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# Catalogue record: 39834 — De seriebus convergentibus et qvantitatibus eodem modo compositis.
# Incipit: Terminatis huius seriei est sector Circuli Ellipseos vel Hyperbolae
# Date: 1679-11
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=39834&katnr=39098
# Work: https://leibnizlegible.com/work/00067993
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folios: Bl. 309–310 (from the shelfmark LH 35, 2, 1 Bl. 309-310): 4 pages, canvases 619–622, page ids 00067993:0619 to 00067993:0622
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=619
# Lines: 123 recognised on 4 of 4 pages, mean confidence 0.84
# 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 309r — 00067993:0619
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 310v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000619.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 54 lines, status machine
Novembi. 1679. ve seriebus convergentilius et quantitatibus
em
itamde Mesolatis
et de inventione indicums seu rexponentium affectorum per
est sector circuli Ellipseos vel
Analylice haberi non posse quantibtem
eadem modo compositum ex X et Y quo
et Q et v. patet, nam ca quantilas
quae ex a eodet modo componitur eodem
formula: Z⊓ C + dX + Cy +fxy
empo
s.
eodem modo compositis per anguli sectionem
Terminatio hujus Serici
Hyperbolae
modo composita est ex a et b.
sit
7 n C + dZ + ex +fqr
a +ab
ba + ba
a6+ 3
2b
a
I. B C + da+ daeb + e ab + eb + fab+ faeb+ fab
 B C +
destrnctis destmendis fiet.
+ dab + dab-
+eba
12fab 12fa b2
dae td at faciendoque d+C p 0. siet:
da + eb + fab = fab aequ0 quod fieri non potest
in definite nisi ponantur d c. f esse 0. contra institutum
loco a
et b
1
faciamus
l. fiet
ponamus fno compendi, causa, et ap. .
3M
13Y
da + cb 70p d, h + e, l
Em
G
quo si hinc potuisset inveniri
d evanescentibus. l. h. haberetur
M vd Y m et Y. ex solis
propositu. Excogitanda igitur sunt theoremata emn  in aequationibus
transcendentibus, quibus ficit ut indeterminatae evanescant. d hoc
loca id fieri hac modo non cpotest ergo nec fieri poluisset si 
reliquissemus nam cusus generalis specialem includit
cagentus
futer rem tenlemus hoc moio
.
se

## Folio 309v — 00067993:0620
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 310r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000620.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 43 lines, status machine
ponatur
1I.
quidare
Y- v.
retentis y et . toleantur a. b. nempe
 eo consilio ut duo termini responventes, ambo sint simplices, fiet.
rgo fiet
ap Ey
y-
ib
eruntque duo primi termini
2
72n-yn
2y-V
V
Gucg
saso
a
2V- 271
dass.
y - v
+
seu (t vyfv
2, y-v
Hinc jam inter
openandum assumere possumus arbitrarios
ex ponentes indeterminatos,
ut
y
v2
Cum alioqui si esset V composita non posset D exprim
nisi per seriem infinitam, ut notum est.
sed
ta si poslea inventione ipsius Z tollere
velimus aequare velimus v verbi gratia
luidam
omposito ex. v. etc. res ut tollamus omnes indeterminatas
res redibit ad indices seu exponentes affectos Ex
quibus jam tum hobemus quadraturam Wallisii methodo
sempe si ponatur
Caeque   V a - v
 ita ut V. maneat indeterminata constat inven-
tionem ipsius Z pendere a quadratura circuli

## Folio 310r — 00067993:0621
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 309v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000621.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 25 lines, status machine
Hac
hoc modo
problemata indices
hhujusmodu inveniendi
muta infinita ad quadraturam circuli revocari possunt
tum scilicet ostenditur ex hoc rujusmodi
calculo dati
tali indice haberi quantitatem eodem modo compositam seu
Quadraturam
in hac serie adeoque quadraturam.
autem ciruuli redux + ad simplicem inventionem cujusdam
logarithmi compositi
nec pronde nempe
1+ + 131.- 
a curva tali pendet verae ab inventione ipsius 
 hae
curon exprimit est proportionalis circulari tianscendenti.
itque ita ope horum verorum exponentium
indices illi affecti inveniuntur
Nota quia fit bp
2y- v
hinc patet
posse metolabum sectione anguli q quodam modo
effici, nempe  inventionem duarum mediarum
per anguli trisectionem

## Folio 310v — 00067993:0622
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 309r); this page is its left half.
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