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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 6
# Folio 9v, page id 00068051:0018
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Nihil hic neui
sequatio po convera augentium generalis data sit 1. nempe
(2)
Ly: dx = X: a. y: a. sit  y: a = Y. D
C
et X: a = g. b fiet: dy: a = d. Z. v et dx. a = d. 3. 
6
M
H
Ergo dy: dx = dZ: v: dz: v. Et ex 1, 2,3, 6, fiet
 (7)
d. Z: d. ZV = 7. v. Z.V Atque ita conversa
si
tangentium generaliter seu differentiatis reducta
esse ad quadraturas seu differentialis implicata
intricata ad extricatam Non previt.
differentio. differentialis generalis data fiet.
a  day: ddx= X: a. y: a. ux et fy: dx. adax: dy
Faciendo  X: a, et y: a, ut in aqu. 2, 3,  et inde ducend
Ce
45, 6. adjiciamus on  3 et 4, adx = a dd 2: B et ddy - a 4 2: 
ils
et fiet ddy: adx = +dZ. 6: dd  
et adex ida a
s
2(12)
et adds: dx = (aa da Z: B: aa qu. d: 0 =) daz: v : 1) dq. V
r V7
Et proinde hoc modo etiam ex aequ. 8 per Z2, 6, 12 sublata est a
13
et habetur ddv: daque = per: _(. v. Z + dv: d7. Zdd7: z
52) 
jam cossumatur e = Z6 et de C 
16 e
e
d Z.  _ e
=EeB g. b.   dv: 4Z dZ fit on dde= fes daque
8
et
sit  dde20=  form. ver v. Z. do: de. dz: de Gllv: a12.
Z1Z.∞
et ope aequ. 15 et 18 ex c4 13 tollendo ZCZ et V, Fet e
ddv: ddZu  do: de. dZ: de. quod ita differentio-
differentialis reducta est at differentialem communem.
Nam faciende
et Hae quidem pulchra
essent, nisi aliquid obsiaret, nempe si itam y, quam X
datur per Z. V, rabuatur ex se monem, contra hypothesin
(20) U
sit ergo X: a = Z: e +. V: C
∞
Ry. 4
1), 
L.V Y.C
fet ex 1, 29 21 dZ: de. dv: de. Z. C. V =0 fiat Z: e
297
fiat Z: e  de adque si jam determinaremus e pe e per Z et V
nihil tucraremum nam si adsit a, redacentur omnia ad Z: 
res reduci potest ad a, ut si fuisset se 
u
=eeraa itu
ex 69. 2t. fieret per 23, 1Z. de = d0: de. V: Z  sed nihil
hinc. sitactum
si obtineri posset ut per 7. C tolle teturz
Res cum e, vel uclius procederet. An ergo sic:
XIA  X.C fAx: Y = V.Z
psaum X et y et e talis ut
esempe sumatur valor
tollento X, y, ax, dy ex aeq. 1
per Z et v,  et e, et toltedo C ut