200 DE CAVTELIS CIRCA 1NVEST. 



Scholion 2. 



56. Haec fpeculatio accuratiorem euolut-^nem 

 meretur , et quia attradtio rationem reciprocam du- 

 plicatam diftantiarum fequitur , pofito Xzz,— 2 , ha- 

 bebimus : 



Af.— a*) B(t — C — «)» ) , C((.— '« )'— a») - 



aa d-aj* -T - a 2 ('— a) 1 — ° leU 



ACi-a^i-a^-Baa^a-saa+a^+Cd-sa+Saa-^a 5 )-© 

 quae fecundum poteftates ipfius a difpofita praebet 



(A-HB)« s -(aA+3B)aM-(A+3B+2C)a , --(A.+-3C)a' 



-H(aA-f-3C)a-A-C=:o 



Vbi fi ftatuamus a — ^ 1 ^-" fit 

 (A+BK-( A -BK-a(A+By-fio(A-B>/«+i7:A+B v a-f7(A-B)-o 

 4- 8 C +24C 



ita vt valor fra&ionis ct a refolutione huius aequa- 

 tionis quinti gradus pendeat. Quodfi bina corpora 

 A et B inter ie eflent aequalia foret 

 Au $ — 2 A«' + i7 A«— o hincque vel «— o et a — 5 



+ 4C +12C 



* A — 2C+ V(+CC— 1« AC- 16 A A) 



vel ««— ^- 



vnde reliqui pro « valores fiunt imaginarfi. Sin 

 autem B repraefentet folem , vt fit quafi B — 00, 

 quia tum a fit minimum proxime erit (A-+3B 



f(A-f-C) 



+2CW— A-C~ o feu »r1 etaccuratius 



nA+3B+2C) 



^fA-hC) 3(A+2C)B-C(5A-f-6C) 





°" VCA+3B+2C; 3(A+3B+3C)^(A+CXA+3B+2C)' 



Scholion 



