S8 OBSERFATIONES 



Corol/. 1. Omnes feries fecundiordinis habent 

 tcrminum quemcunque aequalem triplo praecedcn- 

 tis fcu \ltimi minus triplo penultimi plus antepen- 

 "vltimo. 



Excmpli loco fint numeri trigonales i. 3.^.10. 

 15. 21. &c. erit 21.-3.15. — 3.1 o-\-6 aut 15 — 

 3. 10.- 3.6-4-3. 



Coroll. 2. In omnibus feriebus tertii ordinis 

 eft terminus quiuis zr quadruplo vltimi minus fextu- 

 plo penultimi plus quadruplo antepenultimi minus 

 penantepenultimo. 



Exempli gratia iint cubi numerorum natura- 

 lium I. S. 27. 54. 125. 2i(j. 34.3. &c. crit 34.3=4.. 

 I 25 -<5. (54-1-4.. 27—8. 



5. Apparet ex praecedcntc theorematc, 

 quanam lege feries recurrentes conftrui debeant , ita 

 \t fiant algcbraicac. Si vero alia, quam quac mo- 

 do definita fuit, lex fingatur , fcmper feries oricn- 

 tur tranfccndentes , feu potius exponentuiles , qua- 

 rum tcrminus gencralis \t inueniatur, fcqucns pro- 

 pofitio infcruict. 



Lemma. Qiiaecunque fint coefficientcs m,n^p, 



cj , poterit fcmper exhiberi feries nume- 



rorum continue proportionalium talis, vt denotan- 



tibus iterum litteris A ,B, C, D, Eter- 



minos conciguos ordine retrogrado e fcrie exccr- 

 ptos , quorum nnmerus indicatur pcr N, (it A—?n 

 B-h«C-4-/>D -{-(/E. 



Demonstratio. Si cnim terminus generalis in 

 progreffione geomctrica quaefita fit (X^ , hicque po- 



natur 



