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# Piece: https://leibnizlegible.com/api/records/1176/text
# Catalogue record: 1176 — Scheda quinta Tentaminis ad dimensionem arcus alicuius particularis
# Incipit: Invenimus [dt]/[dy] aequ. [Sonne]/[Mond]. secundum valorem characterum
# Date: 1679-03-20
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1176&katnr=58716
# Work: https://leibnizlegible.com/work/00068073
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folios: Bl. 41–42 (from the shelfmark LH 35, 7, 1 Bl. 41-42): 4 pages, canvases 81–84, page ids 00068073:0081 to 00068073:0084
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068073&page=81
# Lines: 259 recognised on 4 of 4 pages, mean confidence 0.81
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# 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 41r — 00068073:0081
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 42v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000081.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 53 lines, status machine
Invenimus
ascheda quinta
Tentaminis ad
de peculiau dimensioneu arcus
abicurus particularis.
et
dy
t
characterum , et D  naulo ante
 et ex posita relatione.
expressum.
Quaeritur jam relatio aliqua
analytica inter  et y huic tangentium proprietati
satis faciens
finita:
Id est assumatur aequatio inde
t quttere
a + bt + cy + d Fy + e F + fy etc. aequ. 0
Unde nota tangentium Methodo fiet
es
dus
aequ.
quantitates
aequ.
.
aequ. 6
..... aqu. 
6 et
, seu
e
id est dabuntur
adeoque fiet:
6D aequ. 09
quae
taequatio ordinata secundum  et V. coincider
debet cum aequatione
ea posse comparari.
ec debet cum
Qu
S succedat comparatio habemus modum infinitos
arcus
quada in rectas extendendi, uinumquemque
methodo peculiari. et jem si dabus aliquis
arcus in rectum ex tendendus proponatur
a
ut ans
l tatem idt posita ipsa aequ. 0.
inde datus valor oriatur caeleris omnibus
manentibus indeterminatis Aue ita
etiam infinitis modis poterit ede idem
arens in
rectum exlendi, uos omnes coincidere
necesse est, et demonstrationis at

## Folio 41v — 00068073:0082
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 42r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000082.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 44 lines, status machine
constructionis causa
simpliciores.
clrgi possint
Quod si comparatio non succeda
hinc certi crimus
specialem arcum,
datum aliquem
vel etiam ullum
aarcum speciali aliqua methodo
ut
extendi in rectum non os
-
Hoc a autem ita demonstro.
Ponatur arcus analytica  in
rectam ne extendi posse per analus finde
ordudari posse Geometria ordinaria
seu expressionem ejus analyticam ordinaria
haberi sive dari posito dari
vid
aequ. 0. et si ignoretur qualis sit
orhit or relatione ad lvel aliam
a
cognitam.
Quod si ergo datur talis
arcus quadrabilis hoc modo velsi datae
quant
dabitur
ef a poterit
et intelligi aequatio V
NoSe.
000 vus
) in T
aequaa
Sed jam me reptrimo. Video enim id non sequi
nisi assumatur uno arcu quadrabili vel
non quadiabili quardrari posse eadem
regula reliquos omnes iem quod cum
mec
sit impossible statum sequeretur
ircum ulcum posse quadrari reaque puro cepto
)in
habendum dem cesse impossioem
tali aequutatalem aequationem ess
impossibilem alioqui possent y

## Folio 42r — 00068073:0083
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 41v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000083.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 65 lines, status machine
inveniri per Communiem Geometriam
a.
sic ergo assamendum est:
Lvora
adeoque et
∞ vuh ita enim
V. a in 
aequ. a
communis
y non est quantilas analytica et fieri
necestanos  et
potest ut inveniatur aliquis arus positis
ms
L ic 2
et a
aequ. 0.
aequ. 0.
licet generaliter y et a non inveniantior
s
porsso aequationis eennalis
Assumta jam huc aquatione utcunque
utique poterit inveniri y ex dato arcu et
proinde describi curva hujus modi ex supposita
Circuli quadratura
rum posito scilicet
invenori y x pure ex dati t et a
facile enim judicari potest an aequatio ista sit
.At inquies etiam paulo
aute assumsimus curvam bec hujusmodo et
se
impossibilis
mgilominus aequatio cial impossibilis
Recte et ideo video jam non sufficere
hoc assumeo, quomodoquoniam a et b
havent inter se quandam relationem differen
dialem haec ergo substituenda est quare
ita praecedemus: ita videbimus impossibilitate
uti eam paulo ante deprehendimus. Itaque
dvid. NV. a) .ao
Calculo dfferentiali inde fiet:
s
y. a, ay
+
avs, in
V. a. in.
V. a
unde fret t aequ
dys
aequatio generalis:
t
V
and
aequ. a at
ssumaturjam alia
b++da Fey+ fcatgtus +hay
6 fer: R9aequ. OE quae aequalio ordinata secundum
+l+F ma + ny MM aequ.
A2
a
nt
 8 +. a. y. comparetur vel ipsi 8 iniho datae aequatio
i, vel assumtae 2, nam si unicomparari potest comparari potest
ag.
aeq
arisi hac comparmtione litere artillanae determinabentur

## Folio 42v — 00068073:0084
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 41r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000084.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 97 lines, status machine
pssu nan
qurs u
onihna
f.331
p  uo edat 
nio quiq unoni
no sietu
b.9. 9uusse
quigrad disuoe
E-
suiontu
a
5
ac
e
sugao tliiait, spit
qu
d
e
a
3
5-
+
e
geu
e
eri etium finita aequatione oplinde
idculica ad numeri rationales
notun dun gaavent, abo in negnozen t Eht. saein ranoy. V vyums. 6. a toinus no ingehkniu esem
Hser epesuiptum
um vided nhib
or  a diab .te. H.  ibpne 4 i
nos dccompariitione
visunuite lerenam aequ. 8 et aequ.  4 sates
qoium niter se coincidunt et ab initio compatrat
ossant ergo mutilis poste comparatio per
Viferentialis sed vera ratio siendi vera
osvilitatem suppositionis haec est: sumta
rasatione
aequatio differentialis h.  et e in ea
n c. soteatur a; ope aequationis initio dalae
Y et F relationem
E sexstrimens. sed hoc mutile potumus ab hgitio
1+ fVat itaque iau
iptimum fore sicrem revocare ad 
 aequationem unicam possibilem posstta
a Aqu. E+
Z. assumatur alia hurgmod
f5
et pro a oere
in Xq. 8 ponendo hunc ejus valorem abebitur
egratio in qua nula amplius erit a et
infinita.
s
Ex ea extrahatur Tadix
ut Dinveniatur y constateist pure et 
rasro natiler
2
ed difficile est nonnisil judicur
de impossibilitate in hingmodi seriebus
Et nil video quod prohibeat
et invente valore ipsius
et possibilis, etso
V p ex aequ. 8. judicari
non sit explicula
iverium gnlinemus eam lincariter, et exami
hungo limites qui possune facere uno innob
entemus eos evilare
fiat series finita aequatione
Gidetur tandim les redore etiam
c examin andum reduci posse
e
sed tano non opuicurva) an possit poni a aequalis cuidam tangentis
 ad stangentem relationem certam habenti sposita terta tangente. usimarum
etis
4
2
possero angente Radio 1. poniatur cungense ouq b+ c + d A et, etc.
2
=aequ.0. quantitati sinte. Rursus ponatur ago aequ. Bmanst +9 et
s
aequ
aequatu infinita est in aequ. . prose ponatur eiqualor ex
e. maixime in definita, ducatur
s
estabit aequatio sola inter
oco at ponendo
aeqratione
3
et
5’et qua
fres. crs 4 et pro terius vafor in egb. F. exo ce u. l. fet aegl. 5 quuo est
aequ. 57 et seud
ni
vided
infinitis
d