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# Piece: https://leibnizlegible.com/api/records/566/text
# Catalogue record: 566 — Invenire generatricem trochoidis
# Incipit: BP, p. GC, c. dx : dy :: y : p. Ergo dx p aeqv dy y et ∫pdx aeqv 1/2
# Date: 1676
# Akademie-Ausgabe: AA VII,8 N. 077
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=566&katnr=58143
# AA VII,8: 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-8
# In the Akademie-Ausgabe: AA VII,8 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdVII8.pdf#77
# Work: https://leibnizlegible.com/work/00068105
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 10
# Folios: Bl. 8 (from the shelfmark LH 35, 8, 10 Bl. 8): 2 pages, canvases 15–16, page ids 00068105:0015 to 00068105:0016
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068105&page=15
# Lines: 74 recognised on 2 of 2 pages, mean confidence 0.85
# 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 8r — 00068105:0015
# Source image: https://digitale-sammlungen.gwlb.de/content/00068105/jpgs/default/00000015.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 59 lines, status machine
A
AF. TE: dx. dus
dx: dy:: y: P.
Bp p. GC, c.
Ergo de P aequ dusus
Spax aequ  yy. si p. datur
ex data X. Quod si P datur ex y.
fiet X aequ. sdyy
TE aqu:: dx :dg. EC: AB:: de: dx
fiet ECaego de X et TC aequ. TE + EC.
dx
fiit: seu TC aequ d AT du + dc X
2
cx
dx
jam AT + TC aeqo XXaGy. sis ATaeqo D. es+
s
fiet (61 +72 aequ xx +vy sunde differentialiler7
tiet:
 Odb + Z lZ aequ, xdx + y dy
e
AFA AT: AE:: dx: A de seu A qu t=X AE dx
MA: _E MB. seu + -X : X :: AE: BC, y.
at
Ergo AEaequ. +y -xy. Ergo AIago ty -xy dx
X de
est autem + aequ. y du. Ergo AT seu Daequ. 3y x- y dx
dy
Xayde de
jam data curvo quadratura datur (dc. et eadem data
datur
yy
ydx Ergo data curvae quadratura datur
Ax
dy
quam recationem in curva
praesenti habesent AT. TC. AC. eam in
aCB. Bp. PC
trochoide ejus habent
A T ductae in GC, seu e in dc sunt in trochoide
ipsae y ductae in ax + dp. genemtricem
Data curva invenire, ejus dividem, ef
nochoide
educitur ad hoc problema, data curra invenore
elemento caroqdi
dala Tirchorde curva dantur enus AP. ergo et
differentiae ipsarum. sunt autem ipsae eadem
rochoidis
cum ipsis Gc forchuidis, seu cum schrvae gerratiiais
genratio
escil vala sed non contra
Elementis. Eut contin
ircubit exdata generati methodo inveniendi genera
e
dato
hicem, non habetur
mothodus videndum an habeatu
1. +
+Ea

## Folio 8v — 00068105:0016
# Source image: https://digitale-sammlungen.gwlb.de/content/00068105/jpgs/default/00000016.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 15 lines, status machine
methodus invenicnbi curoa, elemensi quaesiti
in
et desideratur ut ex datis differentiis ipsam
Ap habeatur curva; qseu ut ex-
datis X et dx +  Aqu d dyy aego dx x
x
ag
fiet X + dyy A) dx X et Xde + dyy aequs
u
aequ s du Axx.. seu 1XX + L yy ago ax axx
unde patet opus prius esse ad quadraturis, adsioc ut excata
methodo invemendi tro dividis generatricem, reperitur method
pro elemento curvae puius enim inveniendu ho
grochoides) curva cujus A differentio Ax. sint datae
uod fit ut dixiper quadraturas.