PHILOSOPHICAL SOCIETY Oi' WASHINGTON. 63 



and in equation (16) let 



y — y + ^ and X 



x" -I- -^ , then 



y' 



.l-x". 

 v/2 



The following construction results immediately from the above. 

 With reference to a set of co-ordinates X A Y construct a new- 

 set X' A' Y' such that x~x' ^1 andy — v'=--^ and an- 



a -^ •" 2n/2 



other set X" A" Y" such that x — x" = -iL and v — v" — ^ 



2v/2 J J — 2- 



With the first new set construct the parabola a;' =__^ ?/ and 



with the second new set construct the parabola v"' — ^ t". 



v/2 ' 



Fig. 3. 



their intersections will determine the segments x and y, i.e., 

 O E and D of Fig. 2. The construction is shown in Fig. 3. 



Second Construction. —HokQ a rectangle A C B D, Fig. 4, and 

 let AL, BM, the bisectors of A and B, intersect in K; then 

 A K B = 135°. Through B draw B R parallel to A L to meet 



