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# Piece: https://leibnizlegible.com/api/records/1202/text
# Catalogue record: 1202 — De possibilitate quadraturae
# Incipit: (1) a aequ. t/1 - t³/[3r²] + t5/[5r4] - t7/[7r6] + t9/[9r8] -
# Date: 1679-04-09 (79-03-30)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1202&katnr=58742
# Work: https://leibnizlegible.com/work/00068073
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folios: Bl. 78 (from the shelfmark LH 35, 7, 1 Bl. 78): 2 pages, canvases 155–156, page ids 00068073:0155 to 00068073:0156
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068073&page=155
# Lines: 120 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.
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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 78r — 00068073:0155
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000155.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 55 lines, status machine
.
Terminoru
in finitor  explicando
arbitrarius infactis datis adeoque
S
nisi tantum destructis earum
altioribus. data aequationis 2 eris
ita ut infiniti illi  numeri illi b. C. d. F.
sit tantum terminorum hom co efficiente
numero semper finiti, licet expressis
miditinte et e
ut postremi-
quilibet ex ipsis poni possint
Minto aquales it
Cunc
erit inventa ejusmodi relatio generalis
∞
aut demonstrata impossibilitas Sed
pro speciali relatione salis est
poni relationem indefinitem finotam
indefinitam seu generarem inter duas
ex hus tribus literis, ejusque ope tolli
untm liberam ex aequ. 1. debet inde reutur
P
aequatio fimin, vel infinita divisibilis
per ficutam Necesse est enm duas aequali
a
solas,
Relationem inter duas litera exprimentes 
habere commuinem divisorem. Quod sis
impendio et simul casim speciali cipsulere
possumus forte sic facere possemus faciendo:
a aequ. 6+++ dr +Et et
idenim semper
n+x + +cY +∞ treu potest eu
datur fuae aequatione pro tribus literis a. t. Y.
atque hurc valorem subestituendo in aequ. 1. inde
modibit nova aequatio solam exhibens
relationem inter + et Y. quodsi jam
intactis ( V. S eq A. L.B etc assumatur
duta indefinita texprimen)
finistae data
 et r. finitum. eaque dividaso
aequatio aabitnona
datam
elationem inter
relationem indefinitam explicatus ita ipsis td.
arbitrariat
assumtis literis nunc β. V. t. etc. numero finitis ut procedut
2
10
6.
et si id fieri potest habermus quaesitum si non potest impossi
ita
formulam indefinitum artitrariam comperetuirelatioii definitae

## Folio 78v — 00068073:0156
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000156.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 65 lines, status machine
Martii percexant
penultimo
1679
De possibilita se quadraturas
Hic depine methodum analytiminvenimus literater
Egren de usu calculi, in aequationibus infinitis. Hinc
pabet et quam utile non adhibere unitelenilocor.
a aequ. b= l + l
1. 3r2
s
4
+
oro
+
11Y
si jam quaerimus an
generaliter possibile sit inveniri relationem
finicam generalem inter arcum laugentem
et radium sumatur nova aequati
data ieneralis indefinita exhibens
ed
etc.
dosito aeacce et r. radio. a arcu
tangente.
pe
relationem inter arcum tungentem et
Tadium quae eruliait pro erit pro
volibet casu speciati relatoas
Taigante cuuius libet arcus dati
tunc enim sperialis relatio dabitur ope
X inte
conjunnendo duas aequationes et unom
t literam; conjunctione tollendo. rodibit
denem relatio cuilibe casui speciali duatum
darumlibet ex his tribus liseris, cuie vet
censui speciuli upplica bilis.
s
Crer
e
aequ + a+ dt+ er+ faetere
a aequatio in qua literae
b. Ca d. l. f.
omnes datas non
oit
ponuntur datae (quanquam
ex ipsis datas esse infinitas
mgltiplicetur fei per formulam 3. arbi
sit necesse sufficirea
param intin cam inde finitam.
1
V
et
5
+x
N- 1
et ma + nf +potgaeml.
producto adiiciatur aequa
 si placeti
eriqus. pontr
ver
veram. Quod si s
id quod provenit ex summa
ex aequationem quae explicari possit
per
fintam convert possit