# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0595
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0595?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 300r, page id 00068196:0595
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 301v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=595
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000595.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 115 lines, status machine
# Lines: 115 recognised, mean confidence 0.81
# 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.

quae hric bora ut et in scheda 10 sepientr
B. puto nihil referre subestatutio
sit moderata an immogeratu.
ita est. Enpul refert
V. sept. 1690.
Hossunt in scheda 11s plunt
meliu pos
quacquidhicbonum in
panca contractum
4ec
Methodus pingentium inversa per substitationis (moderatas,
assumendio Z= dy: dx. p Itia inventi in pseheda proecedenti in
sol (est demi plagula) 10 septembr. 1690
Resumamus exemplum praecedentis et schedae quia forte erior in calcula et
majoris securtatis causa adhibeamus numeros: Z = dy: dx et dy: dx = yX
fit ZEgX et hujus differentialis dZ= X  + ydx Rursus
G
dujus differentialis
datu XX = LCXdZ- ZdX. Hic jam nullis opus est diffecentialibus novis, et
2 =
daisinde sequentia licit prostare per Numeros. Cllendo Z in 54 E hit tr adu dus in 4 et 5
Se tollumus dyca et x et ex a fiet dqe. dx XZ + y et ex 6(fit dZ.d  dy Xx. dxX + Z. X
q e seu dque : dx = ZX + Z.  seu dz Follamus dy ex aeq. 6. dividendo eam per XdZ, fiet
ady XX: Xdx = aZ XZ. x dx = Zax: X dX seu ZX ~ dX: aX = Z. X. seu fier
ZXX  ex + Z ax = _X dZ. seu saq. Z + a = A LXX +  SdX: X
seu log  seu log. Z - log. X = L XX jam log Z- log X  = log. y. per 5
e
5.Z
log. y  L XX quod est verum, nam ob aeq. 42. fit ag. y+b = xx
A Et ita usi sumus una solum differentiali et
iideamus an liceat uti et altera ,  tollendo in ea dy firt AZ. dx = ZX + y seu (Z: dx = 2X+ Z. X
qu
  hoc est log. y L L XX al aute.
= et prodit, idem Quid si tollere velimus e d X et dx, relicta y et dy.. Nempe in 0g. 4
redividamus per dus firt aZ: dy X + ydx: dy seu pe ex t 1 tollendo dy: dy, et ex 5 lollento
dep aeq. 17. fiet dz. dys  Z: y + y: Z seu _ yZdq = 22dy + yydy Quod quidem verum est
sed non nisi aptum ad solutionem. jam similiter quaeramus valorem ipsius y eat aequationis novae
uut prodeati sive X, simendo ex ag. , Z, X = Z: y fiet: x= ydZ- Z ay et tollendo
Ergo ex aq. 19 et 22  aequando
 duos valores ipsius yydus fit Zy dZ = 2Zdy = GZ aZ - 33 dyue quae est aequatio dentica
t dx per aeq.1 fit yy dy CZy 4 2 - 22 ay
 unde discimus nihil
(2
quo res non parum turbat. Et dubilare facit, an methodus
id sit 7 = dy: dx = et t a b .  aX + by 2 Z. ex aequ + differe
 i hoc nostra semper procedat.
EX psiu aequalionis 3 differertialis est a ax + b dg = dq, et tollendo d fiet
d
2
a ty: Z + bdy = dZ seu  y = (aq: a. Z +b, + _c itaque soluta est aequatio
qu axdx + by aX = dys Nam fit y = S2a2: at bZ +c quae pendet ex
(3)
sit Z2 dys.de et ax + by  = cZX + ∞ eZy. fiet y = aX = CZX,: ez - b
quadratura Hyperbolae.
(2
rujusaeq. e diffralis eit set 4y, (2 ez b = CZ - b adx = CZ1X - CXdZ = aX - C ZX esZ. et tollendo dy per 1
2  faciendoque compensis causa = ez+ b = M et n et 1Z+ a = m. fic
Znv: ax L mH Ex = RCXAZ = 1C em XdZ. seu X - e MA dx - Z MmA. AX: dZ mCt eni
X et yclu et eodem modo y = mindy -Zmm: dy 3: fdZ, se et tollendo dy, per Zax, fiet
2
n
eodem modo, in  do = mnz ax = mm: ax,: fdZ. quos valores X et y ex 7 et 9. substituendo
ec quicquam lucramur. Itaque aliud sed aliunde
itaque si, Inm talis aequalio resolvi pt qualis est 2. quia ibi X et y per se
= in aq. 2. t evanescit sq
et Hi + ax + by= cZX + ezy. fiet adx ebdus= czaxtie
ser adm bay  CZax + Z fiat y= A h ta Y exH h + aX - cZX,: eZ- b
n
Ly: dx
compendii causae eZ b cZ- a = m et ez - b = n fit y = k  h - mx, : n
mum- acz. races rist bueaag  sit An = EdZ et dn edque ergo siet  ex. 6, 7, 8. fiet: synn = - max- ex at -hedr + aus
mun EBB.B
mon = C522- 2acZ + aa
nn - CezZ- 2b0Z + bb
5. 10- 1635-27. 4374
((.. )) sic no
aequationes quae in
omumo sed turitament
causus assumnntur
810 14
1625 
1a
eb
1634 1620 90
p-0+ 3+
ubi rursus ema c, inn = ubi rursus em A c p, et similiter e mc, c p et ende, ne
mm+ + ne dB: gazue. quos duos
et 5 est H=  nx+ ny tunc
fiet aF hpqdque = am Zun +m dx + heazue + pn Zn + tum ax thcdque, ubi sufficit videri
valores substitaenda in g. literarum X et y substituendo in aeq. 2, qua
an maneal aque  seu quod fiet modo non sit pa emqu + enp. e quod experiamur
est pa eemn eeci en  eema eem cen + ec dabebum porer  ex  t 
sit C fingendo sit a = 1 et  et b = 2 et c 3 et e = 4, et Z = 5, ergo
fiet m = per im fi aeq. + fiet m = 14 et  per sy5. fit n - 18 et per ro fit p - 53
et  per 11 fit 9 = 50 ergo p. 4 = cb. 33 50 et emq = 4. 12.50 et cnp = 3. 18.53
ergo deberet esse S in numens veris 53.50 = 4. 14. 50 + 3. 18.53, seu debesret van
esse 53. 25. = 2. 14. 50 + 3. 9. 53 quod fieri non potest quia 2. 14. 50 non po dividi per 53
Similiter si dque destimeretur seu si foret pa = emus + enp. seret deberet etiam defr homons
206 fieri ob reliqua. qa Znn +m  p Z Memm seu fieret m. jam _ Zun +n = 5. 15 +14 = 163+3 
e
actu
bch
 nna enim pars dividitur per
ce
termin
1.+. 5. 5 + 1. 2 = 1. 415 - 23. 5
ligae hio epa cemce-eem- cen in
cep Eb bon 1 E ipbitpa =bere  abiet acce beZ ce Eec ade ee be ingtin toe
p so   . 13 feri non
so e
plicemus.
1ori   f1 092 4 6 0)  pu Zartm  ea satum,  i ses at aspitu
 at
contrahitur calculus
notandum aat