DE FUNCTIONIBUS TRANSSCENDENTIBUS QUAE EX DIFFERENTIATIONE ETC. 
373 
l 
d® i dy f 
x ~F y * * ’ 
dar dy 
x y 9 
unde statini prodit 
/= ì^+'Ì+^+t ) =/+*£(*-*)+*£(*-*) 
1?JL 
dar' 
ar' 
\<hl 
y' 
=/. 
dar" 
ar" 
dar' 
_dl 
r 
: n 
dar" 
ar' 
y' 
tf i 
ar" 
=/+•** V 
etc. 
et prorsus simili modo 
/"=/+ +a' ^ • /'"=/"+ i/ ^ 
Perinde fit 
9 = = +£(•-*)++£(*—0 = 
eodemque modo g" = g" = \g" x ^*~ etc. Nec non hinc patet esse 
/== /+/, /" = /+/+/. /"' = /4-/+/+/" etc. Nullo negotio perspici 
tur , seriem —, —, — etc. celerrime infra omnes limites decrescere, quamobrem 
habebimus per seriem infinitam rapidissime convergentem 
hinc 
/“=/+all^ 
2 dar* 2d?/ 00 
x — ar a; — a; 
a;' 1 a: 
2 d M (ar, ?/) 
y 00 M (ar, ?/) 
dar , d?/ dar d?/1 
. x — ar' ar'—ar" ar"—x'" . . 1 00 A 
■ + +etc. , £ =0 
dar , a?/ r ax 
x ' y "* < x 
dM(<r,j/) = M [pc,y) X Ì^X(i+ 
( . X X , . X X X X li) 
x i hi——•—— + etc. sive 
y 1 i X y > ' 1 X 1 4 a; x 1 
x — x x — ar‘ 
+ ^x(w 
X X X X 
Calculum aliquantum commodiorem nanciscimur sequenti modo: Fit 
x — x' x- y (x — yf {x -p yf — 4 ary ^ x'x' y'y ^ 
ar' x-\-y xx — yy * xx — yy xx — yy 
unde promanat 
dM(<a?, y)=X | ~X[xx —yy+2[ococ—yy )-f-4{pc"x"—y”y")-f-8[x"'x"—y'"y"')■ ■) 
dy. 
-h — X[XX —yy— 2[OC00—yy') — 4[oé'oc'—yy ) — 8{oc"oc"—y"y")...)( 
y 
.. . , ar—ar ar ar —y y x —ar ar ar —y y 
*) et perinde — = 4 ———, —- = 4 - „ „ „ — etc - 
ar xx — y y x xx — y y