Opuscula. 
durotaxat dimenfionem afccndit 2° i^i , ^2 , &c de* 
notant fundiones quafcumque ipfius x, & quantitatum con- 
ftantium; 3° nullum aliud differentiale variabiie prxter //y, 
HulJaeque aJsa: differentialium dimenfiones prxccr iUius, quod 
conftans affumitur, poteftates deprehienduntur . 
Deinceps videbimus quomodo aequationes lineares , quse 
plures variabiles involvunt , ad formuJam prxcedentem revo» 
cari poffint. 
2. Iheorema * iKtegrah finhum atque com^letum cujufcum" 
que aquationts linearis ordtnis indeiimti r , efi hujus form& 
yX — Xi=:K; X cb* Xi exprtmunt funBiones quafcunque x 
cb* quantitatum conjlantium , attamen K efi quantitas arbitra'' 
fia sonfians , 
Nam differentiando hanc xquationem n vicibus , fum- 
pto elemento dx conltante , ac ponendo brevitaiis gratia 
dX^'^=.X''Ux 
dX^^-^^X^'^ d^ 
&c. 
ct 
dXi^Xi^^^dx 
snvenitur 
[n, n {n^t)dy n(tt~-\) {„^t) d\y 
y -f- — A ■; r — — — A - — ; 
n (f}~ i)(n~2) . . . ( «— W-f-2 ) ( » - m+ 1) d'"-'^ y 
I . 2 . 3 .... w - 1 ax"-^ dx 
= X.'"' (2) 
Perspicuum eft, coefficientes eiTe terminos binomii i-f i 
ad poteliatem n evecd , cujus terminus generalis indicis 
primo excepto , quippe qui eft unitati equalis , eil 
n ( n — I ) • • . ( « — >w -f- 2 ) 
i . z . . . . m — 1 
IVfox oftendam quanam rutione formula (i) comparare 
pofiGt formuiam (i) 
3. Integrale completum ordinis immediate inferioris a:qua- 
tionis (i) ordinis efl differentiale ordinis «— i aqnationi» 
fundanjeniaiis j X— XizlK, igitur ponendo in formula (2) 
