DE AEQVILTBRIO VIKIVM.. i 9 $ 



Ponatur <J)~o, erit fin.Cj):— o , ct co£(pzzi , tunc 

 orientur : 



I. AH-Bdof.a-+-Ccof.(A-f-(3) = o 



II. B -f- Ccof (3 4- A cof ( (3 -f- y)rr o 



III. C-+Acofy-f-Bcof (y-f«)z:o 



Eft vero propter ct-f-(3 -4-y = 2ir,cof. (a+-|3)rcofy, 

 cof. ( (3 -f- y ) rr cof. a , et cof ( y -f- a ) ~ cof (3 , qui- 

 bus fubftitutis habebitur : 



A -+ B cof. a -+- C cof y r o ; B •+- C cof (3 -+- A cof a ro; 



C-f- Acof y-i-Bcof (3:no ; 



Eodem modo , pofito Cf)~|7r, propter fin.Cprzi, 

 ct cof (J) n o , obrinebitut: 



Bfin a+-Cfin (aH-(3)rro; (fin (3+Afin.((3+y]ro; 



Afin.y-f-Bfin.(y-f-a)iro j 

 Ex quibus prodit: 



Bfin.anCfin.y ; Cfin. (3 — Afin.a; Afin. y rrBfin.(3; 

 Ex his aequationibus , "valores ipfarum B , G et A ia 

 prioribus fubftituantnr , et habebitur : 



I. A fin. a -+ C fin. y cof a -+- C cof y fin. a n o 



II. B fin. (3 -+- A fin . a cof (3 -+ A cof. a fin. (3 =r o 



III. Cfin. y -f-Bfin. (3co(.y ■+- Bfin. y cof. (3 — o« 

 Ex quibus oritur : 



Afin.a— Cfin.p; Bfin. (3 — A fin. y ; Cfin.y :r Bfin.&j 



13. Inuenimus igitur fex aequationes fequentes: 

 A fin.an Cfin.(3 ; Bfin.(3n Afin.y; Cfin.yrrBfin.a; 

 Bfin.anCfin.y; Cfin (3 = Afin.a; A fin.y — Bfm. (3; 

 quarum , binae inter fe conueniunt ; fed hoc in aliis 



caiibus, 



