ANA1.YTH' GEOMETRY 



fixed points. It is required t<> find the distance /V'a = ^ 

 in terms of the given constants p r p T O r and O r 1" tne 

 triangle 0-PjP, (cf. Art. 16) 



/y7= 0/7 + 0/7-2- 0/V 0/V cos /V>/' - 



* - Pi 2 + ft* - 2^, cos (0, - tfj), 

 benoe <f = Vp t + p, - Hpi^eos ( - V . . . [1] 



-' ) Cartesian coordinates; axes not rectangular. L-t 

 and OF be the coordinate axes, meeting at an m_;l 





/ Fio. ll* / Fta.ll/ 



XOY = a>,* and let P l = (x v y^) and P 2 = (x v y^) be the two 

 given points; it is required to find the distance P l P^ = d 

 in terms of x v x v y r y v and o>. 



Construction : Extend the abscissa L l P l of the point P l 

 to meet the ordinate M^P^ of the point 7' 2 . in Q\ then in 

 the triangle P&1\ (cf. Art 16) 



Pig. 11^, 



which gives, for each figure, 

 <*= 



The demonstration applies to each figure. 



t By examining other possible constructions the student should assure 

 himself of the generality of this formula. 



