# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/36388/text
# Catalogue record: 36388 — Curva quam P. Berthet Osannae proposuerat
# Incipit: A. Annotat Hugenius pag. 80. curvam cuius evolutione hyperbola (circul
# Date: 1673
# Akademie-Ausgabe: AA VII,4 N. 050
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=36388&katnr=Cc2+1112
# AA VII,4: 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-4
# In the Akademie-Ausgabe: AA VII,4, p. 383 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/VII4B.pdf#page=383
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 107–108 (from the shelfmark LH 35, 8, 30 Bl. 107-108): 4 pages, canvases 213–216, page ids 00068124:0213 to 00068124:0216
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=213
# Lines: 184 recognised on 4 of 4 pages, mean confidence 0.76
# 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 107r — 00068124:0213
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 108v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000213.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 11 lines, status machine
Curga quam P. Berthet cannae propojullat ganna mini
ujus tampulegi dumm aream et atia bedi
ritili:
AC,
KP an
lDD AH
MN∞ AC
BR ∞ AD
BIBLIOTHEBA
I
trnimoa

## Folio 107v — 00068124:0214
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 108r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000214.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 8 lines, status machine
BIBLIOTHECA
AEBGIA
HHAIBDEMANa
aA: d1, dti
Ln 1
HR ex d il
d ACxVIK
aR ∞ XN

## Folio 108r — 00068124:0215
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 107v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000215.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 49 lines, status machine
uodqud i volam nouxo ia cdne)
odidu oiroua id d F onua 
ad  eonr 
otr
qnd o.  = tiA ia eedi. p~ L3 1
  A i ABiiua  ad 1
3 - +d 
oonu e +1. =
ne
= ∞ : -. d 2 M. e eA e
ed  pL 5,4 A. GD s F +B
C
 ne NE L E, + AB = 3M. Iu 10  
d. 3 eo d unad moia AIN iasen 13o
 duns e Sauno 3s
d
 C
 asir p a i r
Set = pa1 
Grcpe rEV
dn
= dd 3N sd
alaen  1 
aeod 3. si   ot td quot M ncum
ne at av d.  auti. d
.c
29
H. A
Anop. . si p. C1 4.
Si + a+  eptd su +
nF + d ∞S = E, DE + da 
si CF, p + di
RBCIA.
CHRSAOVEHANA. s mrad ipre pum
s et aillaeuque uint. quia
d 
se eot
on
 ed 1t e d a
e
5. Xi
60
L
un adaa
 _
tue e eno in idia
MIBLIBEIEC -.  1
ut ram
esormo

## Folio 108v — 00068124:0216
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 107r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000216.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 116 lines, status machine
M
n L
at 2a bt β
bit 2aβ + auu ac
ligoetiam ( ado
eilt ut  AD D A
ad DG
pag. 80.
Annotut Hugenius latum curvam cujus exolutione Hyperbola (circularis describitur,) ejus maturam
fore, ul cubus ab X = y - a sit = 27 X5a
ve
+ 
X- y = a. . = X 2XY - 2Xa, +y + 2y a + a, X - y - a
a +. ar X - X + X =
+a3+ aB + aB. () ab + 2aβ + 2ab + 4a (
a
Aequatio hujus figurae naturam explicaus
ita investigabitur Ex punctis e dimittantur
ordinatae ad DC, nempe EM. et ex punctis B, sinus BL
et DL positis X et BL = y, fiet quia DB= a. cidem semper
ent B.y
a X et eodem modo EM posito 
, et DM posito e, fiet
va F V= DE,
DM et quia DE est = a + B, posiso
B esse aucum AB respondenlem pet: DE=
a + β + 2aβ. feq fetque aequatio
hoec, v vel ME=  a +β + 2aβ-3
vel brevius MN sim circuli, in recta
ME incidente posi vocato G
eatquadralum 7e ert
aequale a- 2, vel BN = DM
ergo ME erit = 27+ β4 24 (6
ergo haberi quoque possunt quadrata
omnium ME, sive solitum figurae cuca
uo BC
definient
ductus Fig
revolutione genitum
vactum ubi maxima
sit ptio circuli ABC. sumtisque in eo punctis quotlibet B. ex centro D dmatu radius DB, producatur
eousque dum portio extra circumferentiam producta BE, aequetur dorcui AB. tandem pe omnia
puncta E, transire intelligatur curvea cochleiformis AEF.
centro
Modus hanc curvam describendi hic est. sit modius linea rigida DF indefinite producta ex puncto D
ac circa illud centrum mobilis; inde filum ircui circuli ABC. rigido, circumplicatum intelligaturs quod
in C si placet fixum in A liberum sit. Hoc fil Ac linea tigida in DC constiluta, fitum ita
seuper aperiatur, ut ipsi DF regulae coincidat, eamque ipsa su apertura ab A versus C. propellat.
stilus filo in A. alligatus in plano curvam AEF describet. Idem efficietur, si duo sint
motores, unus qui lineam rigidam crcumagat, alter qui filum ad lineam rigidam quantum
potest extendat.
velut polugoni infinitanguli, latera
Hujus cnvae at invenitumus Tancentes, intelligantur ducta circuli infiniti parvae, AB BD, ex BC.
atque his parallelae a radio producto injodimm productum ducantur rectae infinite quoque paEG
Jam sunta ex chubilis, BB asi B
intelligatur producta
o un
ipsa eF tanens erit ciruli. + manifestum est tuiangula 
n
ponatur
et
quae s
langens
G(2 en usesumilia
to
( Develda ad DG
ad (C) E), ita est (E)B)  ad BF quaesi tam. est autem (C2) ad (G) (E)) ut DG ad D
oregutam ergo tangentium ad hanc cuqvam ducendarum habemqus hanc puncto in ea dato
s inde ducatur ad centrum circuli generptoris recta (ED quae circulum se  arcum xprculi datum
secet ) ductoque circuli tangente Bbi si fiat ut EB ad DA ad  dm extensim ad
l
pa alleta, punctum
() da radium
euit juncta FE curvae tangens
nae vertex
Ut ipsius curvae  longitutinem indagemus cogitandum est latus AB, vel BB aequale ipsi
prodec
e
GE) E esse n latus inscriptum seu chordem sed circumstriplum senta ducenda est perpendicularis e
) in B) putet triangulum (E) (G) H semper esse simile quaecunque sint puncta E et G. quia
quia angulus EGd semperidem et angulus EHG etiam semper idem quia rectus. cumque EGsemps
crescant Arcthimetica proportione, etiam Et+ et HG semper arithmetice rescent. Ex omnibus
autem EH, primum est AH, q cujus magnitudinem investigabimus si aream trianguli ADB quod
irndia
voremus Z dividamus per radium a, fiet Z-
2
2. Vt sequens ita habebitur ut a ad a +1
ita 2Z ad sequentem. fiet: 27 + 27 es posito B esse unitatem. Ergo differentiae omnium EK
authmetice crescentium erunt 27
et ut a ad a + 1 ita s,
a jam si fiat subtruhatur H AH a Eto AB, fiet S-+
42 ad sequentem
a
scilicet quadr BH. ∞ fra + 1.
de
er
id est + 4Z  L  4. et differ dibit
a - +Z + 2a - 824 + 1 = 49
vel:
1 - 12 - 37 - 2 + = + a cn difecdia a 1- 22 sempe eadem cum
per eom sequentes AH Aithmelice crescant: Tantum ergo per nundhos natiales continue mntliphaanda
a
a
est
Tandem additis EH, HG Gradiata habebituo quadr E Cujus radices snt
elementa curvae
Maxima Curvae altitudo est, ubi tangens basi paral-
lela est. producatur FB in R. ubi occurtat basi
Triangula EBF et DBR similia sunt. Ergu.
EB
sive AD
AD Ergo cum tangens
BF AD+BE BR complementi aequatur
arcui et radio simul,. Radii ploductis ocum
curva vertia
a