempe
a
 aequo
ex
X
et
Misr
a +b
X aequ. f+ a +y
Est autem
+ aequ. a
agotra-y
l+m aequ. a. et X aequ
b
2
+ C aequ V. sit y nqu v +x
atq b aequ. v. et C aego X
Erunt ambae ad logarchmicam
et ope differentialis reducentur, ambae
Hyperbolam
ad
Nam ope Hyperbolae et plclou quadraturae
Hyperbolae et calcploram similium possumus revocare
calentum transendentea culcuu exponentium
ad calculum quadraturatum curus oi vel longentium
et
a  differentialem, qui landem reduenum suppositis

## Folio 16v — 00068033:0032
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000032.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 59 lines, status machine
quadraturis reduatur, ad figuras
communes.
s
Quadraturae autem
et serres infinitae eodem recidunt
et possunt omnia ista utiliter revocari
etiam ad periodos decimales seu
reguras charactevuus continuandolum.
d
Quod
Las
d
prprie de
posite tam
2
posito b esse constantem et iL
esse inconstitantem inveniri
L
potest, ope Tangentis logarithnicae
Sed difficilius videtur idem
decenminare cum
d
est
quando tam X. quam
videndum an ut ex priori
videndum quae sit curba
X aequ. b.
m
esse ipsam loganthmicam
inde X aqu b
haberi potest ejus tangens.
L variatur
e
duei possit
Imo jam video
Ergo
et enim
Ihinc jam
quic at huo tangentem quaritur d tungens hujus
3
3
Querauu
a aequ.  uit faqu.2
-
 4
X
C
L 4.
X+
cc 3.
2 4
 id est quaeramque 3-4 +4-7
est autem 3-4, seu -X +XYB aequ. X ax et X- X aequ.
2+1
 dat
dx seu X- X ego ex2 Ergo d aequ.
C
aequ. N dx + dx Z idest posita x aqu. E. sed an
lccat cidendum