522 Aloysii Casweili 



(a-f-c)-t- (i-t-J) 



o?{a-\-c)-\-a' (b-^-d) 

 (a-+-c)-4- (i-4-rf) 



ft^(a-+-c)-i-a (b-+-d) 

 (c — a)-t- (i— <^) 

 « (c — rt)-+-a^(6 — cf ) 

 a^(c — a)-t-a (6 — d) 

 {c—a)-i- ib—d) 

 a (c — a)-i^a?(b — d) 

 a-{c — «)-(-» (p — d) 

 Sed a-+-c=2//i 6-t-fZ=2re c — a=:2/? i — d^=:.2q -^ 

 ergo radices ipsae erunt 



2 w -4- 2 rt / 



a (2m)-Ha'-(2«) 

 a2(2TO)-Ha (2«) 



2 TO -»- 2 ?i 

 a (2/n)-Ha-(2/i) 

 a-^Z^j)-!-!* C2?0 

 2/3 -h2<7 



a(2;3)-HaX27) 

 «2(2p)-f.»(27) 



2/3 -4-27 



a(2/3)-i-a-(29) 



aX2 /»)-+-« (2*7) 



Quae radices sunt binae aequales. 



Si autem subslituerentur in hisce radicibus valores m,n,p,q, 



facile deducemus 



2m-H2«, a(2TO)-Ha\2«), a:\lm)^o{2n) 



esse radices aequationis tertii gradus 



