PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 773 



Another analogy is obtained by comparing the ordinary area of a 

 sector of a circle with our corresponding area of an isosceles triangle. 

 The area of sector of angle A and radius b is 



The area of our isosceles triangle having a vertical angle A and the 

 sides AB = AC = b is 



-b'A 



which can be obtained from the formula Area = bcA, remembering 

 that in the isosceles triangle AB = b, OA = c= — b. Thus in this case 

 angle replaces angle. 



34. In connection with the similarity between the trigonometric 

 formulae in this geometry and in the ordinary geometry, it is interest- 

 ing also to note some of the similarities and differences of the geometric 

 relations of triangles in the two cases. The following theorems are 

 good illustrations. 



I/the sides BC, CA, AB of a triangle are cut by a transversal in the 

 points A\ B', C respectively, then 



C'A A'B B'C^ _ 



C'B A'C B'A 



For writing the three vertices in order to denote the line area of the 

 triangle we have (Figure '22) 



A^B^C C'FA FC^ WC C^A^B _ 

 C'B'A ■ B'C'C ■ C'A'C ■ C'A'B " A'C'A ~ ^' 



Since triangles having the same vertex and bases ou the same line have 



