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# Piece: https://leibnizlegible.com/api/records/568/text
# Catalogue record: 568 — Curvam invenire datae figurae proportionealem
# Incipit: [dc]² aeqv (1) [dx]² + [dy]² dc aeqv. √[dz² + dy²] aeqv (2) e dx
# Date: 1681-12-08 (81-11-28)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=568&katnr=58145
# Work: https://leibnizlegible.com/work/00068105
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 10
# Folios: Bl. 10 (from the shelfmark LH 35, 8, 10 Bl. 10): 2 pages, canvases 19–20, page ids 00068105:0019 to 00068105:0020
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068105&page=19
# Lines: 92 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.
# 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 10r — 00068105:0019
# Source image: https://digitale-sammlungen.gwlb.de/content/00068105/jpgs/default/00000019.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 38 lines, status machine
28 Novembr. 168
Curvam invemre
datae figurae,
proportionalem
de aequ dx + dy
(2
Ac aequ. dx + du aequ e dis
2
e
(21
Z + du aequ ee dX
sumatur aequ. 4 relationem exprimens
inter X et Z. item aequ. 5. relationem exprimi-
inter qet XHy  Ex aequ. 4
quaeratur valor ipsius aZe, ex aequos uala
albeatumm
aequ. 6. Et ex aequ. 5valorizius duss et
habobitur aequ. 7. substitutis ris vatoribus
ex aqu 6. et 7. in aqu. 3. habebitur
aequ. 8. per sola ubi solae 7. 1. e. X, sine
differentialibus Collendoque y et Z. restabit
sola equ inter per X ex aequ. 4 ets
restabit habebitur aequ. 9. in qua sola
 supererit X et e. havebiturque aequatio
identica, funto facilius resolvenda
quod duplices arbitrariae
Brevius si marum differentiarum per
X expressarum quadrata in unum addita
componant quadratum ipsius e.
ut sit eago aa erit ee aequ
a Atx ei quad si e sit aa eut ee aequa
X
(2
Ergo debet quantitas ad componi ex
Tabil
duabus. sed videorem non predere
nisi data saa
X

## Folio 10v — 00068105:0020
# Source image: https://digitale-sammlungen.gwlb.de/content/00068105/jpgs/default/00000020.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 54 lines, status machine
datae figum quad
curvam prxspationo
se dx aequ. 8y. vax aequ
Scodx aequ . et sit vv 40oco aeque
quaeritur Z et _. h VD + coco dx aequ. edx aequ
Ergo WD+ Coc aequ du e dx = dZ des
+2Va x
e dx aequy. (0 dx aequy.
(∞ ax aequ. 9. vn tcocoaequee.
fer: Er seu v aequeecoto
fiet 
ec coco ex aequ. Z
ee 0co aequ vo fiat v aequ e- co h
qu aque C+c0e- corqu e-o t
a
seu etcd aequ. e=cok seu eh- eaequcotot
qula
a 
seu eti- ea aequ 0a + con. sive
a
et W0 aequ. F- a C et vaequesta
R+a
h la
seu vaego et et ph+ . seu vaeque e
et vaequ et eti tahe. sive
a
a
tiata
vaequ (ett etaehre, seu Vaequahe
ha +abe
uaeritur ergo (ahe
1ta
ax ae quque
hh+aa
edx aequ P. eax aequ haraa des
ah taa
rahe dx aequ hh dzue F aa due
baa
aequ thca
aE
hh aa hhedx-aa e dx aequhh dgraadae
fietque (hhe dx- aafedx aequ fhhdcs fraag
- aay
et ita tantum ans est sumi quantitatem quandam
n
indefinitam datae relationis ad X, cujus quadratum
khni e ductum exhibeat cucum quadrabilem quod
ut sent et idem quadcatum in quandam diffecen
tialem ductum ex tribeat etiam quadrobilem. fiat
d aequ.  dgifiet 8 aequh. et habebimq:
the du- aaqu aequ. Shhdh taa. sen
fieistit edx= aaque aego id + aat. sit denius
ih aeq
 habebimus: Zax aaq