# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/861/text
# Catalogue record: 861 — [Aufz. zu Nova methodus de maximis et minimis]
# Incipit: Editae hactenus methodi talem transitum non patiuntur, sive cum
# Date: 1684-07-31 (84-07-21)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=861&katnr=58442
# Work: https://leibnizlegible.com/work/00068043
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 25
# Folios: Bl. 32 (from the shelfmark LH 35, 5, 25 Bl. 32 (= 41663)): 2 pages, canvases 63–64, page ids 00068043:0063 to 00068043:0064
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068043&page=63
# Lines: 147 recognised on 2 of 2 pages, mean confidence 0.78
# 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 32r — 00068043:0063
# Source image: https://digitale-sammlungen.gwlb.de/content/00068043/jpgs/default/00000063.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 99 lines, status machine
a ab ordinatis
Editae hactenus mesbodi salem transitum non patiuntur, sive cum Cartesio ad hibeas
TA, sive cum Slusio T_ unde etiam praeciptunt, ut fractiones p irrationales, quas ingre
ditur indeterminata, tollantur. Sed si ehibeas ipsis e Y e YB, T) dx quartam
proportionalem quam voco de, s  tum ipsae du in locu ipsarum  substitui possunt
perfecta procedit substitutio ipsius dus pro y servatis regulis explicatis. Patet
tam hanc Methodum porrigi ad curpas ranscendentes, quae, ad calculum
Algetraicum revocari non possunt seu quae nullius sunt certi gradus F modo curvarum
nam si ay. y esset quantilas transcendens exempli gratia dna ordinata cycloeidis
tacum haber pota du eaque calculum ingrederetur, et ope ipsius alta curva transcen-
des esset determinata, etiam ape dus u taden utique tangens novo currae
ope, du, (quae haberi potest, quiu tangens Cycloidis habetur) determinari
posset. ipsa mutem tangens cyclocidis similicetaa
haberetur) ex data proprietate tangentium circuli. Ario autem melhodi appri
alia autem methodi propositae ad pro curvis trauscendentibus restrictae sunt ad certas
suppositiones. Placet autem eximplum calculi proponere, sit aequalio
n
a+ bX in C∞XX
+XV99+7y+. 7
quadrat. X +fx
arqu. 0
th+lxim
compendii
puncto exprimens relationem inter X et y, seu inter AB et XZ H primum causi
mada 
oducendi
pro faciamus +bX ) cubamus U pro C- XX, P. pro ex+fNX, q. progg +gy, Y
pro hh + lx + mXX, J. fiet  + ne +ax Ir + yY aequ. 0. jem
quae d
cuibam ex calculo nostro constat esse et
ungal et d ut aequ.
qe
qc
G aequ. + Xdy = ydx; yy per superliora.
ee (+) 2npadq (7) 99nap + qqpan,: q
et daxsr, aequ dr- exr +  dxar et d y7 aequ. X
aequ. ()
2 ex
yyd
es.
2Ir
+
2s
quds
a
2y 4ydy  2sI5. Ergosur
omnes istae quantitates differentiales (a d X usque ad d 27) erunt
in unum additae facient 0. jam du aeq. bdx et dp aego - 2X dR
aequ
t
apxy dy
ir
+ dx
dx ad dyr hoc est
dato) ad
2Fxdx et dr, aequ 2y dy, et asaequ. Cax +2mxdx
tea
Ergo denique fier: +Xdy
2
=
4
Termaliset
dxGe2. aCXY. ∞ISK sad
+)
e
(+) Enpee+2fXdX (
+
l+2nXax 
25
a XY datam, ut-
)-2nx + pb +
L
q
Xy
ry a
2y dy
 dx
xax+ pbax
qu
aeg. 8.
senfint
it angens XT  ex puncto 
+)
s+ -
2y
ad
1
(+) ine et 2tx
r(+)) vy (+2 nX dantur autem  et Y X et y ex dato
25. Y
curra ad cujus tangens quaeritur
M2+ 
la
puncto Y. dantur et valores liferarum
pam sclis impliculum, ideo tantum ascripsimus, ut modus ute
superioribus
na
eut
H quoritu

## Folio 32v — 00068043:0064
# Source image: https://digitale-sammlungen.gwlb.de/content/00068043/jpgs/default/00000064.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 48 lines, status machine
regulis in calcur etiam difficiliore utendi appareret.
intelleuri
Numc srostat
usum in eximplis magis  fac qua magis ex positis ostendere
d a
Data sint duo puncta C et E et redu in eodem cum ipsis plano
qdaeritur punctum rectae F in recta ita sumendum, ut junctis
CF, FE, sit rectangulum CF in aggregatum rectangulom
CF in datam h et FE in datam Y. omnium possibilium
minimum hoc est si a repraesentet densitatem medii inter
C et Rece eeSF et rdensitatem medii inter C et 8, quaeq
e
per
latuat
tur punctum Fitale, ut via a C ad Esit omnium possibilium:
facillima. Ponamus omnia ista rettang ulorum angregata
possibilia repraesentari percuro ipsas KV cuivaG
V
ordinalas ad rectam GF
quersu minimam Xm.
quiadantur puncta C, et E
dabuntur et perpendiculares ad se
nempe ex Etq etisr quam
avocabimusete et C qua vocetur
dabito
 et pese procerea ipsi
pqe quae sit P ipsam
autem gF vocabimus
LX
a
ent e
pF
l
p=X
s
et
CCF, ScC+ pP- EPXIX
e
et EF, SeC XXX
et nyjugatum rectan
gutorum erit
quos satlg. veritis ca posito
ordinatam curvae
quae bie, tale aaperatum
repraseutantem, fiet
d
hscc+pp 2CX+XX +Y seex
Ve