( ) 
Serieficfctibipoflunt^^, &(■ 
Hoc pado, fepofito diviforc dato i, Series revocatur ad 
foimam Propofitionis, exiftentibus a—i, n—\, & 
x — z> Unde fumma Seriei dup licata eft 
X X x-l-i XX 4- 2 , -—o x t XX _ X X X -1- « X X -i- ^ ^ 
3 ■” 3 ’ 
adeoqucliabi t^ rati one divifo ris 2, S umma Seriei ipfius efl 
i X 3 2- X 3 
exiftente x eodem ac z. Ad eundem modum inveniun- 
turfummae cseterorum numerorum figuratorum, quosum 
ormulaejam vulgo innotefcunc. 
Ex. 3. Sine = I, » = X, p = 3. ut (It Series pro- 
pofita 1 X 3 X 5 -j- ? X 5 X 7 5 X 7 X 9 - 1 - In hoc 
ita que ca fu formu la fumm ae fir 
ATXX-l-XXX-l- 4 x.V-|-^ — 1 2^1x3. 
4x X 
XXX 
2 X 
x-1-4^x-|-6+i5 
8 
Verbi gratia, fi quae- 
ratur fumma decern terminorum, fit x = 19 (nempe ter- 
minus decimus in Serie Arithmetice proporcionalium, 
i» 3» 7» adeoque fumma eft ^ M _ L £ 
= x868o. Propofitio vero fie demonftratur. 
Demonfir.atia. Sit Series quantitatum A, 5 , C, D, 
quarum differentiae conftituant Seriem 4, h, c, d, 
(nemp uc fine 4 — 5 — A, b:=zC — B, c :z=: D — C, ) 
Hinc ftatim colligitur elle a -\-b-==.C — A,a-\-b-^ c — 
D — A, a^b-\-e-\-d~E — A: & in genere aggre- 
gatum quGtlibet terminorum Seriei 4, t, c, d, C'^c. sequale 
eft termino proxime infequenci Seriei A, B, C, D, Ey ^c. 
muldato termino primo A. Vio A^ B., C, fume terminos 
a — n 
