PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 777 



its basis some other property. Now the distance from the vertex to 

 the base of a triangle is ordinarily determined by the formula 



h = b sin C. 

 Hence in our system we try the value 



It is evident from the definition that S depends only on the positions 

 of A and BC, for we have 



B 



c 



and hence 



8 = bC=cB = 



a + b + e 



a 



(20) 



The first value of 8 shows that it is independent of the position of B 

 along the line, the second, that it is independent of the position of C 

 along the line. 



FlGtTRE 25 



To determine more exactly the meaning of this quantity 8, we draw 

 lines FA and FB meeting f in P and Q. Let BC cut AQ in C, FP in 

 D, f in R. 



