( -9) 



a ( a b ) sirivj/cosvj/ d( sin'J/ cob'ij' ) J 

 -f-ycosvp esinvj/ = o ............... (7) 



a ( 08iri*4> + Acos'vp -f f/si 



siibstituendo in (8) valorem tang sumptum e (7), prodit 

 a ( flsin'vf/ -f- Acos*\p ) -f- t/sin4/cosv{/ <? ) 



/sinv|/ 

 _ sinvf/ 



a ( a 6 ) sinv(/cos4/ c/( sin'ij/ cos'4/ ) 

 a ( o b ) siiiv|/ciisvp </(sin'J/ cos'4/ ) 



Id est, 



(ysinj/ -f tfcosip) f (esin|/ -/cosv^/) " [ 2 (a-Z) sinvj/cos4/ ^(sin'i^ cos'J/) ]' 

 = a (<*simj/ /cosvj/ )[a(a -^>) simj/cos^x d( sin'vf/ cos'ip ) ] 



fasin'J/ + cos'vl/ + c^siuJ/cosvL el 

 vel 



(/sinvj/ -j-ecosvf/Xesinvf/ /cosv//)' ^a( )siruj/cos4/ d(sin*\^ cos'v(/ )l 

 ^ [ 3 ( a ^ ) siuvj/cosif/ </(sin'vJ/ cos'4/) J (Jsinfy + ecos\{/ ) 5 

 ^ + 3(^sin4/ /cosif/) (asiri'^+^cos'vp) + ^Jsin\|/cos^/ c I " 



lividendo per cos 5 ^/, oritur, 



cos\|/ T 



^ + A + d ^_ J_N( 



cos'4/ ' cos^/ cos'vj' / 1 



haec ultima eequatio, reductionibus factis, lit 



ace df] u \ = o . . . . (9) 

 et cum sit tertii gradus, saltern unani radicem realem vel tangents 

 v{/ prffibebit (Gamier, alg. sectio i): angulo v{/ determinate, fequatio 

 (6) soluuxmodo pi-imi gradus quoad 6, dabit quocfue unum realem valo- 



