AD QUjESTIONEM MATHEMATICAL. a3 



Factorum autcm sccundorum calculus sic expeditur: habcmus [oi]=j/ et 



[n] = <7'$ quamobrcm [02]= [oi] 1 a[n] = /*'' 2*7' ; [i2] = [n] [01] 



= p'q' et [22] = [11]' =<7''. Est igitur aquatic fmalis restituto coefficienle 



/ h;cc : 



(00) / + (01) Ip + (ll)/<7 ) 



=0 



Si ponatur / = 3o 3y , p = 5j' 3oj , q = 3j 3 $ et (2) = 10 , (i) = 

 i \y , (o) = 67 " emerget : 



1 13 j 1 * i3iojy 3 + iQooy ' = o. 

 pro aequatione linali duarum acquationum 



a;' (3o 3j~) a: (5y' 3oj') + 3j" 3 = o. 



10 x' 1 1 xy 6j' =o. 

 34> CoDtempleniur adhuc duas tertii gradus scqualiories. 



Ix ' px' + qx r = o . . (A) 



(o) + (,)* +(a)a:' + (3) * 3 = o (B) 



Posilis * = p',j = p' et -^ r' prima fit a: 3 /?' x.' -\- q' x r 1 = o. 

 Jam operationem ut scqviitur ordino : 



Factores primi. Factores secundi. 



(ooo) + (ooi) + (on)+(ii! 



[002]=[001][1]-2[011]=^"- 



(oi3)+(u3) 



(o33)+(i33) 



+(222) 



+ (223) 



+(233) 

 +(333) 



= P " q'- 2f} "-r'p', [u3] = [in] [2] = 

 r>' 2 /y , [022] = [i 1 2] [i] - [ 1 1 3] = q" 

 - 2 r>',[i22] = [112] [i] -[n3] = ry, 



[023] = [012] [2] 2 [122] [Olfl = [012] 

 M-[oil][3]-[ll3]-2[l22]=f>y + 



3rV aj>" K; [ia3] = [in] [aa] = q'p'r' 

 2 r", [222] = [i n] [i 1 1] = r"; [2 2 3] = 



