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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 298v, page id 00068196:0592
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sit X ddx = ax fint ddx = dx: x quam collendo in aequatione differeulio diffe-
ax
rertiali, restat relutio inter X, d 
sit aequatio differentialis, in qua X, y, dx dys. potenit haberi differentio
differentialis in qua  absit y, et reperiatur X, ex ddx, dy, ddus
y = dg. fiat x= X. a X: a = ax: co seu d  X = dx a.: co
y- a
ax fier dxa = cody y - a
X + y = dy.
a
dx
dut
seu Xdx + ydx = ydy = ady. fit ZXX + Syax = L yy - ay
sydx f  y = xdx tadus da du (3X a
sydx- Sy a by dy
+3
y = x dx + ady: dx - du. seu y = X + a dy: dx, : 1 - dy: dx
seu dy = dx  a 1 - dy: dx dx - a L aysax + X  a dys e axs ot dyi ax
Assimi pt pro arbitrro relatioiu inter X, dx. ddx
dy o ex. dus t dyi dy adys
dys seu
vel inter y, dy dxillyisx + dyito dil
Dal relatu
. Aged dy.:Ax = adys _ - dla Xx dy: dx., et c
Nam et dus a dx: du = idx = ddus ex: dy
Asumi potest ppo arbitio e relatio inter X, dx ddx
seu
Jam si datu sit Asrrposita Aequatio inter _ dy: dx, X; y, 
Haberi pt alia  in qua X, 3, dy, dx, ddx, ddy. Tollatur unc ex leteris
habebitur aequ. ek y, dy, dx, dax, dly; item x, du, dx, dux ddy.
Item esy, X ex, dux, ddque; eteriX,  dy ddx ddus
sed duae literae simul tolli non possunti. Et literae dux duus prorsus non
possant tolli. Aisi per alteratia deinde per assimitionem novae
elationis differentio differentialis inter ae quanta diff. et differentio dif
ob, ad aeq. 3. adjugamus aequationem arbitrariam inter
y, du, ex dg au + dyide dix inter y, dus, diu talem si fieri
potest, ut tollatur simul y et dy et habebitur desiderata
quadratio. Hoc ut fiat, quaeratur aqualio formae 3, pluribus
modis doneo componendo talis  modus obtineatur ubi non
s et dy nisi it ea som exe consistant in una formula, sine aliis literis
X, sine affectionibus ipsius _ X
Nempe omnia redeunt ad has aequationes ex quibus fieri possint
Omnes mul liplicando et conpovendo aequitio inter A. y. dx: dy. Ejus
differentialis quae est inter X, Y, dx, du, dex, ody. post remo
arbitraria generalis relatio inter formulam Xius ejus differentialem
et ejus differientio differentialem. fortaC
se (acilius velimus arbitiaria sumeu solum inter y dus dius, et
possumus elior ati calculis praecedentis parine, ut servemus leges homoglneorum
melius, sola ibi intervenitate dax. Ino inl ibi prosunt
Xc
miru
s