DiSQUISITiO ANALITICA ETC. 1 6 f 



Ex qnibus formnlis facile concludimus lerminum n esimuin 

 vel generalem seriei (6) esse. 



(„_1)(„_2) („_1)(„_2)(„-3) („_1) . . . („_4) 



6-+-44(/i— 1H-1 31 ^ i: +204 ^ -^pr^ ■+^ '^ 



2.3 ^"" 2.i.4 



(„_1) . . ■ (»-5) ^( „-1) ■ . ■ ( „_6) 



+^° T~6.rs -^^^ 2.S.4.5.6 • 



Cocflicienlium aulem 6,44>'5'»2o4, 176,80,15 lex erit, 

 6 = 6 

 44 = 50 —6 

 131 =225 —2.50 + 6 

 204 = 735 — 3.225 + 3.50 — 6 

 176=1960 — 4.735 4- 6.225 — 4.50 +6 

 80 = 4536—5.1960 4-10.735 —10.225+ 5.50 —6 

 15 =9450 — 6.4536 + 15.1960 — 20.735 + 15.225 — 6,50 + G 

 Ex serie (8) Jcduciinus 

 Series (8) 21,274,1624,6769,22149,63273,157773,357123,749463,1474473,2749747 etc. 



DillVr. primae 250,1350,5145,15680,40824,94500,199650/392040,726010,1275274 etc. 



Dillcr. secundae 1100,3795,10535,25144,53676,105150,192390,332970,550264 cic. 



Diller. teniae 2695,6740,14609,28532,51474,87240,140580,217294 etc. 



Differ, quartae 4045,7869,13923,22942,35766,53340,76714 etc. 



DiiTer. quimae 3824,6054,9019,12824,17574,23374 etc. 



Dlflcr. sextae 2230,2965,3855,4750,5800 cte. 



Differ, sepiiinae • 735,840,945,1050, etc. 



Differ, ociavae constantes 105,105,105 etc. 



Primus icrminus seriei (8) est 

 24=24 

 Secundus 274=24+250 



Tenius 1621=24+2.250+1100 



Quarius 6769=24+3.250+ 3.1100+2695 



Quinius 22449=21+1.250+ 6.1100-f- 4.2695+4045 



Scxtus 63273=24+5.250+10.1100+10.2695+ 5.4045+3824 



Septimus 157773=24+6.250+15.11004-20.2695+ 15.4045+ 6.3824+3230 

 Octauus 357423=24+7.250+21.1100+35.2695+ 35.4045+ 21.3824+ 7.3230+735 

 Nonus 749463=244-8.250+28. 1100+56;2695+ 70.4045+ 56.3824+28-3230+8.735+105 



Decimus 1474473=24+9.250+36.11004-84.2695+126.4045+126.3824+84.3230+36.735+9.105 

 eic. eic. etc. etc. 



T. IV. 21 



