546 



Petbi Callegari 



0.1,2,3, (m— 3), (m_2), 



post divislonem per numerura 3 deducitur 



m(m— 1)(m— 2) 



m — 3 m — 4 m— 5 



1 .2.3 



A„=0 ; 



Hoc pacto agendum erk, si aequatio proposila majorem nu- 

 merum radicuin aequalium admittat. 



Si ergo aequatio proposita radices r aequales habeat, series 

 sequentium aequalionuni prodibit, quae sirnul subsisteut. 



m m— 1 m— 2 m — 3 



fli -*-A|ai •♦"A.-iaj -t-A^ai 



m — (r— 1) m—r 



-t-Ar— 1<Il -t-Arfll -t- 



-+-Am=dO, 



Aiai ^ZAjfli -4-3A8ai •+- 



„_2 m— 3 



AiOi -f-SAafli 



m— ^r — 1) m—r 



•(r — 1)Ar— Iflt -t-rArfl) H 



(r_1)(r— 2), — (r-1) r(r_1), m-r 



■ ^^ ^ Ar-iai -^-^ Arfli 



.-4-mAm=^, 



IB— J 



A,ai 



^^^Z^A.=0 



2 



(r_1)(r_2)(r— 3), m_(r-i) r(r—\)(r—2) '»-'■ . 



-Ar— Ifll H ;; — ;; Ar^l H^ 



2.3 



2.3 



m(m— 1)(m— 2) ^ 

 O ^""^^ 



I 



m— (r — 1) m—r 



Ar— 1<2l -t-rArflj H 



m(m— 1) (m— r-4-2) 



2.3 .. . (/-—I) 



Si coefficientes numerici harum aequationum observentur, 

 compertum fit primae aequationis coefficientes esse numeros 

 figuratos primi ordinis; coefficientes secundae aequationis es- 

 se numeros figuratos secundi ordinis; coefficientes tertiae ae- 

 quationis esse numeros figuratos tertii ordlnis, et ita deinceps. 

 Prime multiplicatis istis aecjuatlonibus ordiuatim per quantita- 



tes indeterminatas aW, cc^'P, cc(2) d''~'^\ ac postea earum- 



dem summa coufecta, habebimus 



