# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0103
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0103?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 52r, page id 00068198:0103
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 51v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=103
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000103.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 110 lines, status machine
# Lines: 110 recognised, mean confidence 0.80
# 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: the recognised lines in reading order, one per line.

y. Cddz: dZue
X: a (2)= (ddz: dv. firt dy: dx  (3) = dv: d
sit jam aequatia data (4) in qua yda et x: a, et dyidx Substituendo valores
habebitur aequation in qua sidaz: dZ et sdaz , et dvidz. Unde differentiando
tollatur s, ddz: do, habebitur aequ (6. in qua fddzidzue, do:dz, et ddv: daz
Assumamus constantem pro arbitrio, sed tatem, ut tollendo eam differentiando
novus habatur valor ipsius s,daq. dZ
X: a (2) = fdz: v fiet dy. dx (3) = v. Z
X: a (2) = s, ddz: dv. Fiet dy: dx (3) = du: dz. sis
ia = (1) f, dZ. Z
substitendo valores
jam aequatio data, (4) in qua y: a et X:a, et dy: dx. Substituendo valores
y: a  (1) = si ddz: d7
habetritur aequatiu in qua s, ddz: dz; et s ddz.do; et do:dz. Unde
differentiando habebitur aequatio tollitur s, ddz: do, habebitur aequatio ()
rationu
ddz: dZ, dv: dz, et ddB: ddZ. diperentiatae obe.
constans pro arbitiio, sed talis, ut ejus e aliqua triam, ex aequ. 6.
tolli possit  ubi tamen n quod inde incommodum Cum datis
cadendum ne
non licet facere de = dz sddz: dZ. Nam
ita foret sddz: dz = -1 seu constans quod est contra
in qua
pugnans oriatur. Sit constans de
aequ. 1. si fieret de = dv sadz. dzu, fiet 0 = do ddz: dz + dd v. sddz: dz, 
0= ddZue + ddq sddz: dZ
ubi habebitur ddv: dv ex (ddZ: dZ): ((d. lZ. dz) seu (ddo: dv ex
fieret
Fddz: dZ
unde quidem nihil absurdi statim apparet, sed verendum ne oriatur per consequentiam
si fiat de =  dq(lZ: d0) sddz: dZ inde differentiando fiet  d2ddz: do
0 sed ita dividendo omnia per
In ddz: dx terminint in quibus D, redibunt ad ddv: do, et termini in quibus Z
1+dD, habebimus
+(2 dV d Z ddz- dZ dz adv, : codv) )ddZ. dZ
eredibunt ad ddz: dque  ut ante. quodsi fiat de-
de = B salz + do, fiet 0 = ddz + daz s az + ddv =0 fiet dilo: ddZ = - (daz: d2
sdita habebitur  do ex dZe  accedente tamen de ejusque valore.
si fiat de do (ddZ+de fiet 0
doadz + dans+ si sit vero
odam + ddv duZ + AF ddz, ita
habetur die d d dx et adv: dv, et daz: Z et ddque vel de dv: dZ, ddviddZ
10- du sadz + dufiet 40= 
et denique sddz: dZ. seu (adz: dZ  (9) = (ddZ: dd v) (1 + dv: dZ)
sit rvae aequatio (4) sit. Xx+ys, :laa = dy; dx et _ explicando fiet do: 4Z (5) qusdaz. l
qu satz. dv et differentiando d (dv: d2) 4 2 (ddZ. d2) sad Z: dZ = 2 (daz. d0) (daz: dv. seu fiet
qu d (av: d2) +  ddlaz. d tZ (diZe ddz: d
qu
a daxi quiddque: aV)
et fiet (qu
aeuqu
adeaq s.d
fiet e
videndum an dem isgodeat
d)
dn + de
dzdz
et
dqu
sta 
aZ
di
quo
lesu
qud
qu
lu
d(dv: d7) (ddz. 42) a =
aa
quL +qu. 8y
aZ
qu a
+ qu40
itur idem pros incxumodum quod in
pariomen na pagina praecedente
(dv. 42) (l1Zi dz) (ddz: dZ = (6) dv: dz - qu sddz. de
div dedz, dede
qe adque dudetazd
qddv - a
 dq daque, clouv+ dZ
qu (dedo. 2) (de7. 42) +
qu +qu0
d (dv: d2) (daz. 1Z
dd
qu d’qe
de - i qud 
Aigno C; Namheperta est quantitas sat zd
perg adv
fuerit, n
Talis autem est aequ. 11
alia in ea quantitates existere possiat;
et au ida
ut ubi reducta et ordinata
quam  ddv: dazue
per dazue dav: ddz et per a0: d2Z
sddz: de peu eadem, et his valoribus
uorum Sdaz: dZ et SddZ: db, substitutis in valoribus ipsarum X: a, et y. a
sine valorem substituendo in aeq. S. habetur et
habentur et harum valores per do: dz et ddo: dd2 Unde habita 
iat istum acaten, tiial tus per ho de itequ ca o adi piono
ade qua ontatis ataum uia cestia sdatum in has per aoete, utaque it dis, ide pronatire
ali
dzd
duar
OD - D()
O =
LI =
y4
r e
et nulla