QUICKEST DESCENT. 



v/(n. Aiy — m'An') ~ 



n . «' TT + « • 7 — 7- • F ^ 



_, A^ , . L n\ 



^(n . n' n"* H-m.p'n''-' ) . ^/(n. AlV-m. An') 



Therefore, by substitution, 



n . w r 4- m . , n n' 



. An ^ 



V(n .«'«'* -f- m ./«'*).>/(«. A D — m . A«) 



n.n'V+m.^.p'n" 

 kn' 



Now 



^/(«.;^'n"='-fm. //«''- ) . V(w. Aiy— m. A«0 



these quantities being consecutive and similar, 

 it is evident, that 



n . 7i' r 4- w . . p n' 



A n 



^(n. nn'' + m.pn''). ^(n. AD - m . Aw)"" 



stant quantity. 



Let AD= X, D« = y, nrzzx,rn^zzy, the Curve 

 A « = z,nfi' = 2, the Cord A n = /?, and /? «'= ^. 



