DÉE:S : S © 48 NC als. az 
Series iftæ omnes horizontales funt feries recurrentes quinti 
ordinis, imo funt una eademque feries; numerus tamen ter- 
minorum continuo minuitur. 
Terminus generalis harum ferierum dependet à refolutione 
æquationis x — xŸ — x? = x 4 x — 1 — o, que 
1- V1 —3) 
= ———* ), 
2 
prædita eft hifce quinque radicibus x = 1, x — 77 
M pr NT x) : 
2 
quapropter feriei primæ terminus generalis fiet 
Aa BE} + CEE pe 
HD. MNT +E. ny 
Ad definiendos indeterminatarum valores, pofita fucceflive 
# — 1,2, 3, 4, $, quinque æquationes inftituendæ funt, 
cum quinque primis feriei terminis, quæ æquationes erurt 
hujufmodi, fadta facilitatis caufa 77 + PET 
V(—"——©- = 4) Le 
mAH B—C.a+kD— EF. = r 
2 A+ (B+ Car (D+H+E). bb 7. 
3 A+ (B— C.è + (D — E) D = 2. 
4 A+ (B+C).fé+ /D+H EE). — 2. 
ss A+H(B— C.a+ (D — E).b = 2. 
Ut per has æquationes valores quæfiti determinentur, artificio 
opus efl ad longos moleftofque calculos evitandos. L 
Primam æquationem multiplicatam per 2 2, deme ex tertia 
ut habeas 
6. A.{1—b)+fB—C).(&—abb) = 2 — b8, 
Tertiam multiplicatam per 44, deme ex quinta ut fiat 
7e A.(1—bb) +(B—C).(i—à6)—=2— 201 
Sextam, multiplicatam per aa, detrahe ex feptima ut oriatur 
A. (1i —bb— aa + dl) = 2— 20b — 2aa + à}, 
Y ij 
