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# Catalogue record: 1177 — Tentamen ad dimens. arcus particularis. Scheda sexta
# Incipit: Sit ADR arcus quadrantis cuius centrum Q. AD arcus quadrante minor.
# Date: 1679-03-20 (79-03-10)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1177&katnr=58717
# Work: https://leibnizlegible.com/work/00068073
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folios: Bl. 43–44 (from the shelfmark LH 35, 7, 1 Bl. 43-44): 4 pages, canvases 85–88, page ids 00068073:0085 to 00068073:0088
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068073&page=85
# Lines: 221 recognised on 4 of 4 pages, mean confidence 0.86
# 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 43r — 00068073:0085
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 44v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000085.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 42 lines, status machine
ess
Tentamead dimers. arcus particularis
e
sileda senta
soleda F
bi
a
ejusque resumantur literae
10 Martis
1659
u
ADR quadrantis cujus centrum Q. AD arcus
quadranteminor ZB sinus complementi. AT tangens arcuD.
e2 secans ejusdem. Sit curva coco erc. ehibens
euius ordinatie Bco exhibeant rationes secantium
ad arcus seu ipsarum QT ad arcus AD, patet
primum arcum (incipiendo ab A seu ponendo 
 incidereni A. sine AD esse infinite parvam,
secans vero ei respondens erit ZA. est ergo ratio
sicantis ad arcum hoc casu infinita repraesentanda
per Asymptoton ATW. similiter ultimus prcus
ADR est quantitus finita, at secans ultimus
est quantitas infinita. Ergo ratio secantis ad
prcum in hoc ultimo casu etiam infinita est, quare
re praesentabitur per asumptoton aliam ghL.
Curva autem coco inter has duas asymplitos
describitur, unde patet ab utraque parte verticis
2 jub quam patet primum accedere a partibus
W, versus re ac ubi s AG, et ubi satis accessit
seu ad minimum ab ea distantiam pervenit, quod
ponamus fieri in vertice 2c, eersus ab ea
discedere. Quaeritur punctum seu vertex 2c0,
vel potius quaeritur
punctum ei in axe
respondens 2b. e
omnium Beo minima rit
tangens per tam ducta per 2eo ipsi axi AQ.
a
Si 2 Beco est urvae
parallela. Primum ergo quaeratur
curvae Wo co tangens, ad
sit

## Folio 43v — 00068073:0086
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 44r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000086.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 57 lines, status machine
sit Tiangulum Characteristicum ut indefinite
parvum coGL. In quo coG parallila AB AXI LG paralleta
Aco ordinatae. CoL portio tangentis AcoL.
Est autem coG aequ. dov posita 6V aequ. QB. simu compl.
et B0 appelletur co. ordinata curvae erit GL aequ. deo.
as
B
BC
esse
f
S
a
a. N
4 (+ ds
aco
BB
BCo
= S
a+da a
Ergo 
2 K R
Est autem W aequ. s
posito
1
ca saequ. secanti ET. et a aequ. arcui AD.
Ergo fiet
B aequ
BC0
aam
aequ. 
d.
a
Est autem
d.
a aequ.
aequ. (a+ a ds C a da
a do
a ds- das
a  da a)
si jam eo sit vertex ipse 2co et eo casu Bco manente
finita ipsa  _ DB sit infinito
tangens
D infinite ab hinc absit, adeoque cod sit ipsi AG
parallila, patet, fore rationem BB infinitam
co
nempe quae infinita bB ad finitam pa. ergo
et a dov ad ads- das ratio est infinita
quare em ad cum ado non sit
infinita, necesse est a as - da( ejus com–
paratione esse infinite parvam adeoque fiet
a ds - da ( aequ. 0. seu a aequ. da
d
sit triangulum  circuli characteriticum
cdM erit oD ipsa da. jam  (aequ
v
 qu. quia Radius L b est media proportio-
nempe Aq vel a

## Folio 44r — 00068073:0087
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 43v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000087.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 61 lines, status machine
nalis inter g+ secautem et QB seu N sinum com-
plementi. Erbil a aquese Estgo
as, aequ. 460
fit ergo ex a aequ da
ovr 
a aequ
dae
or
aequ.
dov L
Est autem De aequ. da. et
seu B Cequae
o
62
a aequ.
ov
da
e
ds
da 6.
do
D
aequ. 
aor
Pra
jem Trianus.  characte risticum Circuli D
DHK
simile est Triangulo
ipsi
eDK (quia angulus
DAq aequi angulo  D) ergo erit
aDa on e
D
e
ite nimorum
 ex D demissa DH ipsi
ia BQ aequaeli et parallela.
erit Do
Won
aequ KD, seu _B
DHaequ. B9 B 
qu. 60.
ergo
Ergo fiet  aequ KD, sive a aequ. KD.
V
itaque arcus sequo agitur, nempe A2d est
Est autem KO langens complementi seu
arcus Rd..
Ergo arcus de quo
agitur eta A2d. (ubi scilicet minima est
ratio secantis ad arcum) est ipsi 2k2d
tangent sui complementi
aequalis.
seu arcus R2d
vae Videamqus jam an analytice
investigari
minimam
arcum
possit
Secen habens
rationem ad tuum

## Folio 44v — 00068073:0088
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 43r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000088.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 61 lines, status machine
Quod ut fiat, videamus au fingr
possit curva analytica cujus
aut
ordinata crescat pariter ac decestat
quoties quoties ratio (decrescat
sa
quoties latio secantis ad arcum
cres cit (decrescit.). Quod postulatum
videtur omnium postula bilium Hocillimum
quia arcumm valorem in curvae analysiu
nullo modo ingredi necesse est, sed
tantum aliqquid quod aliu mara
D
minusve semperr esse constat.
a + de
S+
d
+ ds
Ba + da
a ) a + da
taNota signa
ipsis is et da-
praesiva convenore;
quia (et a simul crescunt et decrescunt
sit. Sa.
das (as ds a seu fer
Hic pota sigea commune non
Ergo das fpas a, ergo
Ergo
A
das
da quae determinatio
as l
analytice datur
Niminum si qua
pajor est quam aliquus vicina L
sa etiam
da a
dp
a
seu S+d
a + da
erit
a das H da omnis autem est aliqua
vicina major, (alteratio
a
utrame
Eodem modo si spi aliqua vecina L erit etiam a das ed
 utrage
Omnisantem i ali  vicina minor est, (nisi svel a sit infinita aut
intinite panas praeter in Equidem cum LBS+d
a ada sit etiom
a
a daste da An ergo cum = 1 +0) seucum
a 
licitne tunc ponere at ddas
ca saego
a
a +da respondeo
non licet possunt emm alequa ad Nam cum  aequ. da ad determina
venitur, ubi in summis aequ abitas, non ideo est in differentis