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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 363v, page id 00068196:0722
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V: a = dus.  dv: dq dy: a = dz dax - dA d vdsq: av
_ZX: a = S. aaZ. dx. Ergo dy: dx = dZ d dv: dcz lv - 1
aeddue: adv
Ponamujam du dd ddz esse constantem seu d, apadz: dax = 0
e
eu
(6
His positis videtur solatio haberi. sit dyidx = xa + gy;aa. fet.
dZ dd: ddzue do - 1 = Satz: du + av: de Et differentiando, fit.
ddv: dv = ddz: dv + 243 dy daz: + t - 2d0 de ldzu: d2 seu
fer
d2 dle Z dzd dd q +  AZ  t + 2dq d daque - 2 du ddque quae aequatio hat
est in potestate.
(2
y: a = dv. de Ergo dy: a = dZ ddv - dv ddz,: dzue
X: a = S, dz. d2 seu, dx. 4 = daz. d2. Ergo ex 2 et 3 fit dy: dx = d q ddv -. du aly: du s4
seu du: dx = dd ddv: ddq = dv: dque fiat d dq dd z: div = 0, et fit.
ex ex 5 fiat  dy. dx = d2 av: a z dZ = av: dq. Hel  sit jano
aequatio data resolvenda dy: dx = X: a + gy: aa et t ex 8per 7, 3, 1
fiet dZ Adv: ddzdZ = dv: d3= (daz: dz + do: 42. Et differentiando fiet
Paeg. g. observata aeq. 6. fiet (adv: dqC d Z d: +q) + dv ta. equ = ddz: dq pel valv: 6, - 2av l qecti
Sed hic quod
seu fiet dq de dazue = AZ ddzue + 2 2 de de dav - 2 dv ddz.
mirum cum videamur licita suppo susse incidimus in illicita; nam
cum in aequ. I1. hobeatur daq idao per aZ: dv. sequitur ex aeq. Ic tollendo
dy: dque et ddv: ddzue ope sq a94. 1 et 4, habituros uos relationem inter dui dx et y: a
Itaque iterum natura rei nos elusit
quod est contra syp. seu g aeq. 8.
e sit y: a = v:Z et X: a = (ax: Y et dy: a = = do - vdz:; ZZ
seu b
Ergo dy: ax  Za0 - vaz,: 2Z  dv. de = v. Z = dg: ax. sed hic
non video quomodo evitentur ddae et ddz. simul cum Z et B
X: a = Sav: Z y: a = (av: v ay: x = v: Z
Sit dy: dx= X: a + yy: aa. Ergo ex 1. 2. 3. fit v: Z = (dv. + B fdv: v
seu Zdv- vdq,: p2 = do: Z + 2dv. v sav: V seu ((. Z - vv dz: do22 - v. 2 +e s dvip
et fit, d7:
= 2d0 5dv: D: vv ita quidem aequ. 4 redioa est ad quadiaturas
sed hoc succedit pro c casu particulari
y: a = (dv: v x: a = Z: V dyi a _ = Bdv: v Ax: a = vdz- Zdv,: v
dy. dx = vdv:, vd3 - Zd sed ita habetrius Z, v, aaz, di v, praeter a2. dr
An sic g: a = ( ddv d X: a = Sdax: d dyi dx = dredue dt
fit dy: dx  adro: tdqe = dx: ded sit di Hr aqu set posito daco = 0
sit dyi dx =XX. a +d ig a fiet Aqi deo Star: du + (ddy. d3 et fiet:
Et tollendo ddv: dd3
ddz: (B deo =2dd Z: dz 5 atz: dz + ddv : d2.
fiet dZ: deo = 25 +d7: de + d dezideo quod absurdum. Itaque non nihil
mutandum hpothesis sit hy: x  xxiaa + ry: a sit azideo = saaqe. au + sadr: 
et daz: ded = 2 ddz.: d Sddz. Z + 2 ddv: de jam daque itco = ddv: du pert
Ergo, fit (Ad 7. adq C Satz: dZ  + dd2: deo 0
video aliud ex
his sequi absurdum ut scit. facta tati Hypothesi ut in aeg. 4
semper plane tolli possit omnis affectio ipsius v nam sola adest ddv.
praeteras ex aeg. 4 fit 1d V = L224due +deo. quae a 70r
Et video ulcunque rem mistituas  in aeq.a, assumes recationem inter v
AV et dZ quae tamen quaeri deber
Revera non
sapponimus
licita fatendo
(3 ddz: ddv = deo
constanti 
ita utiu
hafelur
acp inter dz
et av, quaetamen
estquaetenda