^FJmATVRAS COMPJRAmi 105 



^o. lam ob ^^y('.^p^ )— y(i>Hpp)»/> erit : 



V( I ^xx)-^x=zy{ I +jt7)+j'X v( I +^^)+^)c >"( i +;'p)-ri 



■vnde reperitur : 



^jV( H-pp)( H-^^)-l-^y( i-f-p_^)( I -hF)-py(i +^^) 



Qiiare erit : 



(n.a-n^)-(n.^-n.p^ -(^y(i 4/)/))-pV(i4-^^]) ( ^yci +/>p) 



-M^+j:>'))(^"^(^-hF)+i'^(^-^^^ )• 

 Problema i. 



61. Dato arcu parabolae quocunque A^, iii Yer»» Tab. 11 

 tice A terminato , ab alio quocunque pundlo p arcum ^ig. u 

 abfcindere />^, qui arcum illum A^ fuperet quaaiitac© 

 algebraice adignabiii. 



S o 1 u 1 1 o. 



Pofita parabolae parametro :=2, fit & ablcifla 

 arcui Ak conueniens , abfciffae autem pundis p ci q 

 refpondentes fint AP:=:j' et kQjzix\ critque axc.pq 

 — n..v~n.j et 2itc.Ak — U.k\ cum igitur data fit 

 abfciffa AF=:/, fi capiatur altcra 



A Qp-xniiy Vii-{-kk)-{-kV{i -^jy) 

 crit U.x-U.y — U.k-^-kxyj ideoque 



A rc.p ^ =: Arc . A ^ -f- ^ AT/. 

 Superabit ergo arcus pq, qui in dato punAo /> termina- 

 tur , arcum A^ quantitate algebraice affignabili kxy» 



Poterit etiam a punclo p antrorfum abfcindi ar- 



tus /)<7', qui paritet arcum Ai^ quantitate^eometrica fu- 



Tom.VlLNou.Com. O peret f 



