( ) 
for- 
(•pb ^ + B + g = ^ ^ 
' jf X X 4-f Xx’+c 
miila Seriei fiimmabilis. Si (JuatuoE fine Frai^lioncs 
B 
D 
, 'exiftente^ -j- 4 ^ C -}-£>= o) 
i’ j: - f- c’ Jf -j~ 
ad eundem modum invenietur formula Seriei fummabilis 
Abcd-\-Acd-^'^Xo~b X d—h\ x x -YAd^Bxd~b-\^Qx4 — -C; "K x >iC xvj-^ 
X X X b X X~^c X X d . 
Et fic pergere licet ad formulas ad hue magis compo* 
fitas. 
Ca(, i. Et fi plures Tint formula Serierum hujufrao- 
di rumm^bilium,. qparum denominatorum fa<^ores ex* 
cerpantur p:x diverfis .prpgreirionibus Aritlimecjcis, ex 
ifiarum foirmularum quptvis in unam fummam addi* 
tione, conficiecur formula hova Seriei fummabilis. 
Sint e. gr, formulas dux Serierum fummabilium 
& . excerptis a:; ex Progreffipne AricbmeticAj^;, 
a.» 3, 4. &c* ex ProgrefTione Aricnmetica i, 3, 
Turn ex his formulis in unam fummam colledis 
■V X X -j- 3 
fiet formula, nova j 
vel, (expofi^ 
x>tx 4 - 3 X? 
to z per X St numerosdfttdS^}'^^ — — — ; — 
^ 'xxx-\~ix%x IX2X-|-I 
Cor. %* Hinc omnis Series in infinitum cominuata 
I. X z^sx- 4 - » jf:A? ><•■* -17 3 
fummabilis eft, cujus termini defignantur per Fiadfio- 
nem, cujus, denominatoHY faeftores exeerpuntur ex da- 
ti-qualibet Progreflione Arithmetic^, numerator .autera 
eft multinomium, cujus <(im^i)fip;ie^.fu^^"^d minimum 
binario pauciores. quam funt dimenftones E>e^mina- 
tpris. omnis hujufinodf fra^io rcfplvi poreft in 
tot fradiones fimplices, quot funt dimenfion,es, {ho^ 
eft, quot funt faiiftores) Denorfiihatoris, qualriim nume- 
ratorum aggregatum, eft nihil. S^it^exempli gratis, 
, V ^ ' ^ .formula 
f 
