i6o Aloysii Casinelli 



a^i —a,c—2l>-}-a, d—ic+'ib—a, e—id+Gc—ib+a./Se+IOd 

 — 10c-H5i — a etc. 



cujas lermiiius generalis seu n csiraus cxprimiiur formula 



^ . ,^ (^'-1(("- 2) ("-1)("-^)("-3) . 

 ±aip(«— 1J b± czfL ^,-: d 



2.3 



(„_1) {„—<2) {ti — i) in— 4) 

 ^i '■ 



etc. 



sumpto signo superior! si n est niimorus impar, inferiori si n 

 est numerus par. Hanc formulam applicaudo nuineris 2,9, i5, 

 1 1 j3 habebimus 



2 = 2 



9 — _ 24-11 

 15= 2 — 2.11-1-35 

 11 __ 2 4- 3.11 — 3.35 + 85 



3= 2 — 4.11+6.35 — 4.85 4-17.5 



Ex serie (6) deducemus eodem calculo series difTerentiaruni 

 et habebimus 



Series (6) 6,50,225,735,1960,4536,9450,18150,32670,55770,91091 etc. 



Differ, primae 44,175,510,1225,2576,4914,8700,14520,23100,35321 etc.. 

 Differ, sccundae 131,335,715,1351,2338,3786,5820,8580,12221 etc. 

 Differ, teniae 204,380,636,987,1448,2034^2760,3641 etc. 



Differ, quartae 176,256,351,461,586,726,881 etc. 



Differ, quintae 80,95,110,125,140,155 etc. 



Differ, sextae constantes 15,15,15,15,15 etc. 



Primus term, seriei est 

 6=6 

 Secundus 50=:6-t-44 



Tcriius 225=6+2.444-151 



Quarius 735=64-3.44+ 3.131+204 



Quintus 1960=6+4.44+ 6.131+ 4.204+176 ' 



Sexius 4536=6+5.44+10.131+10.204+ 5.176+80 



Septimus 9450=6+6.44+15.131+20.204+ 15.176+ 6.80+13; 



Ociavus 18150=6+7.44+21.131+35.204+ 35.176+ 21.80+ 7.15 



Nonus 32670=6+8.44+28.131+56.204+ 70.176+ 56.80+28.15 



Decimuj 55770=6+9.44+36.131+84.204+126.176+126.80+84.15 



etc. 



etc. 



etc. 



