CRASSITIEI VARIABILIS. 439 



S O 1 U t I O. 

 VIII. Euolutione huius formae fada , reperie- 



mus vt fequitur : 



ddp 



d x^ 



(^'[t^fzdx 



_2 z d p -f- p d z 



J- 11.'? 

 ~ dx* 



dx 



(^"{t-^-fzdx^^^^Ht-^-fzdx) 

 + q ZZ 



p z z 



• 2Z,dq 



■ q d z 



dx 



p IV 



■\- qw 



quocirca fequentes conditiones adimpleri oportet 

 \\ ^^ = 0; fiuep=«A:+p; 

 m izdp-irpdz-^-^^zzo', (iac^z:-i2zdp+pdz) 



111° tZd q -^q dz 



dx 



-\-p z z:=ip iVy 



IV*. q z z-zzqiv^ ideoque zz-=zw, 



Qui poftremus Yalor w '^ zz in penultima fubfti- 

 tutus praebet 



^ z d q -\- qdzzz o, 



quae in q dudta et integrata praebet z qq-zzQ^ 

 Hinc igitur habemus 



zz=-^ tt dz — -'^, 

 vnde noftra fecunda aequatio fit 



ddci I . »Cdp ^ i£Pjj — Q • 

 dX "^ qq q^ ^ ^* 



verum ob 

 pz=ax-^ P erit dxzz^^ ; 



tt per a C diuidendo fiet 



« II2 _1- diP-PAl — Q - 



