PHILUPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 785 



vertex and the segment for base multiplied by the magnitude of the 

 point. Or dually, the product is equal to the angle area of the triangle 

 having the sector A for vertex and a for base line, multiplied by the 

 magnitude of a. If the line a passes through F, the above product be- 

 comes indeterminate since a = and ^ = 00; this can be evaluated by 



remembering the relation bA = aB. Both h and A are finite and the 

 product becomes determinate as before. From the above expression 

 for the product we see that 



Aa = aA. (35) 



44. The product of two unit points was defined as the segment join- 

 ing the two points. This segment we may now consider as represented 

 by the line joining the two points taken with a magnitude equal to the 

 length of the segment. Then making use of the definition of the prod- 

 uct of a point and a line we see at once 



ABC = AB C==ABC. (36) 



That is, the product is associative. Likewise the product of three lines 

 is associative. 



45. The distributive law. The distributive law for points 



(^B + C) = AB -f AC 



(87) 



follows from the definition of addition. Let the magnitudes of the 

 three points be X, ju, v respectively. Then (Figure 29) 



AB = A/xC, AC = Avb. 



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